| (%i1) | load("/home/vcaeken/Desktop/rfMaxima.mac")$ |
Constant-k Section Analysis
(See "Microwave Engineering, 2nd Ed., by D. Pozar, Wiley, 1998, p. 433)
1 Without Assumptions for Z_1 and Z_2
1.1 ABCD-, G-, H-, S-, Y- and Z-Parameters
| (%i2) |
Solution:linsolve([v_in-v_1=Z_1/2*i_in,v_out-v_1=Z_1/2*i_out,v_1=Z_2*i_1,i_in+i_out=i_1],[i_in,i_out,i_1,v_1]); TwoPortMatrices(Solution); |
1.2 Characteristic Impedance, Z_0, and Propagation Constant, %gamma
| (%i4) |
solve(S(s)[1,1]=0,Z_0); doallmxops:true$ solve(determinant(ABCD(s)-pow_e_gamma*ident(2))=0,pow_e_gamma); |
2 Assuming Z_1=s*L and Z_2=1/(s*C)
2.1 ABCD-, G-, H-, S-, Y- and Z-Parameters
| (%i7) |
declare(C,real)$ declare(L,real)$ assume(C>0)$ assume(L>0)$ assume(Z_0>0)$ Z_1:s*L$ Z_2:1/(s*C)$ TwoPortMatrices(Solution); |
| (%i15) | SParameters(S); |
| (%i16) | Stability(S); |
2.2 Characteristic Impedance, Z_iT, and Propagation Constant, %gamma
| (%i17) | solve(ev(S(s)[1,1])=0,Z_0); |
| (%i18) | define(Z_iT(s),rhs(last(%))); |
| (%i19) |
doallmxops:true$ solve(determinant(ev(ABCD(%i*%omega))-pow_e_gamma*ident(2))=0,pow_e_gamma); |
| (%i21) | define(pow_e_gamma(%omega),rhs(last(%))); |
2.3 A (Attenuation per Section), %phi (Phase Shift per Section) and tau_g (Group Delay per Section)
| (%i22) |
define(A(%omega),realpart(ev(log(pow_e_gamma(%omega))))); define(%phi(%omega),imagpart(ev(log(pow_e_gamma(%omega))))); |
| (%i24) |
%omega_c:2/sqrt(L*C); A(%omega_c); %phi(%omega_c); |
| (%i27) |
C:5e-15$ L:75e-12$ Z_0:50$ |
| (%i30) |
PlotSmithChart([ parametric, realpart(S(%i*2*%pi*f)[1,1]), imagpart(S(%i*2*%pi*f)[1,1]), [f,1e6,20e9], [nticks,100]]); PlotSmithChart([ parametric, realpart(S(%i*2*%pi*f)[1,2]), imagpart(S(%i*2*%pi*f)[1,2]), [f,1e6,20e9], [nticks,100]]); PlotSmithChart([ parametric, realpart(S(%i*2*%pi*f)[2,1]), imagpart(S(%i*2*%pi*f)[2,1]), [f,1e6,20e9], [nticks,100]]); PlotSmithChart([ parametric, realpart(S(%i*2*%pi*f)[2,2]), imagpart(S(%i*2*%pi*f)[2,2]), [f,1e6,20e9], [nticks,100]]); |
| (%i34) |
wxplot2d(ev(20*log10(Abs_S11(2*%pi*f*1e9))), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"dB20(|S11|)"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"])$ wxplot2d(ev(20*log10(Abs_S12(2*%pi*f*1e9))), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"dB20(|S12|)"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"])$ wxplot2d(ev(20*log10(Abs_S21(2*%pi*f*1e9))), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"dB20(|S21|)"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"])$ wxplot2d(ev(20*log10(Abs_S22(2*%pi*f*1e9))), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"dB20(|S22|)"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"])$ wxplot2d(ev(Arg_S11(2*%pi*f*1e9)*180/%pi), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"S11 (°)"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"])$ wxplot2d(ev(Arg_S12(2*%pi*f*1e9)*180/%pi), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"S12 (°)"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"])$ wxplot2d(ev(Arg_S21(2*%pi*f*1e9)*180/%pi), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"S21 (°)"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"])$ wxplot2d(ev(Arg_S22(2*%pi*f*1e9)*180/%pi), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"S22 (°)"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"])$ |
| (%i42) |
wxplot2d(ev((R_IN(2*%pi*f*1e9))), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"R_IN [Ohm]"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"])$ wxplot2d(ev((X_IN(2*%pi*f*1e9))), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"X_IN [Ohm]"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"]); wxplot2d(ev((R_OUT(2*%pi*f*1e9))), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"R_OUT [Ohm]"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"])$ wxplot2d(ev((X_OUT(2*%pi*f*1e9))), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"X_OUT [Ohm]"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"])$ wxplot2d(ev((tau_g(2*%pi*f*1e9))*1e12), [f,0.1,20], [legend,false], [xlabel,"Frequency [GHz]"], [ylabel,"Group Delay [pS]"], [style,[lines,3,2]], [gnuplot_preamble,"set grid"])$ |
| (%i47) |
load("/home/vcaeken/Desktop/coma")$ step_response(1/ABCD(s)[1,1]); |
