%PDF-1.4 % 1 0 obj << /Type /Page /Parent 78 0 R /Resources << /ColorSpace << /CS0 124 0 R /CS1 139 0 R /CS2 155 0 R /CS3 153 0 R /CS4 151 0 R /CS5 149 0 R >> /ExtGState << /GS0 127 0 R /GS1 138 0 R >> /Font << /TT0 92 0 R /TT1 86 0 R /TT2 48 0 R /TT3 105 0 R /C2_0 49 0 R /C2_1 50 0 R /TT4 51 0 R >> /XObject << /Im0 180 0 R /Im1 179 0 R /Im2 178 0 R /Im3 177 0 R /Im4 176 0 R /Im5 175 0 R /Im6 174 0 R /Im7 173 0 R /Im8 172 0 R /Im9 171 0 R /Im10 170 0 R /Im11 169 0 R /Im12 168 0 R /Im13 167 0 R /Im14 166 0 R /Im15 165 0 R /Im16 164 0 R /Im17 163 0 R /Im18 162 0 R /Im19 161 0 R /Im20 160 0 R /Im21 159 0 R /Im22 158 0 R /Fm0 157 0 R >> /ProcSet [ /PDF /Text /ImageC /ImageI ] >> /Contents 3 1 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 3 1 obj << /Length 181 0 R >> stream /CS0 cs 0 0 0 scn 1 i /RelativeColorimetric ri /GS0 gs BT /TT0 1 Tf 0.0014 Tc 0.2819 Tw 9 0 0 9 54 394.7403 Tm [(com)6(m)6(unication sy)-12(stem)6(s. The ability)-12( )7(to )7(sim)6(u)1(late )7(hierarchically)-12( )]TJ -0.0001 Tc 0.0968 Tw 0 -1.1733 TD [(enables optimum sy)-13(stem design by)]TJ 0.001 Tc 0.089 Tw 14.4133 0 Td ( providing bi-directional links )Tj 0.0015 Tc 0.2552 Tw -14.4133 -1.1733 Td [(between adjacent levels)4( of the hierarchy)-12(.)-2( F)4(o)2(r this)4( review, we )]TJ 0.0352 Tw T* [(place the behavioral m)6(odel between the IC m)6(odel and the )7(m)6(odule )]TJ 0.0009 Tc 0.2358 Tw T* [(or subsy)-12(s)3(tem. Many)-12( of the reviewed )7(techniques, )7(however, )7(are )]TJ 0.0016 Tc 0.0017 Tw T* (applicable to other levels as well. )Tj /TT1 1 Tf 0.0004 Tc -0.0004 Tw 12 0 0 12 54 318.3 Tm [(2.1 )-350(Simulation and Measurement-Based )]TJ /TT0 1 Tf 0.0005 Tc 0.0362 Tw 9 0 0 9 54 307.3203 Tm (Behavioral models should be de)Tj 0.0004 Tc 0.0296 Tw 12.9933 0 Td (rivable from both simulations and )Tj 0.0016 Tc 0.0751 Tw -12.9933 -1.1733 Td [(m)6(eas)4(urem)6(ents)4(. )-7(Cons)4(ider )-7(a )-7(circuit m)6(odel for an integrated circuit, )]TJ 0.0009 Tc 0.6291 Tw T* [(such )-7(as that which a designer develops from)5( prim)5(itive )]TJ 0.0001 Tc 0.7032 Tw T* (components such as transistor)Tj 0.0008 Tc 0.7025 Tw 14.0867 0 Td [(s, resistors, capacitors )7(and )]TJ 0.001 Tc 0.149 Tw -14.0867 -1.1733 Td [(inductors. )-7(The simulator can be us)]TJ 14.5533 0 Td (ed to stimulate the IC model )Tj 0.0005 Tc 0.4895 Tw -14.5533 -1.1733 Td (and the responses used to de)Tj 0.0011 Tc 0.4889 Tw 13.82 0 Td [(rive a behavioral model )7(for )]TJ 0.129 Tw -13.82 -1.1733 Td (simulation at the next higher leve)Tj 0.1222 Tw 14.04 0 Td [(l of abstraction. However, any)-12( )]TJ 0.0015 Tc 0.3552 Tw -14.04 -1.1733 Td [(m)6(odeling errors at the circuit level will be reflected in the )]TJ 0.0014 Tc 0.4019 Tw T* [(behavioral model. That is, )7(lo)]TJ 0.0008 Tc 0.3959 Tw 13.1333 0 Td (wer level modeling errors can )Tj 0.0016 Tc 0.1017 Tw -13.1333 -1.1733 Td [(accum)6(u)2(late )-7(from)6( level to level up the hierarchy)-12(,)-2( invalidating the )]TJ 0.0009 Tc 0.0024 Tw T* (bottoms up verification. )Tj 0.001 Tc 0.4957 Tw 0 -1.62 TD [(Alternatively)-12(,)-2( behavioral mode)]TJ 0.0007 Tc 0.4893 Tw 13.5067 0 Td [(ls )-7(can )-7(be derived from real )]TJ 0.0003 Tc 0.1697 Tw -13.5067 -1.1733 Td [(measurements )-7(made on the com)]TJ 0.0014 Tc 0.1686 Tw 13.52 0 Td (ponent. Accurate )Tj 0 Tc 0 Tw 7.44 0 Td (measurements )Tj 0.0016 Tc 0.3684 Tw -20.96 -1.1733 Td [(can )-7(therefore lead to m)6(o)2(re accurate behavioral m)6(odels)4( than )]TJ 0.1552 Tw 0 -1.1733 TD [(s)4(t)-1(arting from)6( lower level, pos)4(s)4(i)-1(bly)-12( inaccurate m)6(odels)4(. )7(This)4( )7(als)4(o)2( )]TJ 0.0004 Tc 0.7163 Tw T* [(allows )-7(designers to make be)]TJ 0.7164 Tw 14.16 0 Td (havioral models from real )Tj 0.0007 Tc 0.0026 Tw -14.16 -1.1733 Td (components for which a circuit )Tj 0.0013 Tc 0.002 Tw 12.7267 0 Td [(model may)-12( not be available. )]TJ 0.1888 Tw -12.7267 -1.62 Td [(A )-7(drawback )-7(of )-7(the )-7(m)6(eas)4(urem)6(ent-bas)4(e)-2(d approach is)4( the lack of )]TJ 0.0015 Tc 0.0685 Tw T* [(readily)-12( available )7(high-frequency)-12(,)]TJ 0.0001 Tc 0.0632 Tw 13.4467 0 Td [( nonlinear measurement sy)-13(stems )]TJ 0.0016 Tc 0.0017 Tw -13.4467 -1.1733 Td [(with the required capability)-12(. )]TJ 0.3018 Tw 29.32 32.9 Td [(The m)6(eas)4(urem)6(ent-bas)4(e)-1(d approach )]TJ 0.0012 Tc 0.2955 Tw 14.84 0 Td [(requires )-7(that the behavioral )]TJ 0.0009 Tc 0.0358 Tw -14.84 -1.1733 Td (model be derivable from data that )Tj 0.0015 Tc 0.0352 Tw 14.02 0 Td [(can be m)6(eas)4(ured at )7(the )7(ports)4( )7(of )]TJ 0.0012 Tc 0.4355 Tw -14.02 -1.1733 Td [(the )-7(component connected to the external world. The same )]TJ 0.001 Tc 0.209 Tw T* [(methodology)-12( )-7(can, )-7(of )-7(course, )-7(be applied in the simulator to an )]TJ 0.0016 Tc 0.0017 Tw T* [(existing lower level m)6(odel, if available. )]TJ 0.001 Tc 0.2957 Tw 0 -1.62 TD [(W)5(e)-2( will only)-12( consider techniques in this review that can )7(be )]TJ 0.0013 Tc 0.062 Tw 0 -1.1733 TD (applied to relationships at the exte)Tj 0.001 Tc 0.0557 Tw 14.0467 0 Td [(rnal ports. This is an im)6(portant )]TJ 0.0008 Tc 0.0559 Tw -14.0467 -1.1733 Td [(restriction on the )7(simulation-based )]TJ 0.0017 Tc 0.0483 Tw 14.3467 0 Td [(approaches)4(. It elim)6(inates)4( from)6( )]TJ 0.0011 Tc 0.0622 Tw -14.3467 -1.1733 Td [(consideration all )7(order-reduction )]TJ 0.0004 Tc 0.0563 Tw 13.5667 0 Td [(techniques based on simplify)-13(i)-2(ng )]TJ 0.0012 Tc 0.0021 Tw -13.5667 -1.1733 Td [(explicit model equations and their topological connections [6])8(.)-2( )]TJ /TT1 1 Tf 0.0006 Tc 0.3494 Tw 12 0 0 12 317.88 272.04 Tm [(2.2 Desirable )350(Properties )]TJ /TT0 1 Tf 0.0008 Tc 0.7292 Tw 9 0 0 9 317.88 261.0603 Tm (Other desirable properties of )Tj 0.0009 Tc 0.7224 Tw 14.66 0 Td (behavioral models include )Tj 0.0013 Tc 0.4154 Tw -14.66 -1.1733 Td [(transportability)-12( and cascadability)]TJ 14.1733 0 Td [(. Transportability)-12( m)6(eans the )]TJ 0.002 Tw -14.1733 -1.1733 Td [(m)6(odel )-7(can be used under a variety)-12( of different conditions, whether )]TJ 0.0008 Tc 0.6292 Tw T* [(this refers to )7(the )7(signals )]TJ 0.0014 Tc 0.6219 Tw 12.8933 0 Td [(stim)6(ulating the m)6(odel or the )]TJ 0.022 Tw -12.8933 -1.1733 Td [(environm)6(ents)4( )-7(in )-7(which )-7(the behavioral m)6(odel is)4( to be placed in the )]TJ 0.0015 Tc 0.0418 Tw T* [(intended application. )7(Cascadability)]TJ 0.0011 Tc 0.0356 Tw 14.22 0 Td [( m)6(eans that the cascade of two )]TJ 0.549 Tw -14.22 -1.1733 Td [(behavioral m)6(odels perform)6(s faithfully)-12( with )7(respect )7(to )7(the )]TJ 0.0013 Tc 0.122 Tw T* [(performance )-7(of )-7(the cascade of th)]TJ 0.0011 Tc 0.1222 Tw 13.7333 0 Td (e respective components. Since )Tj 0.2822 Tw -13.7333 -1.1733 Td [(cascading )-7(nonlinear )-7(components )-7(can create a wide variety)-12( of )]TJ 0.0012 Tc 0.1088 Tw T* [(environm)6(ents for the individual behavioral )7(m)6(odels, )7(cascadability)-12( )]TJ 0.0015 Tc 0.0018 Tw T* [(im)6(plies a certain degree of transportability)-12(. )]TJ /TT1 1 Tf 0.0004 Tc -0.0004 Tw 12 0 0 12 317.88 139.86 Tm [(2.3 )-350(Waveforms and Memory )]TJ /TT0 1 Tf 0.001 Tc 0.0823 Tw 9 0 0 9 317.88 128.8803 Tm [(Behind )-7(all )-7(of the techniques descri)]TJ 0.0012 Tc 0.0821 Tw 14.32 0 Td (bed here is the notion that the )Tj 0.0009 Tc 0.1824 Tw -14.32 -1.1733 Td [(behavioral model relates )7(waveform)]TJ 0.1758 Tw 14.7 0 Td [(s to waveform)5(s. That is, the )]TJ 0.0007 Tc 0.136 Tw -14.7 -1.1733 Td [(output )-7(is not an instantaneous f)]TJ 0.001 Tc 0.1357 Tw 13.18 0 Td [(unction only)-12( of the input signal. )]TJ 0.0223 Tw -13.18 -1.1733 Td [(Rather, )-7(the )-7(output )-7(depends upon the shape of the input waveform, )]TJ 0.0012 Tc 0.0755 Tw T* [(or equivalently)-12(, the output depends on the value of the input )7(and )]TJ 0.0011 Tc 0.0622 Tw T* [(past values of the input, and even past values of )7(the )7(output )7(itself. )]TJ ET 1 1 1 scn /CS0 CS 0 0 0 SCN 0.72 w 10 M 0 j 0 J []0 d 50.4 720 504.84 -309.72 re B q 58.02 456.66 152.04 51.24 re W n q 152.04 0 0 -51.24 58.02 507.9 cm /Im0 Do Q Q q 58.02 414.3 152.04 42.36 re W n q 152.04 0 0 -42.36 58.02 456.66 cm /Im1 Do Q Q 101.22 421.86 86.4 14.04 re f 0 0 0 scn BT /TT0 1 Tf -0.0041 Tc 0.0074 Tw 9 0 0 9 101.22 427.7403 Tm [(P)-8(h)-11(y)16(s)-2(i)-6(cal)-6( De)-14(vi)-6(ce M)-8(o)-11(d)-11(el)]TJ ET q 144 0 0 -55.2 137.22 543.9 cm /Im2 Do Q q 144 0 0 -38.52 137.22 488.7 cm /Im3 Do Q BT /TT0 1 Tf 0.0059 Tc -0.0026 Tw 9 0 0 9 194.82 456.6603 Tm [(T)17(r)6(a)10(n)-1(s)8(i)4(s)8(t)4(or)6( Mode)10(l)]TJ ET q 166.0601 0 0 -85.8 194.82 587.1 cm /Im4 Do Q 1.44 w 194.1 587.82 167.16 -87.36 re S 1 1 1 scn 0.72 w 209.22 522.3 64.92 -14.52 re B 0 0 0 scn BT /TT0 1 Tf 0 Tc 0 Tw 9.96 0 0 9.96 209.58 513.6606 Tm ( )Tj -0.0054 Tc 0.0087 Tw 9 0 0 9 212.1 513.6603 Tm [(I)-6(C)-5( Level)-8( D)-17(e)-2(si)-8(gn)]TJ ET q 129.6828 0 0 -11.76 404.46 709.5 cm /Im5 Do Q q 129.6828 0 0 -11.76 404.46 697.7401 cm /Im6 Do Q q 129.6828 0 0 -11.76 404.46 685.98 cm /Im7 Do Q q 129.6828 0 0 -11.76 404.46 674.22 cm /Im8 Do Q q 129.6828 0 0 -11.76 404.46 662.46 cm /Im9 Do Q q 129.6828 0 0 -11.76 404.46 650.7 cm /Im10 Do Q q 129.6828 0 0 -11.76 404.46 638.94 cm /Im11 Do Q q 129.6828 0 0 -11.76 404.46 627.18 cm /Im12 Do Q q 129.6828 0 0 -11.76 404.46 615.42 cm /Im13 Do Q q 129.6828 0 0 -6.96 404.46 603.66 cm /Im14 Do Q 1.44 w 403.62 710.22 131.16 -114.36 re S 1 1 1 scn 0.72 w 445.26 702.3 86.52 -14.52 re B 0 0 0 scn BT /TT0 1 Tf 0 Tc 0 Tw 9.96 0 0 9.96 445.5 693.6606 Tm ( )Tj -0.003 Tc -0.007 Tw 9 0 0 9 448.02 693.6603 Tm [(M)-7(o)-10(du)-10(le o)-10(r)-3( )-13(sub)-10(-)-3(sy)17(ste)-12(m)]TJ ET q 164.131 0 0 -18.42 295.74 666.24 cm /Im15 Do Q q 164.131 0 0 -18.36 295.74 647.82 cm /Im16 Do Q q 164.131 0 0 -18.36 295.74 629.46 cm /Im17 Do Q q 164.131 0 0 -18.42 295.74 611.1 cm /Im18 Do Q q 164.131 0 0 -18.36 295.74 592.68 cm /Im19 Do Q q 164.131 0 0 -18.36 295.74 574.32 cm /Im20 Do Q q 164.131 0 0 -18.42 295.74 555.96 cm /Im21 Do Q q 164.131 0 0 -4.8 295.74 537.54 cm /Im22 Do Q 398.28 593.52 m 397.56 594.24 l 389.82 589.68 l 390.54 588.96 l 398.28 593.52 l f 388.5 591.36 m 385.5 586.68 l 392.04 587.58 l 388.5 591.36 l f* 1 1 1 scn 397.92 556.32 55.74 16.8 re f 1 0 0 scn BT /TT2 1 Tf 0.1541 Tc 0 Tw 6.42 0 0 6.42 403.5 567.18 Tm [(E)-29(m)-88(b)-9(edd)-9(i)96(ng )]TJ 0.1835 Tc 0.757 -1.2056 Td [(Va)20(r)87(i)125(a)29(b)20(l)125(e)29(s)]TJ 0 0 0 scn /TT0 1 Tf 0.9367 Tc 5.34 0 0 5.34 443.7 631.6804 Tm (\(\))Tj 0.0703 Tc 9.18 0 0 9.18 329.22 627.5999 Tm [(\()-459(\))-218(:)-234( )-6( )-2595(\()-623(,)-725(,)-78(..)-6(.,)-529(,)-85(...)-6(,)-1680(\))]TJ /TT3 1 Tf 0 Tc 5.34 0 0 5.34 446.52 631.6804 Tm (n)Tj 0.6019 Tc 9.18 0 0 9.18 323.52 627.5999 Tm [(yt)-2055(i)-1048(f)-225(vv)-1346(i)-1342(i)]TJ /C2_0 1 Tf 0 Tc 4.6601 0 Td <0020>Tj /C2_1 1 Tf 5.8824 0.2156 Td <0005>Tj -2.3268 -0.1699 Td <0005>Tj 1 0 0 scn /TT0 1 Tf 0.5354 Tc 9.12 0 0 9.12 331.38 609.2404 Tm (\(\))Tj /TT3 1 Tf 0.5825 Tc -0.5987 0 Td (vt)Tj /C2_1 1 Tf 0 Tc 0.1513 0.0525 Td <0005>Tj /TT0 1 Tf 0.5354 Tc 0.4079 -1.1117 Td (\(\))Tj /TT3 1 Tf 0.6219 Tc -0.6382 0 Td (vt)Tj /C2_1 1 Tf -0.0501 Tc 0.0132 0.0459 Td <00050005>Tj ET 0 0 0 scn 342.36 625.62 m 342 624.78 l 347.88 623.28 l 348.24 624.12 l 342.36 625.62 l f 347.34 622.32 m 351.48 622.8 l 348.48 625.14 l 347.34 622.32 l f* 345.42 628.02 m 345.12 627.18 l 372.54 622.92 l 372.84 623.76 l 345.42 628.02 l f 372.18 621.9 m 376.26 622.8 l 372.96 624.78 l 372.18 621.9 l f* 1 0 0 scn BT /TT0 1 Tf 0.5232 Tc 9.18 0 0 9.18 330.24 591.4799 Tm (\(\))Tj /TT3 1 Tf 0.7091 Tc -0.5686 0 Td (it)Tj /C2_1 1 Tf -0.0585 Tc -0.0523 0.2157 Td <00050005>Tj /C2_0 1 Tf 0 Tc 28.08 0 0 29.34 341.16 597.061 Tm <005E>Tj 0.2222 -1.3149 Td <005E>Tj 0 0 0 scn 17.1 0 0 9.54 350.46 580.3818 Tm <005E>Tj ET 1 0 0 SCN 0.54 w 397.92 574.62 55.8 -19.32 re S 1 1 1 scn 0 0 0 SCN 398.1 610.8 84.06 -21.78 re B 0 0 0 scn BT /TT2 1 Tf 0.1541 Tc -0.0674 Tw 6.42 0 0 6.42 399.06 604.3199 Tm [(M)-88(ul)96(t)67(i)96(v)9(ar)48(i)96(at)68(e f)77(u)-9(nc)9(t)67(i)96(ons)9( )]TJ 0.0867 Tc 0 Tw 4.1495 -1.5701 Td [(fo)-67(r)-10( )]TJ /TT4 1 Tf 0 Tc 1.8692 0 Td (i)Tj /TT2 1 Tf 4.44 0 0 4.44 439.5 592.68 Tm (1)Tj 0.0867 Tc 6.42 0 0 6.42 442.68 594.24 Tm (, )Tj /TT4 1 Tf 0 Tc 0.7196 0 Td (i)Tj /TT2 1 Tf 4.44 0 0 4.44 449.1 592.68 Tm (2)Tj ET 1 1 1 scn 0 0 1 SCN 0.72 w 338.82 659.1 100.92 -21.72 re B 0 0 1 scn BT /TT0 1 Tf -0.0006 Tc 0.0006 Tw 12 0 0 12 345.78 644.58 Tm [(B)6(e)3(havio)-11(r)2(al Model)]TJ ET 1 1 1 scn 0 0 0 SCN 317.22 443.1 208.92 -21.72 re B 0 0 0 scn BT /TT1 1 Tf 0.004 Tc -0.001 Tw 9.96 0 0 9.96 324.78 429.6596 Tm [(Fi)5(gu)6(re 1 A)3( d)6(e)2(s)8(i)5(gn)6( an)6(d)6( )-12(m)30(o)-14(d)6(e)2(l)5(i)5(n)6(g h)6(i)5(erarch)6(y)]TJ /TT0 1 Tf 0 Tc 0 Tw 9 0 0 9 540.42 414.3003 Tm ( )Tj ET q /GS1 gs /Fm0 Do Q endstream endobj 27 0 obj << /Type /Page /Parent 78 0 R /Resources << /ColorSpace << /CS0 124 0 R /CS1 139 0 R >> /ExtGState << /GS0 127 0 R /GS1 138 0 R >> /Font << /TT0 92 0 R /TT1 105 0 R /C2_0 49 0 R /C2_1 50 0 R /TT2 86 0 R /T1_0 60 0 R >> /XObject << /Fm0 189 0 R >> /ProcSet [ /PDF /Text ] >> /Contents 29 1 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 29 1 obj << /Length 190 0 R >> stream /CS0 cs 0 0 0 scn 1 i /RelativeColorimetric ri /GS0 gs BT /TT0 1 Tf 0.0012 Tc 0.1688 Tw 9 0 0 9 54 711.6003 Tm [(W)5(e)-2( )-7(write )-7(this)4( in functional notation according to Equation 1.1. )]TJ 0.0008 Tc 0.0759 Tw 0 -1.1733 TD (Here we assume the voltage signal )Tj 0.0011 Tc 0.0756 Tw 14.5867 0 Td (is the input and the current is )Tj 0.0016 Tc 0.0017 Tw -14.5867 -1.1733 Td (the output. )Tj 0 Tc 0 Tw 0 -1.9133 TD ( )Tj 0.337 Tc 12 0 0 12 146.64 673.26 Tm [(\(\))-1365([)-360(\()-5(\))345(])]TJ /TT1 1 Tf 0.447 Tc -0.455 0.0003 Td [(It)-995(F)133(V)-32(t)]TJ /C2_0 1 Tf 0 Tc 1.69 -0.0003 Td <0020>Tj /TT0 1 Tf 0.0007 Tc 7.2693 Tw 9 0 0 9 209.04 673.2603 Tm ( \(1.1\) )Tj 0.0012 Tc 0.0488 Tw -17.2267 -1.9333 Td [(The functional can often be represented as a function of the )7(input )]TJ 0.0004 Tc 0.3763 Tw 0 -1.1733 TD [(waveform )-7(and )-7(other )-7(transforms of the input waveform. For )]TJ 0.0019 Tc 0.0014 Tw T* [(exam)6(ple, we m)6(a)-1(y)-11( have the rela)]TJ 0.0009 Tc 0.0024 Tw 12.44 0 Td [(tionship given by)-12( Equation 1.2. )]TJ 0 Tc 0 Tw -12.44 -2.1333 Td ( )Tj 0.697 Tc 12 0 0 12 110.16 615.6 Tm [(\()360(\))-1005([\()360(\))700(])-970(\(\()360(\))700(,)-98(\()355(\))705(\))]TJ /TT1 1 Tf 0.447 Tc -0.455 -0.0047 Td [(It)-995(F)138(V)-37(t)-1430(f)-55(V)-37(t)-230(V)-32(t)]TJ /C2_0 1 Tf 3.4662 Tc 1.69 -0.0003 Td <00200020>Tj /C2_1 1 Tf 0 Tc 8.145 0.265 Td <0005>Tj /TT0 1 Tf 0.0007 Tc 3.216 Tw 9 0 0 9 245.52 615.5403 Tm ( \(1.2\) )Tj 0.0018 Tc 0.1549 Tw -21.28 -1.9333 Td [(This)4( is)4( an exam)6(ple of a )]TJ /TT1 1 Tf 0.0011 Tc 0 Tw 10.5067 0 Td (static)Tj /TT0 1 Tf 0.0013 Tc 0.1554 Tw 2.1733 0 Td ( functional. The output is still an )Tj 0.0009 Tc 0.2491 Tw -12.68 -1.1733 Td [(instantaneous )-7(function of the )]TJ 0.0007 Tc 0.2493 Tw 12.86 0 Td (input waveform, but it does not )Tj 0.001 Tc 0.2823 Tw -12.86 -1.1733 Td [(depend only)-12( on the values of the input signal, )]TJ /TT1 1 Tf 0.0025 Tc 0 Tw 21.04 0 Td [(V\()9(t)]TJ /TT0 1 Tf -0.0003 Tc 0.2836 Tw 1.22 0 Td [(\). A )7(more )]TJ 0.0006 Tc 0.1561 Tw -22.26 -1.1733 Td [(complicated )-7(class )-7(of models is given by)-13( the )]TJ /TT1 1 Tf 0.0015 Tc 0 Tw 18.9667 0 Td (feedback)Tj /TT0 1 Tf 0.0004 Tc 0.1563 Tw 3.5667 0 Td ( model of )Tj 0.0013 Tc 0.002 Tw -22.5333 -1.1733 Td (Equation 1.3. )Tj 0 Tc 0 Tw 0 -2.1333 TD ( )Tj 0.337 Tc 12 0 0 12 122.64 536.76 Tm [(\(\))-1380(\()-360(\()-5(\))345(,)-463(\(\))340(,)-273(\(\))340(\))]TJ /TT1 1 Tf 0.447 Tc -0.455 -0.0047 Td [(It)-1150(f)-60(V)-32(t)-230(V)-37(t)-355(It)]TJ /C2_0 1 Tf 0 Tc 1.69 -0.0003 Td <0020>Tj /C2_1 1 Tf 1.622 Tc 4.135 0.27 Td <00050005>Tj /TT0 1 Tf 0.0007 Tc 4.6026 Tw 9 0 0 9 233.04 536.7003 Tm ( \(1.3\) )Tj 0.0005 Tc 0.0295 Tw -19.8933 -1.9333 Td [(Feedback models embody)-13( the notion )]TJ 0.001 Tc 0.029 Tw 15.1467 0 Td [(of memory)-12(, or internal )7(state. )]TJ 0.0007 Tc 0.2826 Tw -15.1467 -1.1733 Td [(Static )-7(m)5(odels )-7(such )-7(as Equation 1.2 will produce AM to PM )]TJ 0.0008 Tc 0.0292 Tw 0 -1.1733 TD [(distortion, but there is no notion of state or )7(true )7(memory)-12( )7(in )7(such )7(a )]TJ 0.0005 Tc 0.3695 Tw T* [(model. It is the incorporation of )7(long-term )7(memory)-13( )7(bey)-13(ond )]TJ 0.0012 Tc 0.0088 Tw T* (otherwise static nonlinear behavioral)Tj 0.0009 Tc 0.0024 Tw 14.8133 0 Td [( )-7(models that distinguishes the )]TJ 0.001 Tc 0.0023 Tw -14.8133 -1.1733 Td (newer behavioral modeling approaches. )Tj /TT2 1 Tf 0.0005 Tc 0.3495 Tw 12 0 0 12 54 446.88 Tm (2.4 Excitations )Tj /TT0 1 Tf 0.0011 Tc 0.1222 Tw 9 0 0 9 54 435.9003 Tm (Excitation design refers to the set )Tj 0.0016 Tc 0.1151 Tw 14.3733 0 Td [(of stim)6(uli needed to elicit the )]TJ 0.0003 Tc 0.2564 Tw -14.3733 -1.1733 Td [(full dy)-13(namics of the sy)-13(stem re)]TJ 0.0009 Tc 0.2558 Tw 13.4 0 Td [(sponse in order to identify)-12( )7(the )]TJ 0.0007 Tc 0.116 Tw -13.4 -1.1733 Td (behavioral models. It is important)Tj 0.0012 Tc 0.1155 Tw 14.0133 0 Td [( to m)6(a)-2(ke sure the excitation is )]TJ 0.502 Tw -14.0133 -1.1733 Td [(sufficiently)-12( rich to construct a behavioral )7(model )7(that )7(can )]TJ 0.0016 Tc 0.5484 Tw T* [(accurately)-12( )-7(repres)4(ent s)4(i)-1(gnals)4( \223)5(c)-1(los)4(e\224 to thos)4(e us)4(ed in the )]TJ 0.1485 Tw T* (characterization or identification.)Tj 0.0008 Tc 0.1425 Tw 13.6533 0 Td [( Models identified from)5( sim)5(p)1(le )]TJ 0.0692 Tw -13.6533 -1.1733 Td [(excitations m)5(a)-2(y)-12( be )7(less )7(transporta)]TJ 0.0007 Tc 0.0626 Tw 13.8 0 Td (ble than those constructed from )Tj 0.0014 Tc 0.0286 Tw -13.8 -1.1733 Td [(a varied set of )7(excitations. )7(This )7(is)]TJ 0.0015 Tc 0.0218 Tw 13.6067 0 Td [( es)4(pecially)-12( true for s)4(y)-12(s)4(t)-1(em)6(s)4( with )]TJ -0.0022 Tc 0 Tw -13.6067 -1.1733 Td [(me)-5(mory)-15(.)-5( )]TJ /TT2 1 Tf -0.0005 Tc 0.0005 Tw 12 0 0 12 54 331.8 Tm [(3. )-350(TIME DOMAIN TECHNIQUES )]TJ 0.0005 Tc -0.0005 Tw 0 -1.335 TD [(3.1 )-350(Dynamic Neural Netw)8(orks )]TJ /TT0 1 Tf 0.0007 Tc 0.3826 Tw 9 0 0 9 54 304.8003 Tm [(Artificial Neural Networks \(ANNs\) [7,8])7( represent nonlinear )]TJ 0.0011 Tc 0.1356 Tw 0 -1.1733 TD [(m)6(u)1(ltivariate function fitting m)6(e)-2(thods patterned )7(after )7(the )7(nervous )]TJ -0.0005 Tc 0.0038 Tw T* [(sy)-14(ste)-3(m)4(.)-4( )-7(The)-3( ba)-3(sis se)-3(t c)-3(onsists of )]TJ 0.0007 Tc 0.0026 Tw 13.24 0 Td (nested sigmoidal functions which )Tj 0.0009 Tc 0.7424 Tw -13.24 -1.1733 Td [(can universally)-12( and )7(uniformly)]TJ 0.0012 Tc 0.7355 Tw 14.2933 0 Td ( approximate differentiable )Tj 0.0014 Tc 0.1153 Tw -14.2933 -1.1733 Td [(functions)4( )-7(in )-7(a com)6(p)1(act s)4(ubs)4(et of n-dim)6(e)-1(ns)4(ional Euclidian s)4(p)1(ace. )]TJ 0.0011 Tc 0.6689 Tw T* [(Until very)-12( recently)-12(, ANNs for high-frequency)-12( electronic )]TJ 0.0008 Tc 0.1625 Tw T* (modeling were applied almost excl)Tj 0.0009 Tc 14.6733 0 Td [(usively)-12( to static )7(functions )7(of )]TJ 0.0014 Tc 0.0486 Tw -14.6733 -1.1733 Td [(the )-7(input )-7(variables alone. The app)]TJ 0.0006 Tc 0.0494 Tw 13.8533 0 Td (lication of ANNs to functionals )Tj 0.001 Tc 0.0823 Tw -13.8533 -1.1733 Td [(of the inputs, that is, to functions )7(of )7(the )7(input )7(variables )7(and )7(their )]TJ 0.1956 Tw T* [(tim)6(e )-7(derivatives, was first consider)]TJ 0.0012 Tc 0.1955 Tw 14.7867 0 Td [(ed in [9])8(.)-2( This is called the )]TJ 0.0005 Tc 0.0028 Tw -14.7867 -1.1733 Td [(method of dy)-13(namic neural networks \(DNNs\). )]TJ 0.0013 Tc 0.0354 Tw 0 -1.62 TD [(Excellent )-7(results have been )]TJ 0.0001 Tc 0.0366 Tw 11.3467 0 Td (obtained from the DNN method for rf )Tj 0.0013 Tc 0.3287 Tw -11.3467 -1.1733 Td [(am)6(plifiers and m)6(i)-1(xers. Sim)6(p)1(le ex)]TJ 0.0011 Tc 0.3222 Tw 14.58 0 Td [(citations )-7(have been used to )]TJ 0.0222 Tw -14.58 -1.1733 Td [(identify)-12( these models, )]TJ 0.0002 Tc 0.0231 Tw 9.1533 0 Td [(such as continuous wave \(CW\) tones )7(swept )]TJ 0.0011 Tc 0.0156 Tw -9.1533 -1.1733 Td [(in amplitude and frequency)-12(.)-2( In fact)]TJ 0.0089 Tw 14.18 0 Td (, simple single-tone excitations )Tj 0.3157 Tw -14.18 -1.1733 Td [(were )-7(shown to predict the in)]TJ 0.0007 Tc 0.316 Tw 12.9667 0 Td (termodulation response of these )Tj 0.0014 Tc 0.0019 Tw -12.9667 -1.1733 Td (circuits to two tone excitations. )Tj 0.0005 Tc 0.1028 Tw T* (DNN models are nonlinear ordinary)Tj 0.0011 Tc 0.1022 Tw 14.88 0 Td [( differential equations )7(which )]TJ 0.0016 Tc 0.0217 Tw -14.88 -1.1733 Td [(can )-7(therefore be im)6(plem)6(ented in generic com)6(m)6(e)-1(rcial tim)6(e-dom)6(ain )]TJ 0.0011 Tc 0.1089 Tw 0 -1.1733 TD [(simulators. The solution of the circuit )7(equations )7(can )7(be )7(obtained )]TJ 0.0008 Tc 0.0025 Tw T* [(using )-7(any)-12( )-7(of )-7(the simulator algorithms including harmonic balance, )]TJ 0.001 Tc 0.0023 Tw T* (transient envelope, and shooting )Tj 13.2333 0 Td (methods in the time domain. )Tj 0.0008 Tc 0.2492 Tw 16.0867 70.7333 Td [(Training, which is )7(the )7(process )]TJ 0.0006 Tc 0.2427 Tw 13.5267 0 Td (of determining the weights \(or )Tj 0.1561 Tw -13.5267 -1.1733 Td [(coefficients\) in the basis set expansion for the ANNs,)-3( has been )]TJ 0.0009 Tc 0.0558 Tw T* (done in the time domain and in )Tj 0.0008 Tc 0.0492 Tw 13.1067 0 Td [(the )-7(frequency)-12( domain. Combined )]TJ 0.0025 Tw -13.1067 -1.1733 Td [(time and frequency)-12( domain traini)]TJ 0.0009 Tc 13.38 0 Td (ng has also been reported. )Tj 0.0012 Tc 0.1221 Tw -13.38 -1.62 Td [(Proprietary)-12( )-7(software )-7(im)6(plem)6(ents the training and the attachm)6(e)-2(nt )]TJ 0.122 Tw T* [(of )-7(the )-7(neural network m)6(odel to a com)6(m)6(e)-1(rcial sim)6(u)1(lator)]TJ /TT1 1 Tf 0.0016 Tc 0.1217 Tw 23.08 0 Td [( \()8(A)-1(gilent )]TJ 0.0002 Tc 0 Tw -23.08 -1.1733 Td (ADS)Tj /TT0 1 Tf 0.0018 Tc 1.8333 0 Td (\). )Tj 0.0009 Tc 0.1758 Tw -1.8333 -1.62 Td [(Limitations of the DNN approach include the ad hoc )7(nature )7(of )]TJ 0.4091 Tw T* [(selecting the number )7(of )7(independe)]TJ 0.0016 Tc 0.4017 Tw 15.4267 0 Td (nt variables. That is, the )Tj 0.0008 Tc 0.0225 Tw -15.4267 -1.1733 Td (number of time derivatives of the )Tj 0.0012 Tc 0.0221 Tw 13.7667 0 Td (candidate independent variables )Tj 0.001 Tc 0.0423 Tw -13.7667 -1.1733 Td [(to include as dependent )7(variables )]TJ 0.0357 Tw 13.76 0 Td (is not an algorithmic procedure. )Tj 0.0003 Tc 0.183 Tw -13.76 -1.1733 Td (The DNN method depends on standard)Tj 0.001 Tc 0.1757 Tw 16.56 0 Td [( )-7(issues related to neural )]TJ 0.4689 Tw -16.56 -1.1733 Td [(network function fitting, including the neural net )7(topology)-12( )]TJ 0.0002 Tc 0.0698 Tw T* [(\(number of hidden lay)-13(e)-3(rs\), numbe)]TJ 0.0008 Tc 0.0692 Tw 13.94 0 Td [(r and ty)-12(pes of neurons, )7(and )7(the )]TJ 0.0012 Tc 0.0021 Tw -13.94 -1.1733 Td (potential issues associated with overtraining. )Tj /TT2 1 Tf 0.0005 Tc -0.0005 Tw 12 0 0 12 317.88 536.1 Tm [(3.2 )-350(Nonlinear Time Series )]TJ /TT0 1 Tf 0.0006 Tc 0.5427 Tw 9 0 0 9 317.88 525.1203 Tm (Nonlienar time series \(NLTS\) )Tj 0.0008 Tc 0.5359 Tw 14.4067 0 Td [([10-14])7( )-7(is a fundamentally)-12( )]TJ 0.0004 Tc 0.5096 Tw -14.4067 -1.1733 Td [(nonlinear )-7(method based on concepts and procedures from )]TJ 0.0015 Tc 0.0485 Tw T* [(nonlinear dy)-12(nam)6(i)-1(cs)4(. The theory)-12( is)4( )]TJ 0.0011 Tc 0.0489 Tw 14.1867 0 Td [(routed in differential geometry)-12( )]TJ 0.0006 Tc 0.1694 Tw -14.1867 -1.1733 Td [(and )-7(is )-7(related )-7(to )-7(the Whitney)-13( embedding theorem of manifolds )]TJ 0.4227 Tw T* [([14, 15])7(. The method assumes that the unknown nonlinear )]TJ 0.001 Tc 0.3757 Tw T* [(component of arbitrary)-12( complexity)-12( can be )7(represented )7(by)-12( )7(a )]TJ 0.0003 Tc 0.063 Tw T* [(dy)-13(namical sy)-13(stem, governed )7(by)-13( )7(st)]TJ 0.0011 Tc 0.0556 Tw 13.8733 0 Td (ate equations in canonical form )Tj 0.0009 Tc 0.0024 Tw -13.8733 -1.1733 Td (as shown in Equations 1.4 and 1.5. )Tj 0 Tc 0 Tw 0 -2.1333 TD ( )Tj 0.337 Tc 12 0 0 12 400.32 432 Tm [(\(\))-1300(\()-240(\(\))340(,)-338(\(\))340(\))]TJ /TT1 1 Tf 0.3862 Tc -0.5 0.0003 Td [(xt)-1071(g)-99(xt)-351(u)-24(t)]TJ /C2_0 1 Tf 0 Tc 1.735 -0.0003 Td <0020>Tj /C2_1 1 Tf 2.21 Tc -1.69 0.58 Td [<004B004B>1690<004B>695<004B>]TJ 0 Tc 0.04 -0.33 Td <0005>Tj /TT0 1 Tf 0.0007 Tc 6.0493 Tw 9 0 0 9 483.9 432.0003 Tm ( \(1.4\) )Tj 0 Tc 0 Tw -18.4467 -2.2267 Td ( )Tj 0.3395 Tc 12 0 0 12 401.16 411.96 Tm [(\(\))-1187(\()-237(\()-2(\))348(,)-335(\(\))348(\))]TJ /TT1 1 Tf 0.3712 Tc -0.485 0.0003 Td [(yt)-1036(h)-54(x)-15(t)-366(u)-39(t)]TJ /C2_0 1 Tf 0 Tc 1.72 -0.0003 Td <0020>Tj /C2_1 1 Tf 1.515 Tc 1.75 0.58 Td <004B004B>Tj /TT0 1 Tf 0.0007 Tc 6.1026 Tw 9 0 0 9 483.42 411.9603 Tm ( \(1.5\) )Tj 0.0009 Tc 0 Tw -18.3933 -2.2267 Td (Here )Tj 0.337 Tc 12 0 0 12 346.62 391.92 Tm (\(\))Tj /TT1 1 Tf 0.3862 Tc -0.5 0.0053 Td (xt)Tj /C2_1 1 Tf 0 Tc 0.045 0.5747 Td <004B>Tj /TT0 1 Tf 0.0017 Tc 0.0616 Tw 9 0 0 9 361.2 391.9203 Tm [( is)4( the vector of s)4(tate variables)4(,)-2( )]TJ 0.337 Tc 0 Tw 12 0 0 12 487.86 391.92 Tm (\(\))Tj /TT1 1 Tf 0.41 Tc -0.58 0.0053 Td (ut)Tj /C2_1 1 Tf 0 Tc 0.125 0.5747 Td <004B>Tj /TT0 1 Tf 0.0011 Tc 0.0622 Tw 9 0 0 9 502.44 391.9203 Tm (is the vector of )Tj 0.0005 Tc 0.0495 Tw -20.5067 -1.78 Td [(measured inputs, )7(and )]TJ 0.337 Tc 0 Tw 12 0 0 12 406.44 375.9 Tm (\(\))Tj /TT1 1 Tf 0.3661 Tc -0.485 0.0053 Td (yt)Tj /TT0 1 Tf 0.0008 Tc 0.0425 Tw 9 0 0 9 420.66 375.9003 Tm (is a generic measured output sampled )Tj 0.001 Tc 0.1757 Tw -11.42 -1.4867 Td [(in )-7(time \(time series\). The ope)]TJ 0.0008 Tc 0.1759 Tw 12.6867 0 Td [(rational methodology)-12( of apply)-12(i)-1(ng )]TJ 0.0012 Tc 0.0021 Tw -12.6867 -1.1733 Td (nonlinear time series is given in Figure 2. )Tj /TT2 1 Tf -0.0011 Tc 0.0044 Tw 1.9467 -21.56 Td [(F)-4(i)-3(gur)-4(e)-4( 2 Non-Line)-4(ar)-4( Time)-4( Se)-4(r)-4(i)-3(e)-4(s)1( e)-4(m)-1(be)-4(dding pr)-4(oc)-4(e)-4(ss )]TJ /TT0 1 Tf 0.0011 Tc 0.0422 Tw -1.9467 -1.6 Td [(The )-7(outputs, )-7(the )-7(inputs, )-7(and their time derivatives are unfolded in )]TJ 0.0009 Tc 0.0891 Tw 0 -1.1733 TD [(higher and higher dim)5(e)-2(nsional spaces until )7(the )7(output )7(becom)5(e)-2(s )7(a )]TJ 0.1224 Tw T* [(single-valued )-7(function )-7(of these variables. Algorithms to find the )]TJ 0.5224 Tw T* [(proper choice of )7(variables )7(\(t)]TJ 0.0007 Tc 0.516 Tw 13.38 0 Td (he embedding\) are based on )Tj 0.0014 Tc 0.7019 Tw -13.38 -1.1733 Td [(inform)6(ation-theoretic principles)4( [16])8(. W)5(h)1(en the trajectory)-12( )]TJ 0.0011 Tc 0.4422 Tw T* [(becomes a single valued function, the output )7(can )7(then )7(be )]TJ 0.0012 Tc 0.0021 Tw T* [(des)4(c)-2(ribed according to Equation 1.6. )]TJ ET 1 1 1 scn /CS0 CS 0 0 0 SCN 0.72 w 10 M 0 j 0 J []0 d 316.8 338.4 244.62 -164.76 re B 0 0 0 scn 354.78 216.96 1.68 30.24 re f 345.12 219.84 73.32 1.68 re f 0.388 0.675 1 scn 354.9 222.18 m 356.46 221.82 l 356.7 222.96 l 356.7 223.2 l 356.76 224.52 l 356.94 225.84 l 356.1 225.84 l 356.94 225.54 l 357.24 226.68 l 356.46 227.04 l 357.24 226.56 l 357.6 227.22 l 358.08 227.88 l 358.38 228.36 l 358.44 228.54 l 358.44 228.48 l 357.72 228.96 l 357.72 228.06 l 357.96 228.18 l 358.26 228.36 l 357.54 228.06 l 357.9 228 l 358.38 227.82 l 359.1 227.46 l 359.4 228.18 l 358.86 227.64 l 359.46 227.04 l 359.88 226.8 l 360.42 226.38 l 360.9 227.04 l 360.12 226.68 l 360.72 225.72 l 361.26 224.82 l 361.74 223.86 l 362.22 222.96 l 362.94 223.2 l 362.1 223.14 l 362.28 221.82 l 362.28 221.52 l 362.58 220.38 l 362.88 219.48 l 363.24 218.7 l 363.6 217.98 l 364.08 217.2 l 364.62 216.36 l 365.46 215.16 l 365.58 215.04 l 365.88 214.86 l 366.12 214.8 l 366.42 214.8 l 367.26 215.22 l 367.56 215.46 l 368.28 216 l 368.94 216.84 l 369.12 217.14 l 369.72 218.16 l 370.56 220.2 l 370.92 221.22 l 371.28 222.3 l 371.76 224.52 l 371.88 224.82 l 372.24 227.22 l 372.54 229.68 l 372.9 232.14 l 372.06 232.14 l 372.9 231.84 l 373.38 234.18 l 373.74 235.32 l 374.22 236.34 l 374.76 237.36 l 373.92 237.72 l 374.58 237.06 l 375.24 238.02 l 376.02 238.86 l 376.74 239.64 l 376.26 240.3 l 376.02 239.52 l 376.26 239.4 l 376.56 239.52 l 375.78 239.64 l 376.38 239.04 l 376.92 238.38 l 377.58 239.04 l 376.74 238.68 l 377.7 237.3 l 378.42 235.68 l 378.9 234 l 379.26 232.2 l 379.74 230.52 l 380.28 228.84 l 381.12 227.16 l 381.78 227.64 l 381.06 227.46 l 381.24 226.02 l 381.36 225.72 l 381.6 224.22 l 382.08 222.72 l 382.92 221.16 l 383.58 221.64 l 382.86 221.46 l 383.04 220.32 l 383.4 219.18 l 384.24 217.02 l 384.9 216.12 l 385.08 215.82 l 385.74 214.86 l 386.52 214.2 l 386.76 214.02 l 387.6 213.54 l 387.9 213.54 l 388.2 213.66 l 388.44 213.84 l 388.56 213.96 l 389.88 215.7 l 391.2 217.68 l 391.56 218.16 l 392.1 219.06 l 392.4 219.54 l 392.52 219.72 l 392.52 219.66 l 392.58 219.96 l 392.94 221.82 l 393.12 222.84 l 393.54 223.86 l 393.9 224.82 l 394.44 225.54 l 393.6 225.96 l 394.26 225.3 l 394.92 225.96 l 394.38 226.56 l 394.62 225.72 l 395.58 226.2 l 395.22 227.04 l 394.92 226.32 l 395.22 226.2 l 394.74 226.38 l 395.1 226.02 l 395.7 225.48 l 396.72 224.22 l 397.62 222.96 l 398.22 223.56 l 397.44 223.2 l 398.22 221.88 l 398.94 222.3 l 398.22 221.88 l 398.7 220.68 l 399.24 219.48 l 399.42 219.18 l 400.2 218.22 l 400.62 217.86 l 400.92 217.68 l 401.58 217.32 l 401.88 217.32 l 402.18 217.38 l 402.24 217.32 l 403.02 217.68 l 403.74 217.86 l 404.4 218.22 l 404.7 218.46 l 405.36 218.82 l 405.36 218.88 l 405.54 219 l 406.56 220.68 l 407.52 222.3 l 408.42 223.98 l 409.08 225.72 l 409.56 228 l 409.68 228.3 l 410.04 230.52 l 410.4 232.8 l 409.56 232.8 l 410.28 232.38 l 410.76 234.54 l 411.36 236.64 l 412.2 238.56 l 412.74 239.52 l 411.9 239.88 l 412.56 239.22 l 413.1 240.18 l 413.88 241.02 l 414.6 241.8 l 415.68 242.7 l 416.7 243.36 l 416.1 244.02 l 416.4 243.18 l 417.54 243.72 l 418.2 243.84 l 417.78 244.56 l 417.78 243.72 l 418.44 243.84 l 418.44 245.52 l 417.78 245.4 l 417.54 245.4 l 416.88 245.34 l 415.74 244.8 l 415.44 244.56 l 414.42 243.9 l 413.52 243 l 412.68 242.22 l 411.9 241.38 l 411.18 240.18 l 410.58 239.22 l 409.74 237.3 l 409.2 235.2 l 408.72 233.04 l 408.72 232.8 l 408.36 230.52 l 407.94 228.3 l 408.78 228.3 l 407.94 228.66 l 407.52 226.2 l 406.86 224.64 l 405.9 222.96 l 404.94 221.34 l 404.1 219.84 l 404.76 219.48 l 404.28 220.14 l 403.44 219.66 l 404.1 219 l 403.74 219.84 l 403.08 219.48 l 402.36 219.3 l 401.58 218.88 l 401.88 219 l 401.58 218.88 l 401.88 218.16 l 402.24 218.88 l 401.58 219.3 l 401.28 218.46 l 401.88 219.06 l 401.4 219.48 l 400.62 220.38 l 400.08 219.84 l 400.86 220.14 l 400.26 221.34 l 399.72 222.54 l 399.72 222.66 l 399.06 223.86 l 398.88 224.16 l 397.92 225.48 l 396.9 226.68 l 396.36 227.22 l 395.76 227.7 l 395.52 227.82 l 395.22 227.88 l 394.92 227.82 l 394.02 227.34 l 393.72 227.16 l 393.06 226.5 l 392.88 226.2 l 392.28 225.48 l 391.92 224.52 l 391.56 223.5 l 391.38 222.48 l 391.02 220.32 l 391.74 220.14 l 391.08 220.5 l 390.9 220.38 l 390.78 220.2 l 390.54 219.72 l 390.12 219.06 l 390.9 218.7 l 390.36 219.36 l 389.88 218.64 l 388.62 216.96 l 387.24 214.86 l 387.9 215.22 l 387.6 215.16 l 387.36 214.98 l 387.9 214.38 l 388.2 215.16 l 387.42 215.64 l 387.06 214.86 l 387.72 215.46 l 386.94 216.12 l 386.28 217.02 l 385.62 216.36 l 386.52 216.72 l 385.86 217.68 l 385.02 219.84 l 384.6 220.98 l 384.42 221.82 l 384.36 222 l 383.7 223.38 l 383.22 224.88 l 382.92 226.38 l 382.08 226.02 l 382.92 226.02 l 382.62 227.7 l 382.56 227.88 l 382.56 228 l 381.9 229.5 l 381.36 231.18 l 380.88 232.86 l 380.52 234.66 l 380.04 236.34 l 379.26 237.9 l 378.36 239.34 l 378.12 239.64 l 377.58 240.3 l 376.74 240.9 l 376.56 241.02 l 376.26 241.14 l 376.02 241.02 l 375.78 240.9 l 374.76 240.06 l 374.04 239.22 l 373.38 238.32 l 373.2 238.02 l 372.6 237 l 372.12 235.98 l 371.76 234.84 l 371.28 232.5 l 371.22 232.14 l 370.86 229.68 l 370.56 227.22 l 370.2 224.82 l 371.04 224.82 l 370.2 225.18 l 369.72 222.72 l 370.44 222.54 l 369.72 222.84 l 369.36 221.88 l 368.1 218.82 l 367.56 217.8 l 368.28 217.5 l 367.74 218.04 l 367.08 217.2 l 366.36 216.66 l 366.96 216 l 366.6 216.84 l 365.94 216.36 l 366.72 216.18 l 366.42 216.36 l 366.12 216.48 l 366.12 215.64 l 366.9 216 l 366.24 217.02 l 365.7 217.86 l 365.22 218.64 l 364.86 219.36 l 364.44 220.14 l 364.2 221.04 l 363.9 222.18 l 363.12 221.82 l 363.96 221.82 l 363.78 223.32 l 363.78 223.5 l 363.36 224.52 l 362.88 225.48 l 362.28 226.38 l 361.62 227.46 l 361.08 228 l 360.72 228.3 l 360.06 228.84 l 359.76 229.02 l 359.04 229.38 l 358.56 229.56 l 357.9 229.68 l 357.72 229.8 l 357.42 229.68 l 357.12 229.5 l 357.06 229.32 l 356.88 229.2 l 356.76 229.02 l 356.46 228.54 l 356.04 227.88 l 355.86 227.52 l 355.74 227.34 l 355.38 226.2 l 355.26 225.84 l 355.08 224.52 l 354.96 223.2 l 355.86 223.2 l 355.08 223.56 l 354.9 222.18 l f 0 0 0 scn BT /T1_0 1 Tf -0.1022 Tc 0 Tw 13.5 0 0 13.5 330.06 232.8606 Tm [(y\()107(t)]TJ 0 Tc 1.2222 0 Td (\))Tj 2.2622 -1.7911 Td (t)Tj 0.3333 0 Td (i)Tj 0.2356 Tc 0.2756 0 Td (me)Tj ET 352.92 273.72 1.68 26.16 re f 344.76 276.18 62.82 1.68 re f 0.388 0.675 1 scn 354.06 283.38 m 355.62 283.02 l 356.46 285.06 l 357.12 286.08 l 357.72 287.16 l 356.88 287.52 l 357.6 287.16 l 357.96 287.82 l 358.38 288.48 l 358.62 289.02 l 358.74 289.2 l 358.74 289.08 l 357.96 289.56 l 358.26 288.84 l 358.56 289.02 l 358.2 288.72 l 358.62 288.84 l 358.26 289.56 l 358.26 288.72 l 358.74 288.72 l 359.28 288.84 l 359.94 288.72 l 360.6 288.72 l 361.2 288.66 l 361.2 289.5 l 360.9 288.72 l 361.26 288.66 l 361.62 289.38 l 360.96 288.84 l 361.44 288.66 l 361.62 288.54 l 361.86 288.36 l 362.22 289.08 l 361.56 288.54 l 361.74 288.36 l 362.4 289.02 l 361.56 288.66 l 361.74 288.24 l 362.58 288.54 l 361.74 288.54 l 361.74 288.06 l 361.86 287.7 l 361.92 287.22 l 361.92 287.04 l 362.1 286.56 l 362.88 286.98 l 362.04 286.98 l 362.1 286.38 l 362.1 285.54 l 362.04 284.58 l 362.04 283.74 l 362.22 283.2 l 362.94 283.5 l 362.1 283.38 l 362.22 282.66 l 362.28 282 l 362.46 280.74 l 362.58 280.5 l 362.76 279.48 l 363.12 278.58 l 363.54 277.86 l 363.96 277.02 l 364.56 276.18 l 365.22 274.98 l 365.4 274.74 l 365.7 274.56 l 365.94 274.5 l 366.24 274.5 l 367.08 274.98 l 367.38 275.16 l 368.04 275.88 l 368.7 276.72 l 368.88 277.02 l 369.42 278.04 l 370.26 280.38 l 370.62 281.52 l 370.92 282.54 l 371.4 284.82 l 371.4 285.06 l 371.76 287.22 l 372.06 289.32 l 372.42 291.18 l 371.58 291.18 l 372.42 290.88 l 372.9 292.68 l 373.62 294.48 l 374.22 295.32 l 373.38 295.56 l 374.04 295.02 l 374.58 295.86 l 375.36 296.58 l 376.2 297.36 l 375.6 298.02 l 375.36 297.24 l 375.6 297.18 l 375.9 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394.74 295.5 l 394.44 294.72 l 394.74 294.66 l 395.04 294.72 l 394.26 294.84 l 394.38 294.54 l 394.92 295.2 l 394.2 294.84 l 394.38 294.36 l 394.56 293.7 l 394.74 292.98 l 395.52 293.22 l 394.62 293.22 l 394.86 292.32 l 395.04 291.36 l 395.22 289.2 l 395.52 287.04 l 395.58 286.02 l 395.76 285.06 l 395.88 284.22 l 395.94 283.5 l 396.06 283.08 l 396.12 282.54 l 396.36 282.06 l 397.08 282.48 l 396.36 282.18 l 396.6 281.34 l 397.2 280.32 l 397.86 279.18 l 398.76 277.68 l 399.6 276.66 l 400.38 275.58 l 401.1 274.86 l 401.52 274.56 l 401.76 274.38 l 402.18 274.2 l 402.18 274.32 l 402.42 274.2 l 402.72 274.2 l 403.2 274.5 l 403.44 274.68 l 403.92 275.22 l 404.88 276.54 l 405.06 276.84 l 405.6 277.68 l 404.76 277.98 l 405.42 277.38 l 405.9 278.04 l 406.26 278.58 l 406.68 279 l 406.68 279.06 l 406.86 279.18 l 407.52 280.08 l 406.68 280.38 l 407.28 279.84 l 408.06 280.56 l 408.9 281.34 l 409.86 282.18 l 410.76 282.9 l 411.6 283.86 l 412.2 284.7 l 412.38 285 l 412.86 286.08 l 413.22 288 l 413.4 288.72 l 413.52 289.08 l 413.58 289.74 l 413.76 290.82 l 413.94 291.72 l 413.1 291.72 l 413.88 291.36 l 414.18 292.32 l 414.24 292.98 l 414.42 293.58 l 414.72 294.36 l 415.02 295.32 l 415.44 296.4 l 415.92 297.84 l 415.08 298.08 l 415.68 297.54 l 415.86 297.84 l 415.44 297.36 l 416.52 297.84 l 417.42 298.32 l 418.26 298.74 l 419.04 299.16 l 420.24 299.82 l 421.26 300.24 l 422.04 300.66 l 422.7 300.9 l 424.02 301.56 l 423.24 303.06 l 422.04 302.52 l 421.38 302.22 l 420.6 301.86 l 419.58 301.38 l 418.38 300.72 l 417.6 300.36 l 416.76 299.88 l 415.86 299.4 l 414.72 298.86 l 414.54 298.68 l 414.36 298.38 l 413.88 297.06 l 413.4 295.92 l 413.1 295.02 l 412.86 294.24 l 412.68 293.58 l 412.56 292.98 l 412.26 292.02 l 412.26 291.72 l 412.08 290.82 l 411.9 289.74 l 411.78 289.08 l 412.68 289.08 l 411.78 289.38 l 411.6 288.66 l 411.42 287.7 l 411.24 286.5 l 410.76 285.66 l 411.6 285.36 l 410.94 285.9 l 410.4 285.06 l 409.56 284.16 l 408.6 283.38 l 407.7 282.54 l 406.86 281.82 l 406.08 281.04 l 405.9 280.74 l 405.42 280.02 l 406.08 279.66 l 405.6 280.32 l 405.06 279.84 l 404.7 279.24 l 404.22 278.58 l 404.04 278.34 l 403.44 277.5 l 404.28 277.2 l 403.68 277.74 l 403.2 277.08 l 402.24 275.88 l 402.78 275.34 l 402.54 276.06 l 402.18 275.82 l 402.72 275.82 l 402.42 275.88 l 402.42 275.04 l 402.78 275.82 l 402.42 276 l 402.18 275.22 l 402.72 275.82 l 402.36 276.06 l 401.58 276.84 l 400.86 277.86 l 400.02 278.88 l 399.42 278.34 l 400.2 278.58 l 399.42 279.84 l 398.76 280.98 l 398.22 282 l 397.92 282.72 l 397.86 282.72 l 397.74 283.2 l 397.62 283.74 l 396.78 283.5 l 397.62 283.5 l 397.56 284.22 l 397.44 285.06 l 397.26 286.02 l 397.2 287.04 l 396.9 289.2 l 396.72 291.36 l 396.54 292.32 l 396.36 293.22 l 396.36 293.58 l 396.12 294.36 l 395.94 295.02 l 395.76 295.5 l 395.58 295.74 l 395.28 296.16 l 395.04 296.22 l 394.74 296.34 l 394.44 296.22 l 394.02 295.92 l 393.72 295.74 l 393.24 295.32 l 393.06 295.02 l 392.7 294.24 l 392.28 293.4 l 391.92 292.38 l 391.56 291.24 l 391.02 288.84 l 390.42 286.32 l 390.36 286.02 l 389.94 283.56 l 389.58 281.52 l 389.4 280.74 l 389.4 280.32 l 390.12 280.08 l 389.4 280.5 l 389.28 280.38 l 389.04 279.66 l 388.62 279 l 388.44 278.58 l 388.44 278.52 l 387.06 276.48 l 386.4 275.4 l 385.92 274.38 l 386.88 274.74 l 386.58 274.86 l 386.28 274.74 l 386.04 274.56 l 386.58 274.02 l 386.94 274.74 l 386.1 275.34 l 385.74 274.5 l 386.4 275.16 l 385.62 275.88 l 385.08 276.72 l 384.42 276.18 l 385.26 276.48 l 384.72 277.56 l 383.88 279.9 l 383.52 281.04 l 383.28 282 l 383.22 282.18 l 382.62 283.68 l 382.2 285.18 l 381.36 284.88 l 382.2 284.88 l 381.9 286.56 l 381.6 288.36 l 381.54 288.54 l 381.54 288.66 l 380.88 290.04 l 379.92 292.68 l 379.56 293.82 l 379.2 294.9 l 378.54 296.04 l 378.36 296.34 l 377.52 297.42 l 376.92 298.02 l 376.2 298.68 l 375.9 298.74 l 375.6 298.86 l 375.36 298.74 l 375.12 298.68 l 374.1 297.84 l 373.38 297.06 l 372.78 296.22 l 372.6 295.92 l 372.06 295.08 l 371.28 293.34 l 370.86 291.54 l 370.74 291.18 l 370.38 289.32 l 370.08 287.22 l 369.72 285.06 l 370.56 285.06 l 369.78 285.48 l 369.36 283.02 l 369.06 282.18 l 368.7 281.04 l 367.86 278.7 l 367.26 277.68 l 368.04 277.38 l 367.44 277.98 l 366.78 277.08 l 366.12 276.36 l 366.72 275.82 l 366.42 276.54 l 365.7 276.06 l 366.54 275.88 l 366.24 276.06 l 365.94 276.18 l 365.94 275.34 l 366.72 275.7 l 366.12 276.84 l 365.58 277.68 l 365.1 278.52 l 364.74 279.24 l 364.38 280.08 l 364.2 281.16 l 363.36 280.74 l 364.2 280.74 l 363.96 282 l 363.9 282.66 l 363.78 283.56 l 363.78 283.68 l 363.6 284.4 l 362.88 284.04 l 363.72 284.04 l 363.72 284.58 l 363.78 285.54 l 363.78 286.38 l 363.72 286.98 l 363.72 287.22 l 363.42 287.82 l 362.7 287.4 l 363.54 287.58 l 363.42 288.36 l 362.58 288.06 l 363.42 288.06 l 363.42 288.54 l 363.36 288.9 l 363.12 289.32 l 362.94 289.56 l 362.76 289.74 l 362.46 289.98 l 362.28 290.04 l 361.92 289.32 l 362.46 289.98 l 362.22 290.04 l 361.92 290.22 l 361.56 290.34 l 361.2 290.34 l 360.6 290.4 l 359.94 290.4 l 359.28 290.52 l 358.74 290.4 l 357.96 290.4 l 357.78 290.34 l 357.72 290.34 l 357.42 290.16 l 357.36 289.98 l 357.12 289.86 l 357.06 289.68 l 356.76 289.08 l 356.4 288.48 l 356.1 287.88 l 356.1 287.82 l 355.56 286.74 l 354.9 285.72 l 354.42 284.7 l 354.06 283.38 l f 0 0 0 scn BT /T1_0 1 Tf -0.0444 Tc 13.5 0 0 13.5 330.06 286.8606 Tm [(u\()169(t)]TJ 0 Tc 1.28 0 Td (\))Tj 1.7067 -1.5422 Td (t)Tj 0.3333 0 Td (i)Tj 0.2356 Tc 0.2756 0 Td (me)Tj ET 501 257.7 m 499.26 257.7 l 499.2 211.32 l 500.88 211.32 l 501 257.7 l f 491.4 224.34 m 490.74 222.72 l 549.36 198.36 l 550.02 199.98 l 491.4 224.34 l f 509.7 227.88 m 508.5 229.14 l 463.56 184.86 l 464.76 183.66 l 509.7 227.88 l f 0.388 0.675 1 scn 516.18 211.98 m 516.72 210.36 l 517.86 210.84 l 518.82 211.32 l 519.66 211.86 l 519.9 212.04 l 520.68 212.64 l 521.88 213.96 l 522.9 215.22 l 523.08 215.52 l 523.86 217.02 l 524.52 218.52 l 525 219.96 l 525.42 221.46 l 525.42 221.82 l 525.24 223.8 l 525.18 225.84 l 525 227.88 l 524.7 230.04 l 524.4 230.82 l 524.34 231.18 l 523.86 231.96 l 523.68 232.2 l 522.9 232.98 l 522 233.64 l 521.7 233.82 l 520.56 234.36 l 519.36 234.84 l 517.92 235.32 l 516.54 235.68 l 516.18 235.68 l 513.06 236.34 l 510 236.7 l 506.88 237 l 505.56 237.06 l 504.36 237.18 l 504.24 237.18 l 502.2 237.06 l 500.16 237.06 l 498.06 237 l 496.02 236.64 l 495.36 236.52 l 495.06 236.52 l 494.22 236.22 l 492.66 235.68 l 491.88 235.38 l 491.34 235.14 l 490.92 234.96 l 490.74 234.84 l 490.56 234.66 l 490.5 234.48 l 489.9 233.82 l 490.74 233.46 l 490.08 234.06 l 489.72 233.46 l 488.76 232.56 l 488.16 232.14 l 488.76 231.54 l 488.4 232.32 l 487.74 231.96 l 486.9 231.54 l 486 231.18 l 485.7 231 l 485.58 230.82 l 483.72 227.82 l 482.22 224.88 l 482.22 224.64 l 481.74 222.72 l 482.58 222.72 l 481.74 223.02 l 481.38 221.16 l 481.26 220.8 l 481.02 218.88 l 480.9 217.98 l 480.9 217.02 l 481.02 216.12 l 481.02 215.7 l 481.26 214.86 l 481.68 214.02 l 482.22 213.18 l 482.4 212.88 l 483.06 212.16 l 484.02 211.38 l 484.26 211.2 l 485.4 210.54 l 486.84 209.88 l 487.08 210.72 l 486.66 210.12 l 487.08 209.64 l 487.68 209.16 l 488.04 208.8 l 488.34 208.38 l 489.18 207.66 l 489.42 207.48 l 489.84 207.3 l 490.26 207.18 l 490.68 207.12 l 491.04 207.12 l 491.52 207 l 492.06 206.82 l 492.72 206.7 l 492.84 207.54 l 492.54 206.82 l 492.36 206.88 l 492.9 206.46 l 493.56 205.98 l 493.86 205.8 l 495.24 205.02 l 496.02 204.72 l 496.86 204.54 l 497.88 204.3 l 499.08 204 l 499.26 204.84 l 498.9 204.12 l 500.52 203.34 l 502.02 202.68 l 503.7 202.14 l 505.38 201.66 l 509.04 201 l 509.34 200.88 l 513.18 200.34 l 513.24 201.18 l 513.18 200.34 l 513.72 200.22 l 514.2 200.16 l 515.22 200.04 l 515.7 199.98 l 516.06 199.86 l 516.54 199.86 l 519 199.98 l 521.34 200.16 l 526.02 200.46 l 530.58 201 l 535.5 201.72 l 535.56 201.84 l 535.86 201.96 l 536.88 202.8 l 537.72 203.46 l 538.5 203.88 l 539.16 204.48 l 539.7 205.02 l 540.36 205.62 l 540.9 206.46 l 541.08 206.7 l 541.74 207.54 l 541.74 207.66 l 542.58 209.04 l 543.36 210.3 l 543.48 210.54 l 543.54 210.96 l 543.84 211.86 l 544.08 213.3 l 544.5 214.68 l 544.74 216.18 l 544.86 216.84 l 545.04 217.38 l 545.16 217.98 l 545.22 218.34 l 545.22 218.64 l 545.34 218.82 l 545.34 219 l 545.22 219.96 l 545.22 221.88 l 545.34 222.72 l 545.34 223.56 l 545.4 224.34 l 545.52 225.3 l 545.52 225.84 l 545.4 226.5 l 545.4 227.22 l 545.34 228.3 l 545.22 228.96 l 545.16 229.8 l 544.74 231.66 l 544.74 231.96 l 544.32 233.82 l 544.02 234.54 l 543.54 235.38 l 542.82 236.52 l 542.58 236.82 l 541.56 237.84 l 540.48 238.8 l 539.22 239.7 l 538.02 240.66 l 536.88 241.56 l 535.98 242.64 l 535.32 242.04 l 536.16 242.34 l 535.2 243.54 l 534.84 244.02 l 534.66 244.32 l 534.06 244.8 l 533.82 244.98 l 533.16 245.34 l 532.2 245.82 l 531.24 246.18 l 530.16 246.66 l 527.82 247.32 l 525.24 247.98 l 524.88 247.98 l 522.42 248.4 l 520.08 248.82 l 519.06 249 l 518.22 249.06 l 518.16 249.06 l 514.86 248.88 l 513.18 248.82 l 511.5 248.64 l 510.9 248.52 l 510.18 248.4 l 508.56 248.04 l 508.2 248.04 l 507.54 247.86 l 506.88 247.8 l 506.52 247.68 l 506.52 247.56 l 506.34 247.5 l 505.74 247.32 l 505.2 246.9 l 504.72 246.72 l 504.42 246.54 l 503.88 246.3 l 503.4 246 l 502.86 245.82 l 502.56 245.7 l 502.08 245.52 l 501.54 245.34 l 500.76 245.16 l 499.92 244.8 l 499.02 244.38 l 497.76 244.02 l 496.56 243.54 l 496.5 243.54 l 495.84 243.3 l 495.06 243 l 494.7 242.88 l 494.34 242.7 l 494.16 242.7 l 494.22 242.64 l 494.16 242.64 l 493.86 242.4 l 493.08 241.8 l 493.68 241.14 l 493.38 241.98 l 492.42 241.14 l 492.84 240.48 l 492.42 241.2 l 491.88 241.02 l 490.56 240.66 l 490.26 240.48 l 489.9 240.18 l 489.72 240.06 l 489.66 240 l 489.18 239.64 l 488.4 239.04 l 487.56 238.38 l 486.72 237.66 l 486 237 l 485.22 236.4 l 484.92 236.16 l 484.86 236.04 l 484.08 235.32 l 483.36 234.3 l 483.18 234 l 482.52 232.86 l 481.86 231.66 l 481.2 230.34 l 480.66 229.14 l 480.18 228.06 l 479.76 227.16 l 479.76 227.04 l 479.7 226.8 l 479.7 226.68 l 479.88 224.64 l 480.06 222.36 l 480.24 220.2 l 480.66 217.86 l 480.66 217.38 l 480.84 217.02 l 481.02 216.72 l 481.2 216.36 l 481.5 216.18 l 481.92 216 l 482.22 216.72 l 481.86 216 l 483.06 215.34 l 484.2 214.86 l 485.34 214.5 l 486.42 214.14 l 488.88 213.66 l 489.24 213.54 l 490.56 213.36 l 491.88 213.12 l 492.66 213 l 493.5 212.82 l 495.06 212.52 l 495.72 212.46 l 496.26 212.34 l 496.74 212.22 l 496.92 212.22 l 501.66 212.64 l 506.22 213 l 508.5 213.36 l 510.66 213.72 l 511.02 213.84 l 513.06 214.32 l 515.16 214.98 l 515.16 215.04 l 515.4 215.16 l 516.06 215.7 l 516.66 216.18 l 517.5 216.84 l 518.04 217.2 l 518.34 217.5 l 518.58 217.8 l 518.82 218.04 l 519 218.34 l 519.24 218.82 l 519.66 219.48 l 519.66 219.66 l 519.72 219.96 l 519.72 221.16 l 520.08 224.16 l 520.08 225.72 l 520.02 226.56 l 520.02 226.86 l 519.84 227.64 l 519.54 228.36 l 519.06 228.96 l 518.88 229.2 l 518.34 229.86 l 518.04 230.04 l 517.32 230.52 l 516.36 230.88 l 516 231 l 515.04 231.18 l 514.86 230.46 l 515.16 231.18 l 515.4 231.06 l 515.04 231.36 l 514.74 231.72 l 514.38 232.14 l 514.08 232.32 l 513.66 232.56 l 513.54 232.56 l 513 232.8 l 512.22 232.98 l 511.86 232.98 l 510.24 233.22 l 509.52 233.34 l 508.86 233.46 l 508.5 233.52 l 508.32 233.52 l 502.92 233.34 l 500.34 233.22 l 497.7 233.04 l 497.04 232.98 l 496.2 232.86 l 494.58 232.56 l 494.34 232.56 l 493.56 232.38 l 493.02 232.32 l 492.66 232.2 l 492.66 232.14 l 492.54 232.14 l 492.24 231.96 l 492.18 231.72 l 491.04 230.22 l 491.88 229.98 l 491.22 230.52 l 490.2 229.2 l 489.06 227.88 l 488.88 227.64 l 488.04 226.2 l 487.92 226.2 l 487.5 225.36 l 486.9 224.46 l 486.72 224.04 l 486.42 223.8 l 486.36 223.5 l 486.42 223.5 l 486.24 223.14 l 486.36 222.96 l 486.66 221.22 l 487.02 219.54 l 487.56 217.8 l 488.22 216 l 489.24 214.38 l 489.42 214.14 l 490.02 213.3 l 490.74 212.52 l 491.52 211.86 l 492.42 211.2 l 492.72 211.02 l 493.74 210.48 l 495 209.88 l 495.24 210.72 l 494.7 210.12 l 496.26 209.04 l 496.56 208.86 l 498.42 207.96 l 500.58 207.18 l 502.86 206.64 l 503.22 206.52 l 505.68 206.16 l 508.2 205.8 l 513.24 205.38 l 515.04 205.38 l 516.72 205.5 l 518.22 205.5 l 519.66 205.38 l 524.58 205.38 l 526.74 205.62 l 529.02 205.86 l 529.32 205.98 l 531.54 206.46 l 533.88 207.18 l 533.88 207.3 l 534.18 207.48 l 534.36 207.54 l 535.5 209.64 l 536.34 211.62 l 537.06 213.48 l 537.72 215.52 l 537.72 215.82 l 537.54 218.52 l 537.48 221.22 l 537.18 224.16 l 536.7 227.04 l 536.58 227.34 l 536.22 228.72 l 535.86 230.16 l 535.32 231.54 l 534.54 232.98 l 533.82 234.3 l 533.58 234.54 l 532.56 235.86 l 531.48 237.18 l 530.16 238.38 l 529.56 237.72 l 530.16 238.38 l 529.68 238.8 l 528.9 239.34 l 528.18 239.82 l 527.88 240 l 527.04 240.54 l 525.18 241.56 l 524.22 241.98 l 523.2 242.16 l 522.18 242.4 l 521.88 242.52 l 520.56 242.7 l 518.34 243.06 l 518.22 243.18 l 517.38 243.3 l 517.38 242.4 l 517.74 243.3 l 516.9 243.36 l 516.54 243.48 l 516.24 243.54 l 515.88 243.54 l 515.7 243.66 l 510.54 243.66 l 508.56 243.54 l 506.7 243.36 l 505.02 243.06 l 504.72 243 l 504 242.82 l 503.34 242.52 l 502.68 242.16 l 502.38 241.98 l 502.02 241.5 l 503.22 240.36 l 503.58 240.72 l 503.04 241.32 l 503.34 240.54 l 504 240.9 l 504.66 241.2 l 505.38 241.38 l 505.02 242.22 l 505.02 241.38 l 506.7 241.68 l 508.56 241.86 l 510.54 241.98 l 515.82 241.98 l 515.7 242.82 l 515.52 241.98 l 515.4 241.98 l 515.58 241.98 l 515.88 241.86 l 516.24 241.8 l 517.08 241.68 l 517.38 241.56 l 518.04 241.5 l 518.16 242.34 l 518.04 241.5 l 520.56 241.02 l 521.88 240.84 l 521.88 241.68 l 521.52 240.84 l 522.84 240.54 l 523.56 240.36 l 524.52 240 l 526.38 238.98 l 527.22 238.38 l 527.52 239.22 l 526.92 238.56 l 527.7 238.14 l 528.48 237.54 l 529.02 237.06 l 529.08 237.06 l 530.22 235.98 l 531.36 234.66 l 532.38 233.34 l 532.98 234 l 532.2 233.64 l 532.98 232.32 l 533.7 230.88 l 534.24 229.5 l 534.66 228.06 l 535.02 226.68 l 535.86 227.04 l 535.02 227.04 l 535.5 224.16 l 535.74 221.22 l 535.86 218.52 l 536.04 215.7 l 536.88 215.82 l 536.16 216 l 535.5 214.14 l 534.72 212.22 l 533.88 210.3 l 532.98 208.38 l 533.34 208.8 l 533.04 208.62 l 533.58 208.02 l 533.34 208.8 l 530.88 208.02 l 528.66 207.54 l 529.02 206.7 l 529.02 207.54 l 526.74 207.3 l 524.58 207.12 l 519.66 207.12 l 518.22 207.18 l 516.72 207.18 l 515.04 207.12 l 513.24 207.12 l 513.24 206.22 l 513.36 207.12 l 508.2 207.48 l 505.68 207.84 l 503.22 208.2 l 503.22 207.36 l 503.52 208.2 l 501.24 208.8 l 499.08 209.52 l 497.22 210.48 l 496.86 209.64 l 497.52 210.3 l 495.84 211.38 l 495.54 211.5 l 494.4 212.04 l 493.38 212.64 l 493.08 211.8 l 493.68 212.46 l 492.72 213.12 l 492 213.72 l 491.22 214.5 l 490.68 215.34 l 490.02 214.68 l 490.86 215.04 l 489.84 216.66 l 489.18 218.46 l 488.58 220.2 l 488.22 221.88 l 487.92 223.32 l 487.86 222.84 l 487.92 223.14 l 487.08 223.14 l 487.86 222.66 l 487.92 222.84 l 488.04 223.14 l 488.34 223.38 l 488.52 223.8 l 489.06 224.7 l 489.42 225.48 l 488.7 225.84 l 489.42 225.36 l 490.5 226.98 l 489.72 227.22 l 490.26 226.68 l 491.4 228 l 492.42 229.32 l 492.66 229.56 l 493.56 230.88 l 493.08 230.64 l 493.38 230.82 l 492.84 231.36 l 493.02 230.52 l 493.26 230.64 l 493.68 230.7 l 494.22 230.82 l 495 231 l 494.58 231.72 l 494.58 230.88 l 496.2 231.18 l 497.04 231.3 l 497.76 231.36 l 500.34 231.54 l 502.92 231.66 l 508.38 231.84 l 508.32 232.68 l 508.2 231.84 l 508.5 231.84 l 508.86 231.72 l 509.52 231.66 l 510.24 231.54 l 511.86 231.3 l 511.86 232.14 l 511.56 231.36 l 512.34 231.18 l 513.06 231 l 513.24 231.84 l 512.88 231.06 l 513.42 230.7 l 513.72 231.54 l 513.18 230.88 l 513.54 230.52 l 513.84 230.16 l 514.74 229.56 l 516 229.32 l 516 230.16 l 515.7 229.32 l 516.66 228.96 l 517.38 228.48 l 517.68 229.2 l 517.08 228.66 l 517.68 228 l 518.34 228.66 l 517.5 228.3 l 517.92 227.7 l 518.22 226.98 l 518.4 226.2 l 519.18 226.56 l 518.34 226.56 l 518.4 225.72 l 518.4 224.16 l 518.04 221.16 l 518.04 219.84 l 518.88 219.96 l 518.22 220.32 l 517.68 219.48 l 517.38 219 l 517.2 218.7 l 517.92 218.34 l 517.38 219 l 516.84 218.46 l 516.24 218.04 l 515.4 217.38 l 514.86 216.96 l 514.38 216.48 l 514.86 215.82 l 514.56 216.54 l 512.4 215.88 l 510.36 215.46 l 510.66 214.62 l 510.66 215.46 l 508.5 215.04 l 506.22 214.68 l 501.66 214.32 l 496.86 213.96 l 496.86 213.12 l 497.04 213.84 l 496.74 213.96 l 496.26 214.02 l 495.72 214.14 l 495.06 214.2 l 493.5 214.5 l 492.66 214.68 l 492.18 214.68 l 490.56 215.04 l 489.24 215.22 l 489.24 214.38 l 489.54 215.22 l 487.08 215.7 l 486 216.12 l 484.86 216.48 l 483.72 216.96 l 482.7 217.38 l 482.58 217.5 l 482.16 217.8 l 481.86 217.02 l 482.4 217.56 l 482.22 217.98 l 481.56 217.32 l 482.4 217.68 l 482.22 218.04 l 482.22 218.22 l 481.38 218.04 l 482.22 218.16 l 481.92 220.2 l 481.74 222.36 l 481.56 224.64 l 481.38 226.86 l 480.54 226.8 l 481.26 226.38 l 481.74 227.46 l 482.22 228.48 l 482.76 229.68 l 483.42 231 l 484.08 232.2 l 484.74 233.34 l 484.02 233.7 l 484.56 233.04 l 485.34 234.06 l 486 234.84 l 485.4 235.5 l 486 234.84 l 486.42 235.2 l 487.2 235.8 l 487.92 236.4 l 488.76 237.18 l 489.66 237.84 l 490.38 238.38 l 490.86 238.8 l 490.92 238.86 l 491.52 239.22 l 490.92 239.82 l 491.22 239.04 l 492.54 239.4 l 493.2 239.7 l 493.26 239.7 l 494.04 240.36 l 494.34 240.54 l 495.06 241.2 l 494.4 241.86 l 494.7 241.02 l 494.76 241.14 l 495 241.14 l 495.36 241.32 l 495.72 241.38 l 496.5 241.68 l 497.22 242.04 l 496.86 242.82 l 497.16 241.98 l 498.42 242.4 l 499.56 242.82 l 500.58 243.18 l 501.42 243.54 l 502.2 243.72 l 502.74 243.9 l 503.22 244.14 l 503.52 244.2 l 504.06 244.38 l 504.54 244.68 l 505.08 244.98 l 505.38 245.16 l 505.86 245.34 l 506.4 245.7 l 507.18 246.06 l 506.7 246.84 l 506.88 246 l 507.18 246.06 l 507.54 246.18 l 508.2 246.3 l 508.86 246.48 l 508.56 247.2 l 508.56 246.36 l 510.18 246.72 l 510.9 246.84 l 511.68 246.9 l 513.18 247.14 l 514.86 247.2 l 518.22 247.38 l 518.16 248.22 l 518.04 247.38 l 519.06 247.32 l 520.08 247.14 l 522.42 246.72 l 524.88 246.3 l 524.88 247.14 l 524.58 246.36 l 527.16 245.7 l 529.5 245.04 l 530.58 244.56 l 531.54 244.2 l 532.5 243.72 l 533.16 243.36 l 533.52 244.14 l 532.86 243.54 l 533.4 243.06 l 534.06 243.66 l 533.22 243.36 l 533.82 242.7 l 534.54 241.68 l 534.72 241.38 l 535.68 240.36 l 536.82 239.4 l 538.02 238.5 l 539.22 237.54 l 540.36 236.64 l 541.38 235.56 l 541.98 236.16 l 541.2 235.86 l 542.16 234.54 l 542.4 233.88 l 542.7 233.16 l 543.18 231.3 l 543.9 231.66 l 543.06 231.66 l 543.48 229.8 l 543.54 228.96 l 543.72 228 l 544.5 228.18 l 543.66 228.06 l 543.72 227.22 l 543.72 226.5 l 543.84 225.84 l 543.84 225.3 l 543.72 224.34 l 543.66 223.56 l 543.66 222.72 l 543.54 221.88 l 543.54 219.96 l 543.66 218.88 l 544.5 219 l 543.72 219.18 l 543.66 219.3 l 543.66 219 l 543.54 218.64 l 543.48 218.04 l 543.24 217.5 l 543.18 216.84 l 542.88 215.34 l 542.52 213.96 l 542.22 212.52 l 542.04 211.98 l 541.98 211.62 l 541.86 211.2 l 541.98 211.14 l 541.02 209.7 l 540.24 208.38 l 541.02 208.02 l 540.36 208.38 l 539.52 207.36 l 540.36 207 l 539.7 207.66 l 539.16 206.82 l 538.5 206.22 l 537.9 205.68 l 537.24 205.14 l 536.52 204.66 l 535.68 204 l 534.84 203.22 l 535.02 203.34 l 535.32 202.62 l 535.2 203.34 l 530.58 202.68 l 526.02 202.14 l 521.34 201.84 l 519 201.66 l 516.42 201.54 l 516.42 200.7 l 516.54 201.54 l 516.06 201.54 l 515.7 201.66 l 515.22 201.72 l 514.2 201.84 l 513.72 201.96 l 513.42 201.96 l 513.36 202.02 l 509.34 202.62 l 509.34 201.72 l 509.7 202.62 l 506.04 203.22 l 504.36 203.7 l 502.68 204.3 l 501.18 204.96 l 499.74 205.62 l 499.5 205.62 l 498.54 205.86 l 497.52 206.16 l 496.68 206.34 l 495.9 206.64 l 494.52 207.36 l 494.22 206.52 l 494.76 207.18 l 494.16 207.66 l 493.38 208.2 l 493.08 208.32 l 493.02 208.32 l 492.06 208.5 l 491.52 208.68 l 491.04 208.8 l 491.04 207.96 l 491.34 208.68 l 490.92 208.8 l 490.5 208.86 l 490.08 209.04 l 489.72 208.32 l 490.38 208.86 l 490.02 209.22 l 489.54 209.64 l 489.24 210 l 488.88 210.36 l 488.34 210.84 l 487.68 211.38 l 487.38 211.5 l 486.06 212.16 l 484.92 212.82 l 484.56 211.98 l 485.22 212.64 l 484.26 213.36 l 483.66 214.14 l 483 213.48 l 483.84 213.84 l 483.24 214.68 l 482.88 215.52 l 482.58 216.36 l 481.86 216.12 l 482.7 216.12 l 482.58 217.02 l 482.58 217.98 l 482.7 218.88 l 483 220.8 l 482.16 220.8 l 483 220.5 l 483.36 222.36 l 483.42 222.72 l 483.84 224.34 l 483 224.52 l 483.72 224.16 l 485.34 227.16 l 487.02 229.98 l 486.54 229.68 l 486.84 229.86 l 486.24 230.46 l 486.54 229.56 l 487.56 229.98 l 488.4 230.34 l 489.06 230.7 l 489.36 230.88 l 490.02 231.36 l 490.92 232.2 l 491.34 232.86 l 491.52 233.16 l 491.88 233.64 l 491.7 233.52 l 491.16 234.06 l 491.52 233.34 l 491.58 233.34 l 492 233.52 l 492.54 233.82 l 493.26 234.06 l 494.88 234.66 l 495.72 234.96 l 495.36 235.68 l 495.36 234.84 l 496.26 235.02 l 498.06 235.32 l 500.16 235.38 l 502.2 235.38 l 504.36 235.5 l 504.24 236.34 l 504.24 235.5 l 505.56 235.38 l 506.88 235.32 l 510 235.02 l 513.06 234.66 l 516.18 234 l 516.18 234.84 l 515.88 234.06 l 517.32 233.7 l 518.7 233.22 l 519.9 232.8 l 521.04 232.2 l 521.34 232.98 l 520.74 232.38 l 521.7 231.72 l 522.42 231 l 523.02 231.66 l 522.24 231.3 l 522.72 230.52 l 523.56 230.82 l 522.72 230.82 l 523.08 229.8 l 523.32 227.88 l 523.5 225.84 l 523.56 223.8 l 523.74 221.64 l 524.58 221.7 l 523.86 221.88 l 523.38 220.56 l 522.9 219.18 l 522.24 217.68 l 521.52 216.18 l 522.24 215.88 l 521.7 216.48 l 520.68 215.16 l 519.42 213.84 l 518.7 213.3 l 519.24 212.7 l 519 213.48 l 518.16 212.88 l 517.2 212.46 l 516.18 211.98 l f 0.388 0.675 1 SCN 1.68 w 1 j 1 J 510.06 247.14 m 502.56 240.9 l 511.92 238.56 l S 0 0 0 scn BT /TT0 1 Tf 0.4009 Tc 14.88 0 0 14.88 486.24 188.4659 Tm (\(\))Tj /TT1 1 Tf 0.4556 Tc -0.5968 0 Td (ut)Tj /C2_1 1 Tf 0 Tc 0.1814 0.0479 Td <0005>Tj /TT0 1 Tf 0.3968 Tc -0.2823 3.9924 Td (\(\))Tj /TT1 1 Tf 0.4392 Tc -0.5282 0 Td (yt)Tj /TT0 1 Tf 0.3968 Tc 4.4597 -4.2299 Td (\(\))Tj /TT1 1 Tf 0.4392 Tc -0.5282 0 Td (yt)Tj /C2_1 1 Tf 0 Tc 0.0806 0.0479 Td <0005>Tj ET 490.26 275.7 1.74 54 re f 482.16 283.86 63 1.68 re f BT /TT0 1 Tf 0.3968 Tc 14.88 0 0 14.88 529.86 266.5859 Tm (\(\))Tj /TT1 1 Tf 0.4392 Tc -0.5282 0 Td (yt)Tj /C2_1 1 Tf 0 Tc 0.0806 0.0479 Td <0005>Tj /TT0 1 Tf 0.3968 Tc -3.4839 3.5771 Td (\(\))Tj /TT1 1 Tf 0.4392 Tc -0.5282 0.0041 Td (yt)Tj ET 0.388 0.675 1 scn 504.36 295.38 m 504.9 293.82 l 506.88 294.48 l 508.74 294.9 l 510.54 295.5 l 512.4 296.04 l 512.4 296.16 l 512.7 296.34 l 512.88 296.4 l 514.38 298.86 l 515.58 301.08 l 516.84 303.36 l 518.16 305.4 l 518.16 305.58 l 518.22 305.88 l 518.22 306 l 518.16 307.74 l 518.04 309.66 l 517.86 311.52 l 517.74 312.42 l 517.68 312.84 l 517.5 313.56 l 516.72 315.54 l 515.7 317.34 l 515.52 317.58 l 514.32 319.2 l 512.82 320.58 l 511.2 321.84 l 510.9 322.02 l 509.22 323.16 l 507.54 324 l 505.68 324.66 l 505.38 324.72 l 505.32 324.72 l 503.52 324.66 l 501.54 324.54 l 499.68 324.36 l 498.84 324.18 l 498.42 324.18 l 497.58 323.88 l 497.16 323.7 l 496.86 323.52 l 496.56 323.04 l 496.38 322.74 l 496.02 322.08 l 495.72 321.36 l 495.42 320.7 l 495.18 319.92 l 495 319.38 l 494.88 318.9 l 494.88 318.84 l 493.86 315.72 l 492.66 312.54 l 491.52 309.42 l 490.38 306.18 l 490.26 305.88 l 490.26 305.82 l 490.5 303.06 l 490.56 300.24 l 490.68 297.42 l 491.16 294.48 l 491.34 293.52 l 491.4 293.22 l 491.88 292.08 l 492.42 291.18 l 492.66 290.88 l 494.34 289.08 l 495.36 288.24 l 495.66 288.06 l 497.88 286.68 l 500.4 285.54 l 502.86 284.52 l 505.2 283.86 l 506.34 283.56 l 507.42 283.32 l 507.72 283.32 l 509.16 283.38 l 514.38 283.38 l 516.24 283.68 l 516.54 283.68 l 518.34 284.04 l 520.02 284.7 l 520.32 284.88 l 521.7 285.72 l 522.42 286.38 l 523.2 287.04 l 524.58 288.54 l 525.24 289.2 l 525.84 289.74 l 526.08 290.16 l 526.32 290.34 l 526.38 290.58 l 526.5 290.58 l 527.04 292.5 l 527.7 294.54 l 528.18 296.7 l 528.18 297.06 l 528.48 299.22 l 528.54 301.38 l 528.48 302.52 l 528.24 303.54 l 528.24 303.84 l 528 304.86 l 527.52 305.88 l 527.04 306.84 l 526.86 307.08 l 526.32 307.86 l 524.34 310.32 l 522.24 312.36 l 520.08 314.16 l 517.86 315.66 l 517.56 315.84 l 515.22 317.22 l 512.7 318.36 l 510.06 319.38 l 507.06 320.16 l 506.88 320.22 l 506.82 320.22 l 504.84 320.16 l 502.74 320.04 l 500.7 319.92 l 499.68 319.74 l 499.26 319.68 l 498.36 319.38 l 498.66 318.66 l 498.42 319.38 l 498 319.26 l 497.7 319.08 l 497.4 318.84 l 497.16 318.36 l 496.92 318.06 l 496.68 317.52 l 496.08 316.2 l 495.54 314.7 l 495.06 313.08 l 494.7 311.58 l 494.34 310.2 l 494.22 309.66 l 494.16 309.06 l 494.04 308.88 l 494.04 308.82 l 494.16 307.92 l 494.16 306.84 l 494.22 305.4 l 494.34 303.9 l 494.7 300.9 l 494.76 300.66 l 495.18 299.22 l 495.66 298.02 l 496.08 297.18 l 496.26 296.88 l 497.04 296.16 l 497.88 295.38 l 499.08 294.66 l 500.16 294.06 l 501.36 293.7 l 503.82 292.98 l 506.4 292.38 l 506.7 292.38 l 509.22 292.02 l 511.68 291.72 l 512.7 291.66 l 513.54 291.54 l 513.72 291.54 l 515.88 291.72 l 518.16 291.84 l 520.38 292.02 l 522.84 292.32 l 523.74 292.56 l 524.04 292.68 l 525.06 293.16 l 525.36 293.34 l 526.32 294 l 527.22 294.72 l 529.02 296.34 l 529.86 297.06 l 529.2 297.72 l 529.56 296.88 l 530.58 297.66 l 530.7 297.84 l 530.88 298.08 l 531 298.08 l 532.5 302.58 l 531.66 302.88 l 532.5 302.52 l 532.68 303.24 l 532.98 303.9 l 533.16 304.56 l 533.16 304.74 l 533.22 304.86 l 533.22 305.22 l 533.04 306.42 l 532.98 307.74 l 532.74 309.06 l 532.68 309.42 l 532.5 310.56 l 532.02 311.58 l 531.48 312.54 l 531.24 312.84 l 530.58 313.68 l 529.68 314.52 l 528.72 315.36 l 527.58 316.02 l 527.34 316.2 l 524.88 317.58 l 522.36 318.72 l 519.84 319.74 l 517.5 320.4 l 516.42 320.7 l 515.34 320.88 l 515.16 321 l 514.86 320.88 l 513.72 320.52 l 512.82 320.22 l 512.04 319.92 l 511.5 319.74 l 510.54 319.26 l 510.24 319.08 l 509.7 318.66 l 509.22 318.06 l 508.56 317.22 l 508.2 316.74 l 507.66 316.2 l 507.06 315.54 l 506.34 314.7 l 506.16 314.4 l 505.5 312.18 l 505.5 311.88 l 505.2 309.84 l 505.2 307.86 l 505.5 306.06 l 505.56 305.82 l 506.04 304.2 l 506.88 302.7 l 507.06 302.4 l 508.02 301.02 l 509.22 299.7 l 510.54 298.5 l 511.92 297.36 l 512.22 297.18 l 513.84 296.16 l 515.4 295.2 l 518.88 293.34 l 522.24 291.66 l 523.74 291 l 525.24 290.7 l 525.66 290.58 l 527.16 290.34 l 527.16 291.18 l 526.74 290.4 l 528.48 290.04 l 528.66 290.88 l 528.48 290.04 l 529.2 289.86 l 530.22 289.56 l 530.58 289.5 l 531 289.38 l 531.24 289.38 l 531.48 289.32 l 531.84 289.32 l 532.98 289.5 l 532.56 290.22 l 532.56 289.38 l 533.58 289.5 l 534.54 289.68 l 534.84 289.68 l 535.32 289.86 l 535.56 290.04 l 535.86 290.22 l 535.98 290.22 l 536.52 290.82 l 537.06 291.48 l 537.24 291.72 l 538.2 293.22 l 538.56 293.88 l 538.98 294.54 l 539.16 294.9 l 539.16 295.08 l 539.22 295.38 l 539.04 298.38 l 538.98 301.38 l 538.74 304.38 l 538.5 307.5 l 537.66 307.38 l 538.5 307.5 l 538.32 308.58 l 538.2 309 l 537.9 310.08 l 537.48 311.22 l 537 312.18 l 536.82 312.42 l 535.5 314.34 l 534 315.9 l 532.2 317.34 l 531.9 317.52 l 530.04 318.72 l 528.06 319.86 l 526.02 320.88 l 525 321.42 l 523.86 322.2 l 522.42 322.92 l 521.04 323.58 l 519.66 324.18 l 518.34 324.42 l 517.92 324.54 l 517.38 324.54 l 516.84 324.42 l 516.42 324.42 l 516 324.24 l 515.7 324.06 l 515.34 323.7 l 516.54 322.5 l 516.9 322.86 l 516.36 323.4 l 516.66 322.68 l 517.08 322.86 l 516.84 323.58 l 516.84 322.74 l 517.38 322.86 l 517.92 322.86 l 517.92 323.7 l 517.68 322.86 l 519 322.56 l 520.38 322.02 l 521.82 321.36 l 523.2 320.58 l 524.34 319.86 l 525.24 319.38 l 527.4 318.24 l 529.38 317.16 l 531.24 315.9 l 531.66 316.68 l 531 316.08 l 532.74 314.7 l 534.24 313.08 l 535.56 311.22 l 536.16 311.88 l 535.38 311.52 l 535.86 310.56 l 536.34 309.42 l 536.58 308.34 l 537.48 308.58 l 536.58 308.58 l 536.82 307.2 l 536.88 307.2 l 537.06 304.38 l 537.24 301.38 l 537.36 298.38 l 537.54 295.32 l 538.38 295.38 l 537.66 295.74 l 537.54 295.56 l 537.36 295.2 l 537 294.54 l 536.58 293.88 l 535.68 292.38 l 536.4 292.08 l 535.86 292.68 l 535.32 292.02 l 534.9 291.54 l 535.38 290.88 l 534.9 291.54 l 534.36 291.24 l 535.02 290.58 l 534.66 291.48 l 534.18 291.24 l 534.54 290.52 l 534.54 291.36 l 533.58 291.18 l 532.56 291.06 l 532.32 291.06 l 531.48 290.88 l 531.66 291 l 531.66 290.16 l 531.9 290.88 l 531.9 291 l 531.66 291 l 531.24 291.06 l 530.88 291.18 l 529.86 291.48 l 528.9 291.66 l 528.84 291.66 l 527.4 292.02 l 527.16 292.02 l 525.66 292.32 l 525.66 291.48 l 525.9 292.32 l 524.4 292.56 l 523.02 293.16 l 519.54 294.9 l 516.06 296.82 l 514.5 297.72 l 512.88 298.74 l 512.58 298.02 l 513.18 298.56 l 511.74 299.7 l 510.42 300.9 l 509.22 302.22 l 508.32 303.66 l 507.66 303 l 508.5 303.36 l 507.66 304.86 l 507.18 306.42 l 506.34 306.06 l 507.18 306.06 l 506.88 307.86 l 506.88 309.84 l 507.18 311.88 l 506.34 311.88 l 507.06 311.52 l 507.72 313.86 l 506.88 314.16 l 507.54 313.5 l 508.32 314.34 l 508.86 315 l 509.4 315.54 l 509.82 316.02 l 510.42 316.86 l 510.9 317.4 l 511.5 317.88 l 510.9 318.42 l 511.2 317.7 l 511.68 317.88 l 512.16 318.18 l 512.7 318.36 l 513.42 318.66 l 514.38 318.9 l 515.4 319.26 l 515.16 319.26 l 515.16 320.16 l 514.92 319.26 l 515.82 319.08 l 516.84 318.84 l 519.18 318.18 l 521.7 317.16 l 524.22 316.02 l 526.68 314.58 l 526.92 315.42 l 526.38 314.76 l 527.52 314.16 l 528.48 313.32 l 529.38 312.42 l 530.04 311.58 l 530.7 312.24 l 529.86 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[(yt)-1226(f)-336(u)-4(t)-371(u)-4(t)-1426(u)-1034(t)-1556(y)5(t)-491(yt)-1551(y)-900(t)]TJ /C2_0 1 Tf 0 Tc 1.72 -0.0003 Td <0020>Tj /C2_1 1 Tf 6.632 Tc 4.015 0.045 Td [<00050005>5120<0005>6745<0005>]TJ /TT0 1 Tf 0.0007 Tc 13.0826 Tw 9 0 0 9 54 675.6003 Tm [( )1920(\(1.6\) )]TJ 0.0013 Tc 0.4087 Tw 0 -1.62 TD [(Notice that Equation 1.6 is a feedback model of the )7(ty)-12(pe )]TJ 0.0009 Tc 0.1091 Tw 0 -1.1733 TD [(represented by)-12( Equation 1.3. )7(N)]TJ 0.0016 Tc 0.1017 Tw 12.9133 0 Td [(LTS)4( m)6(odels)4( therefore can handle )]TJ -0.0006 Tc 0.7306 Tw -12.9133 -1.1733 Td [(sy)-14(ste)-3(m)4(s with me)-3(mory)-14(.)-4( Equa)-3(ti)]TJ 0.001 Tc 0.7223 Tw 14.1067 0 Td [(on )-7(1.6 essentially)-12( defines, )]TJ 0.0015 Tc 0.2818 Tw -14.1067 -1.1733 Td [(im)6(plicitly)-12(, )-7(a nonlinear differential equation for the behavioral )]TJ 0.0013 Tc 0.502 Tw T* [(m)6(odel. )-7(The )-7(function f is defined by)-12( suitable m)6(u)1(ltivariate )]TJ 0.001 Tc 0.2957 Tw T* [(approxim)6(a)-2(tion 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Multivariate poly)-12(nom)6(ials, radial basis )]TJ 0.0013 Tc 0.1554 Tw T* [(functions,)-2( and artificial neural )]TJ 0.0001 Tc 0.1566 Tw 12.9667 0 Td [(networks have been used.)-3( ANNs )]TJ 0.0012 Tc 0.0888 Tw -12.9667 -1.1733 Td [(generally)-12( give the best )7(results, )7(due)]TJ 0.0009 Tc 0.0824 Tw 14.3133 0 Td [( to their asy)-12(m)5(ptotic properties )]TJ 0.0011 Tc 0.2822 Tw -14.3133 -1.1733 Td [(and becaus)4(e)-2( they)-12( give very)-12( )7(s)4(m)6(ooth )7(res)4(u)1(lts)4( )7(for )7(approxim)6(a)-2(ting )]TJ 0.0007 Tc 0.016 Tw T* (discrete measured and simulated )Tj 0.0008 Tc 13.36 0 Td [(data. In [10])7( and )7([11])7(, )7(MATLAB )]TJ 0.0007 Tc 0.0493 Tw -13.36 -1.1733 Td [(was )-7(used )-7(to train the ANN functions which were then attached to )]TJ 0.002 Tc 0 Tw T* (the )Tj /TT1 1 Tf 0.0016 Tc 0.0017 Tw 1.48 0 Td (Agilent ADS)Tj /TT0 1 Tf 0.0009 Tc 0.0024 Tw 4.9867 0 Td [( simulator by)-12( custom code. )]TJ 0.0005 Tc 0.0095 Tw -6.4667 -1.62 Td (NLTS models have been construc)Tj 0.0006 Tc 0.0027 Tw 13.6067 0 Td [(ted )-7(from )-7(simulated data and also )]TJ 0.0014 Tc 0.0219 Tw -13.6067 -1.1733 Td [(from)6( )-7(s)4(t)-1(ate-of-the-art nonlinear m)6(eas)4(urem)6(ent s)4(y)-12(s)4(t)-1(em)6(s)4( of the vector )]TJ 0.0005 Tc 0.0028 Tw T* [(nonlinear network analy)-13(zer \(VNNA\) ty)-13(pe [17].)-3( )]TJ /TT2 1 Tf 0.0012 Tc 0.2755 Tw 0 -35.48 TD [(Figu)4(re 3 Non)4(lin)4(ear Netw)-10(ork)4( meas)4(u)4(remen)4(ts)4(: \(a\) in)4(cid)4(e)-2(n)4(t)1( )]TJ -0.0009 Tc 0.6242 Tw 0 -1.1733 TD [(w)-12(ave)-4(s at a single)-4( fr)-4(e)-4(que)-4(nc)-4(y)-8( sc)-4(atte)-4(r)-4( fundame)-4(ntal )7(and )]TJ 0.1976 Tw T* [(har)-4(m)-1(onic)-4( fr)-4(e)-4(que)-4(nc)-4(ie)-4(s.)-4( \(b\) by)-8( apply)-8(i)-3(ng tw)-12(o offse)-4(t)-1( tone)-4(s )7(at )]TJ 0.0004 Tc 0.1096 Tw T* [(ports 1 & 2 a large volume of the device signal space )7(can )7(be )]TJ 0.0019 Tc 0.0014 Tw T* [(covered)5( in)5( a s)4(in)5(g)2(le meas)4(u)5(remen)5(t. )]TJ 0.0004 Tc -0.0004 Tw 12 0 0 12 54 128.16 Tm [(3.3 )-350(Comparison betw)8(een methods )]TJ /TT0 1 Tf 0.0008 Tc 0.0225 Tw 9 0 0 9 54 117.1803 Tm [(The NLTS methodology)-12( can be cons)]TJ 0.0006 Tc 0.0161 Tw 14.8933 0 Td (idered a superset of the DNN )Tj 0.0005 Tc 0.0295 Tw -14.8933 -1.1733 Td [(approach.)-3( Up to this point,)-3( the work )7(on )7(DNNs )7(has )7(been )7(limited )7(to )]TJ 0.0009 Tc 0.0091 Tw T* [(static models [9])7(,)-2( although there )]TJ 0.0007 Tc 0.0093 Tw 13.2333 0 Td (is nothing fundamental about this )Tj 0.0008 Tc 0.4425 Tw -13.2333 -1.1733 Td (restriction. Moreover, NLTS ha)Tj 0.0014 Tc 0.4353 Tw 14.0467 0 Td [(s)4( )-7(as)4(s)4(o)1(ciated algorithm)6(s)4( with )]TJ 0.0005 Tc 0.2895 Tw -14.0467 -1.1733 Td [(which )-7(to define, more sy)-13(stema)]TJ 0.0019 Tc 0.2881 Tw 13.44 0 Td [(tically)-11(, the choice of variables)4( )]TJ 0.0006 Tc 0.3561 Tw 15.88 70.74 Td [(\(how many)-13( time derivatives of )]TJ 0.0011 Tc 0.3489 Tw 14.3267 0 Td (the variables to use for the )Tj 0.0015 Tc 0.1618 Tw -14.3267 -1.1733 Td [(em)6(bedding\). )-7(The )-7(notion of phas)4(e)-1( s)4(p)2(ace dens)4(ity)-12(, inherent in the )]TJ 0.6084 Tw T* [(nonlinear tim)6(e s)4(e)-1(ries)4( approach, is)4( a )7(way)-12( )7(to )7(gauge )7(the )]TJ 0.0011 Tc 0.5689 Tw T* [(com)6(p)1(leteness )-7(of )-7(the excitations with im)6(plications for the )]TJ 0.0008 Tc 0.3759 Tw T* [(transportability)-12( of the m)5(odel. While sy)-12(stem)5(s with )7(long-term)5( )]TJ 0.0004 Tc 0.0629 Tw T* [(memory)-13( can be modeled )7(with )7(Equa)]TJ 0.0006 Tc 0.0561 Tw 14.52 0 Td (tion 1.6, the process of NLTS )Tj 0.0012 Tc 0.5421 Tw -14.52 -1.1733 Td [(m)6(odel identification can get cum)6(b)1(ersom)6(e)-2( if )7(the )7(problem)6(s )]TJ 0.0015 Tc 0.0085 Tw T* [(cons)4(idered have tim)6(e-s)4(cales)4( of )7(ve)]TJ 0.0011 Tc 0.0022 Tw 13.5533 0 Td [(ry)-12( different orders of magnitude. )]TJ 0.0007 Tc 0.0026 Tw -13.5533 -1.1733 Td (A new technique is proposed to ame)Tj 0.0015 Tc 0.0018 Tw 14.5867 0 Td [(liorate this difficulty)-12( in [18])8(. )]TJ /TT2 1 Tf -0.0009 Tc 0.0009 Tw 12 0 0 12 317.88 607.5 Tm [(4. )-350(FREQUENCY DOMAIN TECHNIQUES )]TJ /TT0 1 Tf 0.0011 Tc 0.1889 Tw 9 0 0 9 317.88 596.5203 Tm [(Traditionally)-12(, microwave modeling techniques in the )7(frequency)-12( )]TJ 0.0008 Tc 0.4092 Tw T* [(domain )-7(have been limited to )]TJ 0.0009 Tc 0.4091 Tw 13.7133 0 Td (narrow-band models, that are )Tj 0 Tc 0.05 Tw -13.7133 -1.1733 Td [(described as memory)-13(less or quasi)]TJ 0.0001 Tc 0.0432 Tw 13.66 0 Td [(-memory)-13(l)-2(ess \(high frequency)-13( or )]TJ 0.0005 Tc 0.0962 Tw -13.66 -1.1733 Td [(short-term memory)-13(\). These te)]TJ 0.0003 Tc 0.0897 Tw 12.2533 0 Td [(rms )-7(correspond to the narrow-band )]TJ 0.0011 Tc 0.3489 Tw -12.2533 -1.1733 Td [(AM)4( to AM)4( and AM)4( to P)4(M)4( )7(characteris)4(tics)4( )7(of )7(the )7(s)4(y)-12(s)4(t)-1(em)6(, )]TJ 0.0004 Tc 0.4496 Tw T* [(respectively)-13(.)-3( Such modeling me)]TJ 0.001 Tc 0.4423 Tw 14.2133 0 Td [(thods )-7(have been applied to )]TJ 0.129 Tw -14.2133 -1.1733 Td [(wireless power am)6(plifiers. Excitation designs are usually)-12( sim)6(p)1(le )]TJ 0.0005 Tc 0.3362 Tw T* (single-tone measurements of th)Tj 0.0016 Tc 0.3351 Tw 13.5467 0 Td [(e am)6(plifier, and the )7(m)6(odel )7(is )]TJ 0.0009 Tc 0.3624 Tw -13.5467 -1.1733 Td [(identified by)-12( fitting odd-order poly)-12(nom)5(ial functions )7(to )7(these )]TJ 0.002 Tc 0 Tw T* [(characteris)5(tics)5(.)-1( )]TJ 0.0005 Tc 0.1628 Tw 0 -1.62 TD [(Several )-7(extensions to such mode)]TJ 0.0006 Tc 0.1627 Tw 13.7267 0 Td [(ls to account for ')-6(l)-2(ong-term')-6( or )]TJ 0.0004 Tc 0.2763 Tw -13.7267 -1.1733 Td [(low-frequency)-13( memory)-13( effects ha)]TJ 0.0006 Tc 0.2694 Tw 14.3933 0 Td [(ve )-7(been proposed in [19,20])7( )]TJ 0.0008 Tc 0.0159 Tw -14.3933 -1.1733 Td [(based )-7(on Wiener-Volterra theory)-12(, though mostly)-12( these approaches )]TJ 0.001 Tc 0.0023 Tw 0 -1.1733 TD [(rem)6(a)-2(in lim)6(ited to narrow-band sy)-12(stem)6(s and weak nonlinearities. )]TJ 0.1423 Tw 0 -1.62 TD [(An extension to the Volterra technique [21])7( allows the )7(Volterra )]TJ 0.0008 Tc 0.5025 Tw 0 -1.1733 TD [(kernels in the nonlinear frequency)-12( domain solution to )7(be )]TJ 0.0016 Tc 0.0751 Tw T* [(calculated as)4( a function of the )7(in)]TJ 0.0011 Tc 0.0689 Tw 13.4867 0 Td (stantaneous envelope amplitude. )Tj 0.0014 Tc 0.2686 Tw -13.4867 -1.1733 Td [(The kernel functions)4( them)6(s)4(e)-1(lves)4( are calculated from)6( two-tone )]TJ 0.0005 Tc 0.0028 Tw T* [(measurements )-7(using a single fixed )]TJ 0.0012 Tc 0.0021 Tw 14.06 0 Td (carrier tone and a second swept )Tj 0.3287 Tw -14.06 -1.1733 Td [(tone to describe the kernel as a function )7(of )7(the )7(distance )7(in )]TJ 0.0007 Tc 0.2426 Tw T* [(frequency)-13( )-7(from the carrier. Good results for power amplifier )]TJ 0.001 Tc 0.809 Tw T* [(m)6(odeling )-7(across )-7(a m)6(u)1(lti-channel bandwidth have been )]TJ 0.0009 Tc 0.0024 Tw T* (demonstrated. )Tj 0.0013 Tc 0.042 Tw 0 -1.62 TD [(An attem)6(p)1(t to incorporate this )]TJ 0.0421 Tw 12.4867 0 Td [(nonlinear m)6(odeling into a )7(transient )]TJ 0.0011 Tc 0.3422 Tw -12.4867 -1.1733 Td [(sim)6(u)1(lator has been dem)6(onstrated in [22])7(. Here the )7(am)6(plifier )]TJ 0.0008 Tc 0.1759 Tw 0 -1.1733 TD [(model itself computes )7(the )7(narro)]TJ 0.0009 Tc 0.1691 Tw 13.3733 0 Td (w-band spectral response to the )Tj 0.001 Tc 0.149 Tw -13.3733 -1.1733 Td [(tim)6(e-dom)6(ain m)6(odulated input. This approach is )7(successful )7(for )7(a )]TJ 0.0014 Tc 0.0553 Tw T* [(single )-7(com)6(ponent )-7(instance, )-7(but )-7(m)6(a)-1(y)-12( be difficult to scale to m)6(u)1(lti-)]TJ 0 Tc 0.6767 Tw T* [(component sy)-13(stem simulation,)]TJ 0.0007 Tc 0.6693 Tw 13.5667 0 Td [( )-7(where it would be more )]TJ 0.001 Tc 0.3223 Tw -13.5667 -1.1733 Td (appropriate to perform the simulation in a harmonic balance )Tj 0.0009 Tc 0.0024 Tw T* [(sim)5(u)1(lator )]TJ /TT2 1 Tf 0.0003 Tc 0.3497 Tw 12 0 0 12 317.88 248.04 Tm [(4.1 Describing )350(Functions )]TJ /TT0 1 Tf 0.0011 Tc 0.3556 Tw 9 0 0 9 317.88 237.0603 Tm [(The describing function technique is )7(an )7(inherently)-12( )7(nonlinear )]TJ 0.0007 Tc 0.196 Tw T* (formulation based in the freque)Tj 0.0008 Tc 0.1959 Tw 13.36 0 Td [(ncy)-12( domain [23])7(. The )7(model )7(is )]TJ 0.1692 Tw -13.36 -1.1733 Td [(based )-7(on the assumption of a harmonic balance solution of the )]TJ 0.0013 Tc 0.0087 Tw T* [(circuit equations, which )7(can )7(therefor)]TJ 0.001 Tc 0.0023 Tw 14.7 0 Td (e be written as Fourier Series )Tj 0.0009 Tc 0.1824 Tw -14.7 -1.1733 Td [(according to Equations)3( 1.7 )7(and )7(1.)]TJ 0.0014 Tc 0.1753 Tw 14.3467 0 Td [(8. The expans)4(ion coefficients)4( )]TJ 0.0007 Tc 0.016 Tw -14.3467 -1.1733 Td (are complex number representing )Tj 0.0093 Tw 13.74 0 Td (the harmonic components of the )Tj 0.0011 Tc 0 Tw -13.74 -1.1733 Td (signal. )Tj 0 Tc 0 -2.1333 TD ( )Tj 0.0004 Tc 12 0 0 12 385.32 154.5 Tm [(\()-337(\))-1012(Re)-2346(exp\()-1847(\))]TJ /TT1 1 Tf 5.5049 Tc 7.02 0 0 7.02 444.6 151.4999 Tm (kk)Tj 0 Tc -2.2222 -1.2051 Td (k)Tj 0.4842 Tc 12 0 0 12 376.08 154.5036 Tm [(Vt)-3273(V)-2000(j)-528(t)]TJ /C2_0 1 Tf 0 Tc 12 0 3.899 12 477.5995 154.5 Tm <005A>Tj 12 0 0 12 400.08 154.5 Tm <0020>Tj 18 0 0 18 424.38 151.743 Tm <00A6>Tj /TT0 1 Tf 0.0007 Tc 4.216 Tw 9 0 0 9 500.4 154.5003 Tm ( \(1.7\) )Tj 0 Tc 0 Tw -20.28 -3.4467 Td ( )Tj 0.0012 Tc 12 0 0 12 384.54 123.54 Tm [(\()-336(\))-1011(Re)-2285(e)10(xp\()-1846(\))]TJ /TT1 1 Tf 5.5049 Tc 7.02 0 0 7.02 443.1 120.4799 Tm (kk)Tj 0 Tc -2.1197 -1.1966 Td (k)Tj 0.447 Tc 12 0 0 12 379.08 123.4836 Tm [(It)-3440(I)-2125(j)-565(t)]TJ /C2_0 1 Tf 0 Tc 12 0 3.899 12 476.0995 123.48 Tm <005A>Tj 12 0 0 12 399.36 123.48 Tm <0020>Tj 18 0 0 18 423.66 120.783 Tm <00A6>Tj /TT0 1 Tf 0.0007 Tc 4.3826 Tw 9 0 0 9 498.9 123.4803 Tm ( \(1.8\) )Tj 0.2961 Tw -20.1133 -2.9333 Td (A describing function model can )Tj 0.0009 Tc 0.2958 Tw 14.86 0 Td [(be defined by)-12( the )7(complex )]TJ 0.001 Tc 0.009 Tw -14.86 -1.1733 Td [(mapping relating )7(the )]TJ /TT1 1 Tf 0 Tc 0 Tw 8.56 0 Td (I)Tj 6 0 0 6 397.92 85.02 Tm (k)Tj /TT0 1 Tf 0.001 Tc 0.0023 Tw 9 0 0 9 400.56 86.5203 Tm (s as nonlinear functions of the )Tj /TT1 1 Tf 0 Tc 0 Tw 12.3133 0 Td (V)Tj 6 0 0 6 516.9 85.02 Tm (k)Tj /TT0 1 Tf 0.0013 Tc 0.002 Tw 9 0 0 9 519.54 86.5203 Tm [(s. Usually)-12(, )]TJ 0.001 Tc 0.389 Tw -22.4067 -1.1733 Td [(however, )-7(a )-7(change )-7(of variables is done and the describing )]TJ ET 1 1 1 scn /CS0 CS 0 0 0 SCN 0.72 w 10 M 0 j 0 J []0 d 50.4 489.6 237.96 -284.04 re B 0.54 w 58.32 485.28 222.18 -275.7 re B 0.988 0.004 0.157 scn 82.8 445.62 m 81.54 445.86 l 81.72 445.86 l 81.72 446.16 l 81.96 446.16 l 81.96 446.34 l 82.14 446.34 l 82.14 446.64 l 82.32 446.64 l 82.32 446.82 l 82.98 446.82 l 82.98 447.12 l 84.3 447.12 l 84.3 446.82 l 84.9 446.82 l 84.9 446.64 l 85.14 446.64 l 85.14 446.34 l 85.38 446.34 l 85.38 444.72 l 85.14 444.72 l 85.14 443.52 l 84.9 443.52 l 84.9 442.32 l 85.14 442.32 l 83.82 442.32 l 83.82 442.86 l 83.64 442.86 l 83.64 442.56 l 83.46 442.56 l 83.46 442.32 l 82.8 442.32 l 82.8 442.14 l 81.96 442.14 l 81.96 442.32 l 81.54 442.32 l 81.54 442.56 l 81.3 442.56 l 81.3 443.04 l 81.06 443.04 l 81.06 444.06 l 81.3 444.24 l 81.3 444.42 l 81.54 444.42 l 81.54 444.72 l 81.96 444.72 l 81.96 444.96 l 82.8 444.96 l 82.8 445.14 l 84.12 445.14 l 84.12 444.42 l 83.64 444.42 l 83.64 444.24 l 82.8 444.24 l 82.62 444.06 l 82.32 444.06 l 82.32 443.52 l 82.14 443.52 l 82.32 443.34 l 82.32 443.16 l 83.46 443.16 l 83.46 443.34 l 83.64 443.34 l 83.64 443.52 l 83.82 443.52 l 83.82 444.24 l 84.12 444.42 l 84.12 445.32 l 84.3 445.32 l 84.3 445.86 l 84.12 445.86 l 84.12 445.92 l 83.82 445.92 l 83.82 446.16 l 83.46 446.16 l 83.46 445.92 l 82.98 445.92 l 82.98 445.86 l 82.8 445.86 l 82.8 445.62 l f* 87.24 442.02 m 87.42 442.74 l 87.66 442.74 l 87.66 443.04 l 88.02 443.04 l 88.02 443.22 l 88.38 443.22 l 88.38 443.46 l 88.56 443.46 l 88.56 443.64 l 88.8 443.64 l 88.8 443.94 l 89.34 443.94 l 88.56 439.44 l 87.84 439.44 l 88.38 442.44 l 88.02 442.44 l 88.02 442.26 l 87.66 442.26 l 87.42 442.02 l 87.24 442.02 l f* 0.988 0.004 0.157 SCN 0.78 w 1 j 1 J 82.5 437.04 m 92.4 437.04 l S 95.58 437.34 m 91.32 439.74 l 95.58 437.34 l 91.32 435.06 l 91.32 439.74 l 95.58 437.34 l f* 103.5 458.22 m 103.5 475.32 l S 103.5 479.28 m 101.04 475.38 l 103.5 479.28 l 105.84 475.38 l 101.04 475.38 l 103.5 479.28 l f* 112.62 467.1 m 112.62 467.52 l 111.36 469.98 l 110.34 467.52 l 112.62 467.52 l 112.62 467.1 l 110.34 467.1 l 109.86 466.32 l 109.56 466.08 l 109.56 465.6 l 109.86 465.6 l 109.86 465.42 l 110.34 465.42 l 110.34 465.12 l 108.42 465.12 l 108.42 465.42 l 108.78 465.42 l 108.78 465.6 l 109.08 465.84 l 109.08 466.08 l 109.38 466.08 l 109.38 466.5 l 111.54 471.42 l 113.82 466.32 l 114 466.08 l 114 465.84 l 114.3 465.84 l 114.3 465.6 l 114.6 465.6 l 114.6 465.42 l 115.08 465.42 l 115.08 465.12 l 112.62 465.12 l 112.62 465.42 l 112.98 465.42 l 112.98 465.6 l 113.28 465.6 l 113.28 466.08 l 112.98 466.08 l 112.98 466.32 l 112.62 467.1 l f* 120.12 463.5 m 120.12 463.74 l 120.18 463.74 l 120.18 463.8 l 120.36 463.8 l 120.36 464.04 l 120.54 464.22 l 120.54 464.82 l 120.12 464.82 l 120.12 465.3 l 120.18 465.3 l 120.18 465.54 l 120.78 465.54 l 120.78 465.12 l 120.84 465.12 l 120.84 464.22 l 120.78 464.22 l 120.78 464.04 l 120.54 464.04 l 120.54 463.8 l 120.36 463.8 l 120.36 463.74 l 120.18 463.74 l 120.18 463.5 l 120.12 463.5 l f* 124.74 469.38 m 125.34 469.38 l 125.34 469.2 l 125.76 469.2 l 125.76 468.9 l 126 468.9 l 126 468.72 l 126.18 468.72 l 126.18 468.18 l 126.36 468.18 l 126.36 467.52 l 126.54 467.52 l 126.54 466.8 l 126.36 466.8 l 126.36 466.2 l 126.18 466.2 l 126.18 465.72 l 126 465.72 l 126 465.54 l 125.76 465.54 l 125.76 465.24 l 125.58 465.24 l 125.58 465 l 124.74 465 l 124.74 465.24 l 125.1 465.24 l 125.1 465.54 l 125.34 465.54 l 125.34 465.72 l 125.58 465.72 l 125.58 466.2 l 125.76 466.2 l 125.76 468 l 125.58 468 l 125.58 468.72 l 125.34 468.72 l 125.34 468.9 l 125.1 468.9 l 125.1 469.2 l 124.74 469.2 l 124.74 463.02 l 124.26 463.02 l 124.26 465 l 123.6 465 l 123.42 465.24 l 123.24 465.24 l 123.24 465.54 l 123.06 465.54 l 123.06 465.72 l 122.76 465.72 l 122.76 466.2 l 122.58 466.2 l 122.58 468.18 l 122.76 468.18 l 122.76 468.72 l 123.06 468.72 l 123.06 468.9 l 123.24 468.9 l 123.24 469.2 l 123.6 469.2 l 123.6 469.38 l 124.26 469.38 l 124.26 469.2 l 123.78 469.2 l 123.78 468.9 l 123.6 468.9 l 123.6 468.72 l 123.42 468.48 l 123.42 467.7 l 123.24 467.7 l 123.24 466.8 l 123.42 466.68 l 123.42 466.02 l 123.6 466.02 l 123.6 465.54 l 123.78 465.54 l 123.78 465.24 l 124.26 465.24 l 124.26 471.72 l 124.74 471.72 l 124.74 469.38 l f* 116.76 466.08 m 117.36 466.38 l 117.54 466.38 l 117.54 462.42 l 117.84 462.42 l 117.84 462.24 l 116.76 462.24 l 116.76 462.42 l 117.06 462.42 l 117.06 466.08 l 116.76 466.08 l 116.76 465.84 l 116.76 466.08 l f* 128.34 466.08 m 129.12 466.38 l 129.3 466.38 l 129.3 462.42 l 129.6 462.42 l 129.6 462.24 l 128.52 462.24 l 128.52 462.42 l 128.82 462.42 l 128.82 466.08 l 128.52 466.08 l 128.52 465.84 l 128.34 466.08 l f* 88.98 458.4 m 131.58 458.4 l S 103.5 455.04 m 103.5 454.74 l 102.84 454.74 l 102.36 452.7 l 102.36 452.34 l 102.06 452.34 l 102.06 451.62 l 101.94 451.62 l 101.94 451.02 l 101.76 451.02 l 101.76 450.54 l 101.46 450.54 l 101.46 450.06 l 101.28 450.06 l 101.28 449.82 l 101.04 449.52 l 101.04 449.34 l 100.8 449.34 l 100.62 449.16 l 100.38 449.16 l 100.38 448.86 l 99.42 448.86 l 99.42 449.16 l 99.3 449.16 l 99.3 449.52 l 99.42 449.52 l 99.42 449.82 l 99.6 449.82 l 99.6 449.52 l 99.9 449.52 l 99.9 449.34 l 99.6 449.34 l 99.6 449.16 l 100.38 449.16 l 100.38 449.34 l 100.62 449.34 l 100.62 449.52 l 100.8 449.52 l 100.8 450.06 l 101.04 450.06 l 101.04 450.72 l 101.28 450.72 l 101.28 451.62 l 102.06 454.74 l 101.28 454.74 l 101.46 455.04 l 102.06 455.04 l 102.06 455.22 l 102.36 455.22 l 102.36 455.7 l 102.6 455.7 l 102.6 456.24 l 102.84 456.24 l 102.84 456.6 l 103.08 456.6 l 103.08 456.9 l 103.32 456.9 l 103.32 457.14 l 103.5 457.14 l 103.5 457.2 l 103.98 457.2 l 103.98 457.44 l 104.82 457.44 l 104.82 457.2 l 105 457.2 l 105 457.14 l 105.3 457.14 l 105.3 456.6 l 104.7 456.6 l 104.7 457.2 l 103.98 457.2 l 103.98 457.14 l 103.74 457.14 l 103.74 456.9 l 103.5 456.9 l 103.5 456.42 l 103.32 456.42 l 103.32 455.7 l 103.08 455.7 l 103.08 455.04 l 102.84 455.04 l 103.5 455.04 l f* 106.02 452.46 m 106.02 452.22 l 105.6 452.22 l 105.6 452.04 l 105.36 452.04 l 105.36 451.56 l 105.18 451.56 l 105.18 451.14 l 105.12 451.14 l 105.12 450.36 l 104.88 450.36 l 104.88 448.32 l 105.6 448.32 l 105.6 448.86 l 105.84 448.86 l 105.84 449.22 l 106.02 449.22 l 106.02 449.76 l 106.26 449.94 l 106.26 450.84 l 106.44 450.84 l 106.44 452.04 l 106.26 452.04 l 106.26 452.22 l 106.02 452.22 l 106.02 452.46 l 106.44 452.46 l 106.44 452.22 l 106.62 452.22 l 106.62 451.86 l 106.92 451.86 l 106.92 450.12 l 106.62 450.12 l 106.62 449.46 l 106.44 449.46 l 106.44 449.04 l 106.26 449.04 l 106.26 448.86 l 106.02 448.86 l 106.02 448.56 l 105.84 448.56 l 105.84 448.32 l 105.6 448.32 l 105.6 448.26 l 104.88 448.26 l 104.88 448.32 l 104.64 448.32 l 104.64 448.56 l 104.46 448.56 l 104.46 449.22 l 104.22 449.22 l 104.22 449.94 l 104.46 449.94 l 104.46 450.84 l 104.64 450.84 l 104.64 451.32 l 104.88 451.32 l 104.88 451.56 l 105.12 451.86 l 105.12 452.04 l 105.18 452.04 l 105.18 452.22 l 105.6 452.22 l 105.6 452.46 l 106.02 452.46 l f* 0 1 0 scn 82.68 412.8 m 83.94 419.28 l 85.38 419.28 l 84.9 417.06 l 84.9 417.36 l 85.38 417.36 l 85.38 417.6 l 85.92 417.6 l 85.92 417.78 l 86.4 417.78 l 86.4 417.6 l 86.94 417.6 l 86.94 417.36 l 87.24 417.36 l 87.24 417.06 l 87.42 417.06 l 87.42 416.7 l 87.72 416.7 l 87.72 414.48 l 87.42 414.48 l 87.42 414.06 l 87.24 414.06 l 87.24 413.58 l 86.94 413.58 l 86.94 413.4 l 86.76 413.4 l 86.76 413.1 l 86.1 413.1 l 86.1 412.8 l 84.9 412.8 l 84.9 413.1 l 84.42 413.1 l 84.42 414.78 l 84.42 414.06 l 84.6 414.06 l 84.6 413.76 l 85.08 413.76 l 85.08 413.58 l 85.56 413.58 l 85.56 413.76 l 85.92 413.76 l 85.92 414.06 l 86.1 414.06 l 86.1 414.48 l 86.4 414.48 l 86.4 415.2 l 86.58 415.2 l 86.58 415.98 l 86.4 415.98 l 86.4 416.4 l 86.1 416.4 l 86.1 416.7 l 85.08 416.7 l 85.08 416.4 l 84.9 416.4 l 84.9 416.28 l 84.6 416.28 l 84.6 415.86 l 84.42 415.86 l 84.42 413.1 l 84.12 413.1 l 84.12 413.4 l 83.94 413.4 l 83.94 413.58 l 83.76 412.8 l 82.68 412.8 l f* 89.22 412.68 m 89.46 413.22 l 89.46 413.4 l 89.88 413.4 l 89.88 413.7 l 90.3 413.7 l 90.3 413.88 l 90.48 413.88 l 90.78 414.06 l 90.96 414.06 l 90.96 414.3 l 91.14 414.3 l 91.14 414.48 l 91.62 414.48 l 90.78 409.98 l 89.88 409.98 l 90.48 412.98 l 90.3 412.98 l 90.3 412.8 l 89.88 412.8 l 89.7 412.68 l 89.22 412.68 l f* 82.14 424.26 m 86.22 426.66 l 82.14 424.26 l 86.22 421.98 l 86.22 426.66 l 82.14 424.26 l f* 0 1 0 SCN 86.1 423.96 m 96 423.96 l 101.46 387.84 m 101.46 402.9 l S 101.4 407.28 m 98.76 403.02 l 101.4 407.28 l 103.56 403.02 l 98.76 403.02 l 101.4 407.28 l f* 112.98 388.14 m 112.98 394.2 l S 112.68 398.22 m 110.22 394.32 l 112.68 398.22 l 115.14 394.32 l 110.22 394.32 l 112.68 398.22 l f* 123.6 388.14 m 123.6 392.1 l S 123.3 396.3 m 120.84 392.1 l 123.3 396.3 l 125.7 392.1 l 120.84 392.1 l 123.3 396.3 l f* 87.84 388.32 m 130.44 388.32 l S 102.36 384.84 m 102.36 384.66 l 101.58 384.66 l 101.22 382.56 l 101.22 382.44 l 100.92 382.14 l 100.92 381.42 l 100.74 381.42 l 100.74 380.76 l 100.56 380.76 l 100.56 380.22 l 100.38 380.22 l 100.38 379.86 l 100.14 379.86 l 100.14 379.56 l 99.9 379.56 l 99.9 379.44 l 99.42 378.96 l 99.12 378.96 l 99.12 378.72 l 98.28 378.72 l 98.28 378.96 l 97.98 378.96 l 97.98 379.44 l 98.28 379.44 l 98.28 379.56 l 98.46 379.56 l 98.46 379.44 l 98.76 379.44 l 98.76 379.14 l 98.46 379.14 l 98.46 378.96 l 99.12 378.96 l 99.12 379.14 l 99.42 379.14 l 99.42 379.44 l 99.6 379.44 l 99.6 379.86 l 99.9 379.86 l 99.9 380.76 l 100.14 380.76 l 100.14 381.42 l 100.92 384.66 l 100.14 384.66 l 100.38 384.84 l 100.92 384.84 l 100.92 385.14 l 101.22 385.14 l 101.22 385.44 l 101.4 385.44 l 101.4 385.92 l 101.58 385.92 l 101.58 386.34 l 101.88 386.34 l 101.88 386.64 l 102.06 386.64 l 102.06 386.82 l 102.36 386.82 l 102.36 387 l 102.84 387 l 102.84 387.3 l 103.68 387.3 l 103.68 387 l 103.86 387 l 103.86 386.82 l 104.04 386.82 l 104.04 386.64 l 103.86 386.64 l 103.86 386.34 l 103.38 386.34 l 103.38 387 l 102.84 387 l 102.84 386.82 l 102.6 386.82 l 102.6 386.64 l 102.36 386.64 l 102.36 386.16 l 102.06 386.16 l 102.06 385.44 l 101.88 385.44 l 101.88 384.84 l 101.58 384.84 l 102.36 384.84 l f* 104.82 382.14 m 104.82 382.02 l 104.46 382.02 l 104.46 381.84 l 104.22 381.84 l 104.22 381.42 l 103.98 381.42 l 103.98 380.94 l 103.74 380.94 l 103.74 380.04 l 103.68 380.04 l 103.68 378.12 l 104.22 378.12 l 104.46 378.42 l 104.46 378.66 l 104.64 378.66 l 104.64 379.02 l 104.82 379.02 l 104.82 379.62 l 105 379.62 l 105 380.52 l 105.3 380.52 l 105.3 381.84 l 105 381.84 l 105 382.02 l 104.82 382.02 l 104.82 382.14 l 105.3 382.14 l 105.3 382.02 l 105.48 382.02 l 105.48 381.66 l 105.66 381.66 l 105.66 379.86 l 105.48 379.86 l 105.48 379.32 l 105.3 379.32 l 105.3 378.84 l 105 378.84 l 105 378.66 l 104.82 378.66 l 104.82 378.42 l 104.64 378.42 l 104.64 378.12 l 104.46 378.12 l 104.46 377.94 l 103.68 377.94 l 103.68 378.12 l 103.5 378.12 l 103.5 378.42 l 103.2 378.42 l 103.2 378.84 l 103.02 378.84 l 103.02 379.62 l 103.2 379.86 l 103.2 380.52 l 103.5 380.76 l 103.5 381.12 l 103.68 381.12 l 103.68 381.42 l 103.74 381.66 l 103.74 381.84 l 103.98 381.84 l 103.98 382.02 l 104.22 382.02 l 104.46 382.14 l 104.82 382.14 l f* 247.74 407.22 m 249.06 413.88 l 250.5 413.88 l 250.02 411.6 l 250.2 411.78 l 250.5 411.78 l 250.68 412.08 l 251.76 412.08 l 251.94 411.78 l 252.12 411.78 l 252.12 411.6 l 252.42 411.6 l 252.42 411.42 l 252.6 411.42 l 252.6 411 l 252.9 411 l 252.9 409.08 l 252.6 409.08 l 252.6 408.42 l 252.42 408.42 l 252.42 408.12 l 252.12 408.12 l 252.12 407.88 l 251.94 407.88 l 251.94 407.58 l 251.76 407.58 l 251.76 407.4 l 251.46 407.4 l 251.28 407.22 l 250.68 407.22 l 250.68 406.92 l 250.5 406.92 l 250.2 407.22 l 249.54 407.22 l 249.54 407.4 l 249.24 407.4 l 249.24 407.58 l 249.06 407.58 l 249.06 408.12 l 249.24 409.08 l 249.24 408.9 l 249.54 408.72 l 249.54 408.18 l 249.72 408.18 l 250.02 408.12 l 250.86 408.12 l 250.86 408.18 l 251.04 408.18 l 251.04 408.42 l 251.28 408.42 l 251.28 408.9 l 251.46 408.9 l 251.46 410.82 l 251.28 410.82 l 251.28 411 l 251.04 411 l 251.04 411.18 l 250.5 411.18 l 250.5 411 l 250.02 411 l 250.02 410.82 l 249.72 410.82 l 249.72 410.28 l 249.54 410.28 l 249.54 409.62 l 249.24 409.62 l 249.24 409.08 l 249.06 408.12 l 248.82 407.22 l 247.74 407.22 l f* 255.12 407.52 m 254.28 407.52 l 254.28 407.82 l 254.46 407.82 l 254.46 408.18 l 254.76 408.18 l 254.76 408.42 l 254.94 408.42 l 255.12 408.72 l 256.5 408.72 l 256.5 408.42 l 256.74 408.42 l 256.74 408 l 256.98 408 l 256.98 406.98 l 256.74 406.98 l 256.74 406.62 l 256.68 406.62 l 256.68 406.32 l 256.5 406.32 l 256.5 406.2 l 256.26 406.2 l 256.26 405.9 l 256.02 405.9 l 256.02 405.72 l 255.84 405.72 l 255.84 405.48 l 255.6 405.48 l 255.6 405.3 l 255.36 405.3 l 255.36 405 l 255.12 405 l 256.74 405 l 256.68 404.28 l 253.92 404.28 l 253.92 404.7 l 254.1 404.7 l 254.1 405 l 254.28 405 l 254.28 405.3 l 254.46 405.3 l 254.46 405.48 l 254.76 405.72 l 254.94 405.9 l 255.12 406.2 l 255.36 406.32 l 255.6 406.32 l 255.6 406.62 l 255.84 406.62 l 255.84 406.8 l 256.02 406.8 l 256.02 407.22 l 256.26 407.22 l 256.26 407.82 l 256.02 407.82 l 256.02 408 l 255.36 408 l 255.36 407.7 l 255.12 407.7 l 255.12 407.52 l f* 262.56 417.78 m 258.18 415.38 l 262.56 417.78 l 258.18 420.3 l 258.18 415.38 l 262.56 417.78 l f* 258.96 417.48 m 248.04 417.48 l 229.14 442.26 m 229.14 468.42 l S 228.78 472.62 m 226.08 468.42 l 228.78 472.62 l 231.24 468.42 l 226.08 468.42 l 228.78 472.62 l f* 240.6 442.32 m 240.6 455.34 l S 240.24 459.42 m 237.9 455.22 l 240.24 459.42 l 242.7 455.4 l 237.9 455.22 l 240.24 459.42 l f* 251.04 442.32 m 251.04 450.24 l S 250.68 454.32 m 248.34 450.06 l 250.68 454.32 l 253.14 450.06 l 248.34 450.06 l 250.68 454.32 l f* 215.22 442.62 m 257.82 442.62 l S 229.8 439.14 m 229.8 438.96 l 229.14 438.96 l 228.78 436.86 l 228.78 436.56 l 228.48 436.56 l 228.48 435.78 l 228.3 435.78 l 228.3 435.24 l 228.12 435.06 l 228.12 434.58 l 227.7 434.58 l 227.7 434.16 l 227.52 434.16 l 227.52 433.86 l 227.22 433.86 l 227.22 433.68 l 227.04 433.44 l 226.86 433.44 l 226.86 433.38 l 226.56 433.38 l 226.56 433.08 l 225.84 433.08 l 225.84 433.38 l 225.54 433.38 l 225.54 433.68 l 225.84 433.68 l 225.84 433.86 l 226.02 433.86 l 226.02 433.68 l 226.08 433.68 l 226.08 433.44 l 226.02 433.44 l 226.02 433.38 l 226.56 433.38 l 226.56 433.44 l 226.86 433.44 l 226.86 433.68 l 227.04 433.68 l 227.04 434.16 l 227.22 434.34 l 227.22 435.06 l 227.52 435.06 l 227.52 435.78 l 228.48 438.96 l 227.52 438.96 l 227.7 439.14 l 228.48 439.14 l 228.48 439.44 l 228.78 439.56 l 228.78 439.74 l 228.84 439.74 l 228.84 440.22 l 229.14 440.22 l 229.14 440.76 l 229.32 440.76 l 229.32 441.06 l 229.5 441.06 l 229.5 441.24 l 229.8 441.24 l 229.8 441.42 l 230.28 441.42 l 230.28 441.72 l 231.24 441.72 l 231.24 441.42 l 231.42 441.42 l 231.42 441.24 l 231.72 441.24 l 231.72 441.06 l 231.42 441.06 l 231.42 440.76 l 230.94 440.76 l 230.94 441.42 l 230.28 441.42 l 230.28 441.24 l 230.1 441.24 l 230.1 441.06 l 229.8 441.06 l 229.8 440.46 l 229.5 440.46 l 229.5 439.92 l 229.32 439.92 l 229.32 439.14 l 229.14 439.14 l 229.8 439.14 l f* 232.26 436.44 m 232.26 436.38 l 232.02 436.38 l 232.02 436.14 l 231.78 436.14 l 231.78 435.96 l 231.6 435.78 l 231.6 435.24 l 231.42 435.24 l 231.42 434.58 l 231.24 434.58 l 231.24 433.38 l 230.94 433.38 l 230.94 432.96 l 231.24 432.78 l 231.24 432.48 l 231.78 432.48 l 232.02 432.78 l 232.02 432.96 l 232.08 432.96 l 232.08 433.38 l 232.26 433.38 l 232.26 433.98 l 232.44 434.28 l 232.44 435.06 l 232.74 435.06 l 232.74 436.14 l 232.44 436.14 l 232.44 436.38 l 232.26 436.38 l 232.26 436.44 l 232.74 436.44 l 232.74 436.38 l 232.92 436.38 l 232.92 435.96 l 233.1 435.96 l 233.1 434.34 l 232.92 434.34 l 232.92 433.74 l 232.74 433.56 l 232.74 433.38 l 232.44 433.14 l 232.44 432.96 l 232.26 432.96 l 232.26 432.78 l 232.08 432.78 l 232.08 432.48 l 232.02 432.48 l 232.02 432.36 l 231.24 432.36 l 231.24 432.48 l 230.94 432.48 l 230.76 432.78 l 230.76 433.14 l 230.58 433.14 l 230.58 434.28 l 230.76 434.28 l 230.76 435.06 l 230.94 435.06 l 230.94 435.48 l 231.24 435.48 l 231.24 435.96 l 231.42 435.96 l 231.42 436.14 l 231.6 436.14 l 231.6 436.38 l 231.78 436.38 l 232.02 436.44 l 232.26 436.44 l f* 1 1 1 scn 0 0 0 SCN 1.14 w 0 j 0 J 134.4 447.84 67.68 -40.02 re B 0 0 0 scn 117.6 431.34 17.88 1.2 re f 117.6 422.88 17.88 1.2 re f 202.74 432.06 17.94 1.2 re f 202.74 423.6 17.94 1.2 re f 1 1 1 scn 138.78 413.22 59.64 28.62 re f 0 0 0 scn BT /TT0 1 Tf -0.0314 Tc 0 Tw 8.28 0 0 8.28 152.76 431.4 Tm [(No)-17(nl)-14(i)-29(n)-2(e)-8(a)-15(r)]TJ -0.0103 Tc 0.0652 -1.1884 Td [(Tw)52(o-)11(P)10(o)4(rt)]TJ ET q 209.9711 0 0 -15.96 64.02 359.46 cm /Im0 Do Q q 209.9711 0 0 -15.96 64.02 343.5 cm /Im1 Do Q q 209.9711 0 0 -16.02 64.02 327.54 cm /Im2 Do Q q 209.9711 0 0 -15.96 64.02 311.52 cm /Im3 Do Q q 209.9711 0 0 -15.96 64.02 295.56 cm /Im4 Do Q q 209.9711 0 0 -15.96 64.02 279.6 cm /Im5 Do Q q 209.9711 0 0 -16.02 64.02 263.64 cm /Im6 Do Q q 209.9711 0 0 -15.96 64.02 247.62 cm /Im7 Do Q q 209.9711 0 0 -5.7 64.02 231.66 cm /Im8 Do Q q /GS1 gs /Fm0 Do Q endstream endobj 42 0 obj << /Type /Page /Parent 78 0 R /Resources << /ColorSpace << /CS0 124 0 R /CS1 139 0 R >> /ExtGState << /GS0 127 0 R /GS1 138 0 R >> /Font << /TT0 92 0 R /TT1 105 0 R /C2_0 49 0 R /C2_1 50 0 R /TT2 86 0 R >> /XObject << /Fm0 220 0 R >> /ProcSet [ /PDF /Text ] >> /Contents 44 1 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 44 1 obj << /Length 221 0 R >> stream /CS0 cs 0 0 0 scn 1 i /RelativeColorimetric ri /GS0 gs BT /TT0 1 Tf 0.0006 Tc 0.2094 Tw 9 0 0 9 54 711.6003 Tm (functions are defined in terms of)Tj 0.001 Tc 0.209 Tw 14.0933 0 Td ( incident and scattered waves )Tj 0.0008 Tc 0.0825 Tw -14.0933 -1.1733 Td (rather than voltages and currents.)Tj 0.0012 Tc 0.0821 Tw 13.6667 0 Td [( The com)6(p)1(lex scattered wave )7(is )]TJ 0.0014 Tc 0.1886 Tw -13.6667 -1.1733 Td [(therefore repres)4(ented as)4( a nonlinear com)6(p)1(lex \(but )7(not )7(analy)-12(tic\) )]TJ 0.0011 Tc 0.0022 Tw 0 -1.1733 TD (function of the incident wa)Tj 0.0009 Tc 0.0024 Tw 10.8133 0 Td [(ves given by)-12( Equation 1.9. )]TJ 0 Tc 0 Tw -10.8133 -2.1333 Td ( )Tj 0.582 Tc 12 0 0 12 180.06 660.72 Tm (\(\))Tj /TT1 1 Tf 1.285 Tc -2.3 0.0003 Td [(bf)688(a)]TJ /C2_0 1 Tf 0 Tc 0.815 -0.0003 Td <0020>Tj /C2_1 1 Tf 1.265 Tc -0.67 0.83 Td <004B004B>Tj 0 Tc 2.62 -0.25 Td <004B>Tj /TT0 1 Tf 0.0007 Tc 8.6026 Tw 9 0 0 9 197.04 660.7203 Tm ( \(1.9\) )Tj 0.0008 Tc 0.0292 Tw -15.8933 -1.9333 Td [(The components of the )7(vector )7(re)]TJ 0.0006 Tc 0.0227 Tw 13.1267 0 Td (present the harmonic components )Tj 0.0011 Tc 0.1289 Tw -13.1267 -1.1733 Td [(of )-7(the )-7(waves )-7(in )-7(the frequency)-12( domain. The length of the vector )]TJ 0.0004 Tc 0.1229 Tw T* [(corresponds )-7(to the number of fre)]TJ 0.0007 Tc 0.1226 Tw 13.7133 0 Td [(quency)-13( components kept in the )]TJ 0.0009 Tc 0.1958 Tw -13.7133 -1.1733 Td [(approximation of the signal. In this theory)-12(, the waves have )7(an )]TJ 0.0018 Tc 0.1015 Tw T* [(abs)4(o)2(lute s)4(ize as)4(s)4(o)2(ciated with th)]TJ 0.0949 Tw 12.9933 0 Td [(em)6(, unlike the cas)4(e of \(linear\) S)5(-)]TJ 0.0009 Tc 0.0891 Tw -12.9933 -1.1733 Td [(parameters which are defined )7(only)-12( )]TJ 0.0007 Tc 0.0826 Tw 14.5533 0 Td [(in term)5(s of ratios of scattered )]TJ 0.0009 Tc 0.2558 Tw -14.5533 -1.1733 Td [(to )-7(incident waves. Describing )]TJ 0.0007 Tc 0.256 Tw 13.1933 0 Td (functions reduce to standard S-)Tj 0.0014 Tc 0.0019 Tw -13.1933 -1.1733 Td [(param)6(e)-1(ters in the lim)6(it of sm)6(all signals. )]TJ 0.001 Tc 0.0557 Tw 0 -1.62 TD (The function f in Equation 1.9 is )Tj 0.049 Tw 13.7 0 Td [(expanded )-7(in )-7(a suitable bases set )]TJ 0.4823 Tw -13.7 -1.1733 Td [(and fitted from)6( a set of data )7(obtained )7(by)-12( )7(m)6(easuring )7(\(or )]TJ 0.0005 Tc 0.2828 Tw 0 -1.1733 TD [(simulating\) )-7(the )-7(response of the sy)-13(stems to incident waves of )]TJ 0.0006 Tc 0.0494 Tw T* [(vary)-13(ing amplitudes and recording )]TJ 0.001 Tc 0.049 Tw 13.9533 0 Td [(the magnitude and phase )7(of )7(the )]TJ 0.0006 Tc 0.2294 Tw -13.9533 -1.1733 Td [(response. Applications based )7(on )]TJ 0.0011 Tc 0.2222 Tw 14.06 0 Td (real microwave )Tj 0 Tc 0 Tw 6.9 0 Td (measurements )Tj 0.0004 Tc 0.0163 Tw -20.96 -1.1733 Td (require the VNNA instrument describe)Tj 0.0013 Tc 0.0154 Tw 15.6333 0 Td [(d earlier,)-2( in order to get the )]TJ -0.0002 Tc 0.0769 Tw -15.6333 -1.1733 Td [(re)-3(la)-3(tive)-3( pha)-3(se)-3(s be)-3(twe)-3(e)-3(n suc)-3(c)-3(e)-3(ssive)]TJ 0.001 Tc 0.0757 Tw 14.2267 0 Td ( harmonics. The model can be )Tj 0.0009 Tc 0.1358 Tw -14.2267 -1.1733 Td [(directly)-12( implemented in a harmoni)]TJ 0.001 Tc 0.1357 Tw 14.4133 0 Td [(c balance simulator by)-12( )7(using, )]TJ 0.2357 Tw -14.4133 -1.1733 Td [(for example, a frequency)-12( domai)]TJ 0.0009 Tc 0.2358 Tw 13.7267 0 Td (n nonlinear modeling element, )Tj 0.0013 Tc 0.002 Tw -13.7267 -1.1733 Td [(s)4(u)1(ch as)4( the F)4(r)1(equency)-12( Dom)6(a)-1(in Device \(F)4(DD\) in )]TJ /TT1 1 Tf 0.0016 Tc 0.0017 Tw 19.66 0 Td (Agilent ADS)Tj /TT0 1 Tf 0.0033 Tc 0 Tw 4.9867 0 Td (. )Tj 0.0015 Tc 0.3418 Tw -24.6467 -1.62 Td [(A us)4(eful interm)6(ediate cas)4(e ex)]TJ 0.0011 Tc 0.3422 Tw 13.2267 0 Td (ists between the full nonlinear )Tj 0.109 Tw -13.2267 -1.1733 Td (describing functions and the linear )Tj 0.0009 Tc 0.1091 Tw 14.66 0 Td [(S-parameter case. In )7([24])7( )7(the )]TJ 0.0011 Tc 0.5156 Tw -14.66 -1.1733 Td [(describing functions are linearized )7(around )7(the )7(fundamental )]TJ 0.0012 Tc 0.4088 Tw T* [(response to a large am)6(plitude signal, which can be )7(highly)-12( )]TJ 0.001 Tc 0.0757 Tw T* [(nonlinear. The resulting approximate model has )7(the )7(property)-12( )7(that )]TJ 0.0012 Tc 0.1955 Tw T* (it is linear in the harmonics ar)Tj 0.0005 Tc 0.1895 Tw 13.1467 0 Td [(ound )-7(this fundamental response. )]TJ 0.0004 Tc 0.6029 Tw -13.1467 -1.1733 Td (This \223harmonic superposition\224 )Tj 0.0005 Tc 0.5962 Tw 14.4 0 Td [(approximation )-7(is useful in )]TJ 0.001 Tc 0.0023 Tw -14.4 -1.1733 Td [(simplify)-12(i)-1(ng )-7(the excitation design and the subsequent identification )]TJ T* (of the approximate model for a power amplifier. )Tj 0.0001 Tc 0.0899 Tw 0 -1.62 TD [(Unlike DNN and NLTS models,)-3( )7(whic)]TJ 0.0006 Tc 0.0827 Tw 15.6133 0 Td (h can be used in all modes )Tj 0.0008 Tc 0.2225 Tw -15.6133 -1.1733 Td (of simulation, describing functi)Tj 0.0005 Tc 0.2162 Tw 13.2467 0 Td [(on models can be used only)-13( in )]TJ 0.0016 Tc 0.1951 Tw -13.2467 -1.1733 Td [(harm)6(onic )-7(balance and linear anal)]TJ 0.001 Tc 0.1957 Tw 14.0467 0 Td [(y)-12(s)4(is in the frequency)-12( domain. )]TJ 0.0014 Tc 0.0086 Tw -14.0467 -1.1733 Td [(They)-12( can not be used directly)-12( to )]TJ 0.0006 Tc 0.0094 Tw 13.2067 0 Td [(simulate the response of )7(a )7(sy)-13(stem )]TJ 0.0027 Tw -13.2067 -1.1733 Td (to modulated signals such as W-CDMA. )Tj /TT2 1 Tf -0.0007 Tc 0.3507 Tw 12 0 0 12 54 284.28 Tm [(5. ENVELOPE )350(METHODS )]TJ /TT0 1 Tf 0.0017 Tc 0.335 Tw 9 0 0 9 54 273.3003 Tm [(Thes)4(e )-7(techniques)4( )-7(com)6(b)2(ine )-7(s)4(o)2(m)6(e)-1( as)4(pects)4( of the tim)6(e dom)6(ain )]TJ 0.0003 Tc 0.5697 Tw 0 -1.1733 TD [(formulations with some )7(as)]TJ 0.0008 Tc 0.5625 Tw 12.2867 0 Td [(pects of the frequency)-12( domain )]TJ 0.0012 Tc 0.0221 Tw -12.2867 -1.1733 Td [(techniques. The basic assum)6(p)1(tion is that the solution )7(of )7(the )7(circuit )]TJ 0.001 Tc 0.329 Tw T* (equations can be represented by)Tj 14.1333 0 Td [( a Fourier Series, sim)6(ilar )7(to )]TJ 0.0009 Tc 0.3291 Tw -14.1333 -1.1733 Td (Equations 1.7 and 1.8, but this )Tj 0.0018 Tc 0.3215 Tw 14.42 0 Td [(tim)6(e the coefficients)4( of this)4( )]TJ 0.0013 Tc 0.182 Tw -14.42 -1.1733 Td [(expansion )-7(can )-7(vary)-12( in tim)6(e. That is, the solution of the circuit )]TJ 0.0007 Tc 0.0026 Tw T* (equations is assumed to be gi)Tj 0.0009 Tc 0.0024 Tw 11.72 0 Td [(ven by)-12( equations 1.10 and 1.11: )]TJ 0 Tc 0 Tw -11.72 -2.1333 Td ( )Tj 0.0004 Tc 12 0 0 12 115.44 190.8 Tm [(\()-337(\))-1012(Re)-2236(\()-342(\))-117(exp\()-1847(\))]TJ /TT1 1 Tf 7.2399 Tc 7.02 0 0 7.02 174.72 187.7399 Tm (kk)Tj 0 Tc -2.2222 -1.1966 Td (k)Tj 0.4842 Tc 12 0 0 12 106.2 190.7436 Tm [(Vt)-3273(V)-235(t)-2018(j)-528(t)]TJ /C2_0 1 Tf 0 Tc 12 0 3.899 12 219.8995 190.74 Tm <005A>Tj 12 0 0 12 130.2 190.74 Tm <0020>Tj 18 0 0 18 154.5 188.043 Tm <00A6>Tj /TT0 1 Tf 0.0007 Tc 3.0493 Tw 9 0 0 9 242.52 190.7403 Tm ( \(1.10\) )Tj 0 Tc 0 Tw -20.9467 -3.4467 Td ( )Tj 0.337 Tc 12 0 0 12 114.66 159.72 Tm [(\(\))-675(R)334(e)-1839(\(\))215(e)346(x)337(p)337(\()-1515(\))]TJ /TT1 1 Tf 7.2399 Tc 7.02 0 0 7.02 173.22 156.7199 Tm (kk)Tj 0 Tc -2.1197 -1.2051 Td (k)Tj 0.447 Tc 12 0 0 12 109.2 159.7236 Tm [(It)-3440(I)-360(t)-2055(j)-565(t)]TJ /C2_0 1 Tf 0 Tc 12 0 3.899 12 218.3995 159.72 Tm <005A>Tj 12 0 0 12 129.48 159.72 Tm <0020>Tj 18 0 0 18 153.78 157.023 Tm <00A6>Tj /TT0 1 Tf 0.0007 Tc 3.216 Tw 9 0 0 9 241.02 159.7203 Tm ( \(1.11\) )Tj 0.0017 Tc 0.2816 Tw -20.78 -2.9333 Td [(Thes)4(e )-7(tim)6(e-dependent )-7(coefficients)4( are the com)6(p)2(lex envelopes)4(.)-2( )]TJ 0.0012 Tc 0.4621 Tw T* [(The transient envelope solution technique [2,3])8( is efficient )]TJ 0.0554 Tw T* [(provided that the tim)6(e vary)-12(ing coefficients)4( )7(vary)-12( )7(s)4(l)-1(owly)-12( )7(com)6(p)1(ared )]TJ 0.0011 Tc 0.3956 Tw T* [(with )-7(the carriers. This is )]TJ 0.0009 Tc 0.3958 Tw 11.9533 0 Td [(usually)-12( the case for narrow-band )]TJ 0.001 Tc 0.0023 Tw -11.9533 -1.1733 Td (communication circuits excited by)Tj 0.0013 Tc 0.002 Tw 13.8533 0 Td [( digitally)-12( modulated signals. )]TJ 0.001 Tc 0.2823 Tw 15.4667 68.9467 Td [(By)-12( addressing the envelope behavior in the time-domain, the )]TJ 0.0008 Tc 0.0159 Tw T* [(long-term memory)-12( effects can be included in )7(the )7(nonlinear )7(model. )]TJ -0.0005 Tc 0.5705 Tw T* [(Sy)-14(stems with long-term memory)]TJ 0.0013 Tc 0.5687 Tw 14.8667 0 Td [( can have very)-12( different )]TJ 0.0007 Tc 0.016 Tw -14.8667 -1.1733 Td [(behaviors depending on the )7(dy)-13(namics)]TJ 0.0094 Tw 15.2 0 Td ( of the envelopes It becomes )Tj 0.0017 Tc 0.0083 Tw -15.2 -1.1733 Td [(im)6(portant )-7(to s)4(tim)6(ulate the s)4(y)-12(s)4(tem)6( in way)-12(s)4( that affect the dy)-12(nam)6(ics)4( )]TJ 0.0013 Tc 0.082 Tw T* (of the envelopes. Excitation de)Tj 0.0007 Tc 0.0826 Tw 12.7267 0 Td [(signs will need to )7(go )7(well )7(bey)-13(ond )]TJ 0.0012 Tc 0.1155 Tw -12.7267 -1.1733 Td (the conventional two-tone techni)Tj 0.0008 Tc 0.1159 Tw 13.52 0 Td [(ques. Using digitally)-12( modulated )]TJ 0.0002 Tc 0.3765 Tw -13.52 -1.1733 Td (signals or band-limited noise ma)Tj 0.0021 Tc 0.3679 Tw 14.5733 0 Td [(y)-11( be neces)5(s)5(a)-1(ry)-11(. S)5(p)2(ecialized )]TJ 0.0005 Tc 0.0028 Tw -14.5733 -1.1733 Td [(hardware sy)-13(stems have been de)]TJ 0.0011 Tc 0.0022 Tw 12.6467 0 Td [(veloped to do this [17, 21])7(. )]TJ 0.0012 Tc 0.0621 Tw -12.6467 -1.62 Td [(A key)-12( requirem)6(e)-2(nt is the ability)-12( for the m)6(odeler to interface )7(with )]TJ 0.3155 Tw T* [(the envelope sim)6(u)1(lator. Som)6(e)-2( )]TJ 0.0006 Tc 0.3094 Tw 13.42 0 Td [(models )-7(are based on variables )]TJ 0.0012 Tc 0.3221 Tw -13.42 -1.1733 Td [(characteristic )-7(of )-7(the envelope and RF carriers independently)-12(. )]TJ 0.0015 Tc 0.1285 Tw T* [(M)4(o)2(s)4(t)-1( )-7(s)4(i)-1(m)6(u)2(lators)4( )-7(do )-7(not )-7(y)-12(e)-1(t have the interface to directly)-12( enable )]TJ 0.0008 Tc 0.0025 Tw T* (modelers to exploit su)Tj 0.0012 Tc 0.0021 Tw 8.88 0 Td (ch behavioral models. )Tj /TT2 1 Tf -0.0007 Tc 0.3507 Tw 12 0 0 12 317.88 550.68 Tm (6. CONCLUSIONS )Tj /TT0 1 Tf 0.0014 Tc 0.0753 Tw 9 0 0 9 317.88 539.7003 Tm [(Behavioral m)6(odeling techniques)4( have recently)-12( been increas)4(ing )7(in )]TJ 0.0012 Tc 0.0355 Tw T* [(sophistication and capability)-12(. Severa)]TJ 0.0288 Tw 14.8267 0 Td [(l techniques, notably)-12( those in )]TJ 0.001 Tc 0.1957 Tw -14.8267 -1.1733 Td [(the )-7(frequency)-12( domain and the enve)]TJ 0.0017 Tc 0.195 Tw 15.0533 0 Td [(lope dom)6(ain, are intim)6(ately)-12( )]TJ 0.0008 Tc 0.4292 Tw -15.0533 -1.1733 Td [(related )-7(to )-7(the )-7(underly)-12(i)-1(ng simulator algorithm used in their )]TJ 0.0009 Tc 0.8758 Tw T* (solution. Successful applica)Tj 0.0008 Tc 0.8692 Tw 12.9133 0 Td (tion of behavioral modeling )Tj 0.1492 Tw -12.9133 -1.1733 Td [(techniques to im)5(portant desi)]TJ 0.0009 Tc 0.1491 Tw 11.7733 0 Td [(gn challenges will depend upon )7(the )]TJ 0.0011 Tc 0.2556 Tw -11.7733 -1.1733 Td [(ease of interfacing with the underly)-12(i)-1(ng )7(simulation )7(engine, )7(the )]TJ 0.0013 Tc 0.4354 Tw T* [(ability)-12( to sy)-12(stem)6(atically)-12( apply)-12( the techniques )7(to )7(significant )]TJ 0.182 Tw T* [(quantities )-7(of data, and the ability)-12( to distribute these behavioral )]TJ 0.0011 Tc 0.2156 Tw T* [(m)6(odels )-7(to custom)6(ers. Finally)-12(, the ability)-12( to perform)6( waveform)6( )]TJ 0.0015 Tc 0.1485 Tw T* [(m)6(eas)4(urem)6(ents)4( at m)6(i)-1(crowave frequencies)4( in order to apply)-12( )7(thes)4(e )]TJ 0.0013 Tc 0.2354 Tw T* [(techniques to real data will be a big advantage to get )7(around )]TJ 0.2221 Tw T* [(accuracy)-12( lim)6(itations)4( of building behavioral m)6(odels)4( )7(from)6( )7(lower )]TJ 0.0016 Tc 0.0017 Tw T* [(level m)6(odels. )]TJ /TT2 1 Tf -0.0007 Tc 0.3507 Tw 12 0 0 12 317.88 378.78 Tm (7. ACKNOWLEDGMENTS )Tj /TT0 1 Tf 0.0004 Tc 0.0163 Tw 9 0 0 9 317.88 367.8003 Tm (Thanks to Hassan Tanbakuchi, Domi)Tj 0.0008 Tc 0.0092 Tw 14.94 0 Td (nique Schreurs, Alex Pekker, )Tj 0.0011 Tc 0.0422 Tw -14.94 -1.1733 Td [(Darry)-12(l )-7(Okahata, Alex Cognata, Br)]TJ 0.0006 Tc 0.0427 Tw 13.94 0 Td [(ian Hughes, Derry)-13( Hornbuckle, )]TJ 0.0009 Tc 0.4358 Tw -13.94 -1.1733 Td [(Jerry)-12( Gladstone, and Agilent )]TJ 0.0008 Tc 0.4292 Tw 13.5267 0 Td (Technologies Management for )Tj 0.0006 Tc 0.0027 Tw -13.5267 -1.1733 Td (supporting this work. )Tj /TT2 1 Tf -0.0014 Tc 0.3514 Tw 12 0 0 12 317.88 310.5 Tm [(8. REFERENCES )350( )]TJ /TT0 1 Tf 0.0027 Tc 0 Tw 10.02 0 0 10.02 317.88 298.5 Tm [([1])6( )]TJ 0.0012 Tc 0.1821 Tw 9 0 0 9 335.88 298.5003 Tm [(Kundert, )-7(K. S., Sangiovanni-Vincentelli. A., Sim)6(u)1(lation of )]TJ 0.6754 Tw T* [(nonlinear circuits in the frequency)-12( dom)6(ain. 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Kluwer Acad)Tj 0.0005 Tc 0.0028 Tw 8.8267 0 Td (emic Publishers 1990 )Tj ET q /GS1 gs /Fm0 Do Q endstream endobj 45 0 obj << /Type /Page /Parent 78 0 R /Resources << /ColorSpace << /CS0 124 0 R /CS1 139 0 R >> /ExtGState << /GS0 127 0 R /GS1 138 0 R >> /Font << /TT0 92 0 R /T1_0 85 0 R >> /XObject << /Fm0 229 0 R >> /ProcSet [ /PDF /Text ] >> /Contents 47 1 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 47 1 obj << /Length 230 0 R >> stream /CS0 cs 0 0 0 scn 1 i /RelativeColorimetric ri /GS0 gs BT /TT0 1 Tf 0.0027 Tc 10.02 0 0 10.02 54 710.5801 Tm [([6])6( )]TJ 0.0008 Tc 0.7292 Tw 9 0 0 9 72 710.5803 Tm (Phillips, J.R. Projection-ba)Tj 12.2333 0 Td [(sed approaches for m)5(odel )]TJ 0.0009 Tc 0.1824 Tw -12.2333 -1.1733 Td [(reduction of weakly)-12( nonlinear )7(tim)5(e-vary)-12(ing )7(sy)-12(tesm)5(s. )7(IEEE )]TJ 0.3824 Tw 0 -1.1733 TD [(Trans. Computer-aided design of )7(integrated )7(circuits )7(and )]TJ 0.0006 Tc 0.0027 Tw T* [(sy)-13(stems, Vol 22, No. 2, \(February)-13(,)-3( 2003\) )]TJ 0.0027 Tc 0 Tw 10.02 0 0 10.02 54 663.3 Tm [([7])6( )]TJ 0.0008 Tc 0.1159 Tw 9 0 0 9 72 663.3003 Tm [(Zhang, Q. J. and Gupta, )7(K. )7(C.)]TJ 0.0003 Tc 0.1097 Tw 12.6533 0 Td ( Neural networks for RF and )Tj 0.0009 Tc 0.0024 Tw -12.6533 -1.1733 Td (microwave design. Artech House \(2000\). )Tj 0.0027 Tc 0 Tw 10.02 0 0 10.02 54 637.14 Tm [([8])6( )]TJ 0.0009 Tc 0.1291 Tw 9 0 0 9 72 637.1403 Tm [(Hay)-12(k)1(in, )-7(S. Neural Networks: a comprehensive foundation. )127( )]TJ 0.0011 Tc 0.0022 Tw T* (2nd ed. Prentice-Hall \(1999\). )Tj 0.0027 Tc 0 Tw 10.02 0 0 10.02 54 610.98 Tm [([9])6( )]TJ 0.0013 Tc 0.1754 Tw 9 0 0 9 72 610.9803 Tm [(Xu, )-7(J., )-7(Yagoub, M. C. E., Ding, )]TJ 14.22 0 Td (R., Zhang, Q. J. Neural )Tj 0.0009 Tc 0.2291 Tw -14.22 -1.1733 Td [(based )-7(dy)-12(namic modeling of nonlinear microwave circuits. )227( )]TJ 0.0007 Tc 0.0026 Tw T* (IEEE MTT-S 2002 \(June 2002\) pp. 1101-1104. )Tj 0.0028 Tc 0 Tw 10.02 0 0 10.02 54 574.26 Tm [([10])7( )]TJ 0.0009 Tc 0.3558 Tw 9 0 0 9 72 574.2603 Tm (Wood, J. and Root, D. E. )Tj 0.001 Tc 0.3557 Tw 12.46 0 Td [(The behavioral modeling )7(of )]TJ 0.0003 Tc 0.3364 Tw -12.46 -1.1733 Td (microwave/RF ICs using non-linear)Tj 0.0013 Tc 0.3287 Tw 15.38 0 Td [( )-7(time series analy)-12(s)4(is. )327( )327( )]TJ 0.0006 Tc 0.0027 Tw -15.38 -1.1733 Td (IEEE IMS2003 \(June 2003\). )Tj 0.0028 Tc 0 Tw 10.02 0 0 10.02 54 537.54 Tm [([11])7( )]TJ 0.0013 Tc 0.2087 Tw 9 0 0 9 72 537.5403 Tm [(Root, )-7(D. )-7(E., Wood, J., Pekker, )]TJ 0.0008 Tc 0.2092 Tw 13.6867 0 Td [(A. Sy)-12(stematic behavioral )]TJ 0.0006 Tc 0.2627 Tw -13.6867 -1.1733 Td (modeling of nonlinear microwav)Tj 0.0015 Tc 0.2618 Tw 13.94 0 Td [(e/RF circuits in the tim)6(e )]TJ 0 Tc 0.0633 Tw -13.94 -1.1733 Td [(domain )-7(using techniques from non)]TJ 0.0019 Tc 0.0614 Tw 14.1533 0 Td [(linear dy)-11(nam)6(ical s)4(y)-11(s)4(tem)6(s)4(.)-1( )60( )]TJ 0.0006 Tc 0.0027 Tw -14.1533 -1.1733 Td (IEEE BMAS 2002 \(October 2002\). )Tj 0.0028 Tc 0 Tw 10.02 0 0 10.02 54 490.26 Tm [([12])7( )]TJ 0.0011 Tc 0.1022 Tw 9 0 0 9 72 490.2603 Tm [(Schreurs, )-7(D., Wood, J., Tufilla)]TJ 0.0014 Tc 0.1019 Tw 12.72 0 Td (ro, N., Barford, L. and Root, )Tj 0.0007 Tc 0.2626 Tw -12.72 -1.1733 Td [(D. )-7(E. Construction of behavioural models for microwave )]TJ 0.0015 Tc 0.4285 Tw T* [(devices)4( from)6( tim)6(e-dom)6(ain large-s)4(i)-1(gnal )7(m)6(eas)4(urem)6(ents)4( )7(to )]TJ 0.0006 Tc 0.0494 Tw T* [(speed up high-level design )7(simula)]TJ 0.0012 Tc 0.0421 Tw 13.82 0 Td (tions. International Journal )Tj 0.001 Tc 0.0357 Tw -13.82 -1.1733 Td [(of RF)4( and M)4(i)-1(crowave Com)6(puter-Aided )7(Engineering: )7(S)4(p)1(ecial )]TJ 0.0006 Tc 0.0427 Tw T* [(Issue )-7(on )-7(')-6(M)3(easurement Techniques for Effective CAD')-6( 13\(1\) )]TJ 0.0008 Tc 0.0025 Tw T* (pp. 54-61 \(2003\). )Tj 0.0028 Tc 0 Tw 10.02 0 0 10.02 54 411.3 Tm [([13])7( )]TJ 0.001 Tc 0.0623 Tw 9 0 0 9 72 411.3003 Tm [(Schreurs, D.,Wood, J., )7(Tufillaro)]TJ 0.0014 Tc 0.0553 Tw 13.0667 0 Td (, N., Usikov, D., Barford, L. )Tj 0.0011 Tc 0.4422 Tw -13.0667 -1.1733 Td [(and Root, D. E. The construction )7(and )7(evaluation )7(of )]TJ 0.0006 Tc 0.2561 Tw T* (behavioral models for micr)Tj 0.0008 Tc 0.2559 Tw 11.64 0 Td (owave devices based on time-)Tj 0.0015 Tc 0.3618 Tw -11.64 -1.1733 Td [(dom)6(ain large-s)4(i)-1(gnal m)6(eas)4(urem)6(en)]TJ 0.0014 Tc 0.3619 Tw 14.0133 0 Td [(ts. International )7(Electron )]TJ 0.001 Tc 0.1757 Tw -14.0133 -1.1733 Td [(Devices )-7(Meeting 2000, \(Decem)6(ber 2000\) IEDM Technical )]TJ 0.0008 Tc 0.0025 Tw T* (Digest pp. 819 -822. )Tj 0.0028 Tc 0 Tw 10.02 0 0 10.02 54 342.9 Tm [([14])7( )]TJ 0.0016 Tc 0.0084 Tw 9 0 0 9 72 342.9003 Tm [(Kantz, H. and S)4(c)-1(hreiber, T. Nonlinear )7(Tim)6(e)-1( )7(S)4(e)-1(ries)4( )7(Analy)-12(s)4(is)4(, )]TJ 0.0003 Tc 0.003 Tw T* [(Cambridge University)-13( Press \(1997\) )]TJ 0.0028 Tc 0 Tw 10.02 0 0 10.02 54 316.7401 Tm [([15])7( )]TJ 0.0006 Tc 0.0094 Tw 9 0 0 9 72 316.7403 Tm [(Stark, )-7(J. )-7( Delay)-13( embeddings and )]TJ -0.0007 Tc 0.0107 Tw 13.2667 0 Td [(forc)-3(e)-3(d)-1( sy)-14(ste)-3(m)4(s,)-4( J.)-4( Nonline)-3(a)-3(r)-1( )]TJ 0.0009 Tc 0.0024 Tw -13.2667 -1.1733 Td (Science, 9 pp255-332 \(1999\). )Tj 0.0028 Tc 0 Tw 10.02 0 0 10.02 317.88 710.5801 Tm [([16])7( )]TJ 0.0013 Tc 0.3754 Tw 9 0 0 9 335.88 710.5803 Tm [(Kennel, M. B., Brown, )7(R., )]TJ 0.001 Tc 0.369 Tw 12.7267 0 Td (Abarbanel., H. Determining )Tj 0.0357 Tw -12.7267 -1.1733 Td [(em)6(bedding dim)6(e)-2(ns)4(ion for phas)4(e)-2(-s)4(pace recons)4(truction us)4(ing )7(a )]TJ 0.0007 Tc 0.2626 Tw T* [(geometrical )-7(construction, )-7(Phy)-13(s)3(. )-7(Rev. A 45 pp3403-3411 )]TJ 0.0009 Tc 0 Tw T* (\(1992\). )Tj 0.0028 Tc 10.02 0 0 10.02 317.88 663.3 Tm [([17])7( )]TJ 0.0009 Tc 0.1491 Tw 9 0 0 9 335.88 663.3003 Tm [(Verspecht, J., Verbey)-12(st, F.. Vanden Bossche, M. )7(Network )]TJ 0.0007 Tc 0.156 Tw T* [(analy)-13(s)3(is bey)-13(ond )7(S-parameters)]TJ 0.0011 Tc 0.1489 Tw 12.2867 0 Td (: characterizing and modeling )Tj 0.0008 Tc 0.9959 Tw -12.2867 -1.1733 Td (component behaviour under modulated large-signal )Tj 0.4225 Tw T* [(operating conditions)3(. ARF)4(T)-2(G )7(56 )7(Colorado )7(\(Decem)5(ber )]TJ 0.0001 Tc 0 Tw T* (2000\) )Tj 0.0028 Tc 10.02 0 0 10.02 317.88 605.46 Tm [([18])7( )]TJ 0.0009 Tc 0.1558 Tw 9 0 0 9 335.88 605.4603 Tm [(Schreurs, )-7(D. )-7(and )-7(Rem)5(l)-1(ey)-12(, )-7(K. Use of m)5(u)1(ltisine signals for )]TJ 0.0012 Tc 0.2421 Tw T* (efficient behavioural modelling )Tj 0.0005 Tc 0.2362 Tw 13.6133 0 Td (of RF circuits with short-)Tj 0.0007 Tc 0.0026 Tw -13.6133 -1.1733 Td [(memory)-13( effects. ARFTG 61Philadelphia \(June 2003\). )]TJ 0.0028 Tc 0 Tw 10.02 0 0 10.02 317.88 568.7401 Tm [([19])7( )]TJ 0.0012 Tc 0.2955 Tw 9 0 0 9 335.88 568.7403 Tm [(Ku, H., McKinley)-12(, M. D., Kenney)-12(,)-2( J. S. )7( )7(Extraction )7(of )]TJ 0.5355 Tw T* [(accurate behavioral m)6(odels)4( for power )7(am)6(plifiers)4( )7(with )]TJ 0.0004 Tc 0.0096 Tw T* [(m)5(e)-2(m)5(ory)-13( effects using two-tone)]TJ 0.0016 Tc 0.0017 Tw 12.52 0 Td [( m)6(easurem)6(ents. IEEE MTT-S)4( )]TJ 0.0006 Tc 0.0027 Tw -12.52 -1.1733 Td (2002 \(June 2002\) pp. 139-142. )Tj 0.0028 Tc 0 Tw 10.02 0 0 10.02 317.88 521.46 Tm [([20])7( )]TJ 0.002 Tc 0.5013 Tw 9 0 0 9 335.88 521.4603 Tm [(Reig, )-7(P)5(., )-7(LeG)4(a)-1(llou, N)4(., N)4(e)-1(bus)5(, J)5(-)2(M)5(., and N)4(goy)-11(a, E. )500( )]TJ 0.001 Tc 0.409 Tw T* [(Accurate RF)4( and m)6(i)-1(crowave )]TJ 0.0004 Tc 0.4029 Tw 13.3667 0 Td [(sy)-13(stem level modeling of )]TJ 0.0008 Tc 0.0492 Tw -13.3667 -1.1733 Td [(wideband )-7(nonlinear )-7(circuits. )-7( IEEE MTT-S2000 \(June 2000\) )]TJ 0.001 Tc 0.0023 Tw T* (pp. 79-82. )Tj 0.0028 Tc 0 Tw 10.02 0 0 10.02 317.88 474.1801 Tm [([21])7( )]TJ 0.0019 Tc 0.0014 Tw 9 0 0 9 335.88 474.1803 Tm [(LeG)4(a)-1(llou, )-7(N)4(., )-7(N)4(goy)-11(a, )-7(E., Buret, H)4(., Barataud, D)4(., and N)4(e)-1(bus)4(, )]TJ 0.0004 Tc 0.1163 Tw T* (J-M. An improved behavioral)Tj 0.0007 Tc 0.1093 Tw 12.6133 0 Td ( modeling technique for high )Tj 0.0009 Tc 0.2358 Tw -12.6133 -1.1733 Td [(power am)5(plifiers with m)5(e)]TJ 11.02 0 Td [(m)5(o)1(ry)-12(. IEEE )7(MTT-S2001 )7(\(May)-12( )]TJ 0.0024 Tw -11.02 -1.1733 Td (2001\) pp. 983-986. )Tj 0.0028 Tc 0 Tw 10.02 0 0 10.02 317.88 426.9 Tm [([22])7( )]TJ 0.0007 Tc 0.0693 Tw 9 0 0 9 335.88 426.9003 Tm [(Tuinenga, P., Models rush )7(in )7(wh)]TJ 0.0016 Tc 0.0617 Tw 13.4067 0 Td [(ere s)4(i)-1(m)6(u)2(lators)4( fear to tread: )]TJ 0.0011 Tc 0.1422 Tw -13.4067 -1.1733 Td [(extending the baseband-equivalent m)6(e)-2(thod. . IEEE BMAS )]TJ 0.0006 Tc 0.0027 Tw T* (2002 \(October 2002\). )Tj 0.0028 Tc 0 Tw 10.02 0 0 10.02 317.88 390.18 Tm [([23])7( )]TJ 0.0006 Tc 0.2694 Tw 9 0 0 9 335.88 390.1803 Tm [(Verspecht, )-7(J. 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  3!1AQa"q2B#$Rb34rC%Scs5&DTdE£t6UeuF'Vfv7GWgw5!1AQaq"2B#R3$brCScs4%&5DTdEU6teuFVfv'7GWgw ?̺e<4YߪX wmkf!irX̷1pd ?ތe( tޠ2 9 jhAMG1n kOe/;/?D4jαfD?ht|=?VwLΙ)֣XC\ o(&͞䖳Uz?*uHkZv%[pOtƼ*^ULީ\KvQkǔn5:[,ΰ<liDs8Jֲ<;*^Rz?*B{^Rz?*p'òFcNU_Gxoҩz={IV3斳Uz?*>k`[sD&nƳ䖺 ީZ[mOk^HpqBY &X{ܸKXOe1φz\nV気.%[9Ho~LbX4i~& Эu7ُvGO]>4D)*޻YJgیr/ IW+e;ZKt ܤzdvHOuUw[^+n݄B|Q?mu4S}F4!播赎5)9\^`KuFmnt\<|B oPg-g˺{c+/{*ŽK2g㽲g-u>1kƛZ]iwS~ޯbS 8'OsGZi!c}':jpCEXۉhE>O;"zc1)\[3je ݅'XW1XaeahkpoIV>JQ8ο`{d%@Yk_o>i]Plk!a5Buuڭƿ+ f;XϸY;`BJ5y4=g66>H)$c\NJfKZLTk5[gŎkcͲel6x8{ߝ~;&5qGe+3I%8{99%leB~캎P׶Is+}ɭrqnunUxs l-߉_)z=31i`UXn$x"uWf}u nCw{KZ}2 Գ ?䓷d:chHvHqD7 KN[՛XY $j 'E{t^er-m861CiwQlN. -i> ɨn0`&u|5r zO[?Y={tSqXƦ ;x8}8Mn5ܢzÜ-lMIQRn}OAontܶ~?ܱWYpoNqGV_*з ӳh|:R%=-%8z/g˞9ţ;KFEDd/sZaL8H% OO8z/grrߗB}PK@{3c`:%EOK8z/grrh}]?9'f0-h}ns:IOG8z/g`e -elp50{l.lC }G"+`h*/m;a.n!KkGla}M]IhPv<]EH utDwSe"ӈ p;tvYERLj?Q)L2qDZa;nƗ8848Odl^Y 5ׂ\ ba-sִ9\@#"kNmb\[[;}{ CvmF tn=x{Qcc , s]$^A-a#2Q gUGM],IH"tTzwי]ӑK`DKY`gD:'+Plw9̸⚭5[L2!=vH8W?kԶto{\+Y,hkZր#.%ykw6CLqւ\.iL=2dԶ%n_һC_߹Ekv5 MjdT,u'̧8okf_ױ}21zd#ⵟ@!ӂ;O cq$!"O[cNj+tf$; 5s?rsKXw4?g{b,jݐ(t8nW麓]-x^}UaO%#XȐ~jӸ~))65z+uwk2@c[EXƴT!5A GQXm h{9sH5Ӻ2,i,.qÉE,3qNaelunsjs[: -U C\qH16+9;c眛Oq p]%ǸaȈNRNUŰMN/W?W^UI>멵uN蝮gTIǦc q;_H=qXoܿ×ܯKM51Y&8ו[m-lC"=ӬAxpY{s[[վVtE@zv 1(b}ZjjT8ω*to%C]VeoݔڙkaD) j̨XkxbIߧ ռkXnͤn$' U a[hcdX7햎(Ϲۻ׊uHs)Ƨ߇~Y{ퟳlm- iYGt܌1&uVWK/ I9O}6[ʿCqcSCly#Z&PX@9հ~+ŒQq[cZoyW|SBǿb_sElFN!ܷhZY=[!pN4 *NC|G%g?K%z>pdCӰm{fs{y|՚O /AO /IO /IO /IO /IO /IO /IO /IO /IOеGʒ$ endstream endobj 165 0 obj << /Type /XObject /Subtype /Image /Width 342 /Height 39 /BitsPerComponent 8 /ColorSpace 124 0 R /Length 5536 /Filter /DCTDecode >> stream Adobed     $$''$$53335;;;;;;;;;;  %% ## ((%%((22022;;;;;;;;;;'V"? 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IhUhOc{Gdi͙"e{4!g=WTw]Qu,GI ۩ۓ{z~C^Z֐TCI#OWK}QXΣcԶ,3_(OզF&l=$؇*n{ 7wK:$ܭ>ӯf1sg}Qq{ݹ"?r,nVkzͯ gt)Ui ^4K&f潬 A ]Wõ3'՛Q o`N1gj y:}>{RވWv˫:PnoJsˎ繮ˎbVf7֟3`Lj%Nn,D91 KfsUcѲVAgLT 2[Kk閱P O-<ls ?9YCnXWƷ}0U0}_`s-~_P ͫ7yX2gֿ4Y5-;H0FԽ)UktZϤ\PU32c8TAK_uN;9یZ;vӂkL!ͳv C{Rޅk]PO?CsܗtXկ/v4U(e"a w;5'7\c- }nINHMt>rvӯ#8U /ͽ!FW=kGW:>Gb'-cEHnM3V;[KZ+A2{~@_:mc\A|Bc)qAk&\sNp~U}oSf濁p$)U@sTc>mdk3yX2_o3V;vC?Pv6NߴYKGj<gA/c7? {R1ӯ3: %^Sk_L/piKˌ[Yo_VIg4%f7?Jwtkk*eC^XΨ8 ~ϽkTOCNf&;ۈ=f}nyd\s\6d׹iۧIg3/E}v[Kǧ`p0idK۟V:?[cd;"^aݹ^'6Lknne։;$*_VLZY}F; 3Խ9Ap,: 5I'8gtúy# Nm?>#lVz{_xղ.kkEUR8^{ /kYjv#)Z̋I:?FNIx|է,Z[Y_7[>c\_x>'N\^cFGi? $lܼ$ύq+Om^k*kń[S6rr,oOdk]M/i5Q}ѷ>~b־o{2pj_y{]m|EnK:+[lƶ٬Tx #&;|_Zx'K^x햌{;O:7Uw0֨9]Hti%yHK.}Od:gsVX&c_Ou^ʬյ#vz7I}l<_J4ruv0~w=T?xZ/쵽:Gi0I&~?i}Ku[nCFW?6ntvXc't&Ԕz} OGM/sw\I~*;chɥ62wN?kI/z|^ld?;m5Τ_>/E62wN?i͌ӿ6RK^?;m4OGMs%?WO͌ӿ6_c't&ԒWOGM/sw\IOU_c't&;chɮu$Uz/swKld:_~*;chɣ}\ʫ?љ, fe·%r ~Fz|_iɛ[pe.6<8_}wo"dՏT_}nm67{;F$/"IeFN {럳rsWP"w~'ψ:$$[S endstream endobj 166 0 obj << /Type /XObject /Subtype /Image /Width 270 /Height 15 /BitsPerComponent 8 /ColorSpace 124 0 R /Length 1358 /Filter /DCTDecode >> stream Adobed     $$''$$53335;;;;;;;;;;  %% ## ((%%((22022;;;;;;;;;;"?   3!1AQa"q2B#$Rb34rC%Scs5&DTdE£t6UeuF'Vfv7GWgw5!1AQaq"2B#R3$brCScs4%&5DTdEU6teuFVfv'7GWgw ?pyv.9,h |5D&?_AKo[QJ?c5_ӘdJqŽN/N{@kJ;2Ex\7QHpl<*rm}4ݽZ{?4pyJyP}Fwu_7Ke%q1?q]y[+ )>q1m2?DzK et+ F6+q;i-`%%8P00CtkƼ3[15qbvW_7IO? mtbc\s~b6W_7IO7[:~F=>q1AoyJ&Wf=dѤxNJw a[ p1x8Awe-۾у6;Gr1 L}-WS6N&<ƿOLl%oaAF_a5c]y[+ ) }3q7Hh TCnv+k#O+_7Ke%4Uoa^&^>v@ݻX]fd+ghp2٘⒟ endstream endobj 167 0 obj << /Type /XObject /Subtype /Image /Width 270 /Height 25 /BitsPerComponent 8 /ColorSpace 124 0 R /Length 1060 /Filter /DCTDecode >> stream Adobed     $$''$$53335;;;;;;;;;;  %% ## ((%%((22022;;;;;;;;;;"?   3!1AQa"q2B#$Rb34rC%Scs5&DTdE£t6UeuF'Vfv7GWgw5!1AQaq"2B#R3$brCScs4%&5DTdEU6teuFVfv'7GWgw ?1չ o[QJ/e*j2ꔔ裸I)I$JRI$I$&%>i.k־P4 YۓtCQzy#aUKC|>i:?7n%(RI$)$IJI$RI$I%)$IJI$RI$g߿h L#VpRSlȨxFRR2E JJwI$I%)$IJI$R*ju08{5N8Y.Un}\&f hcZG(]H]cw7k@ׅx'O$u/SvAm4>4:A9TPʯn$IRI$7'UbRI$~N>8Pv/ J*? 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