Passivity: Test, Visualize, and Enforce Passivity of Rational Fit Output
This example shows how to test, visualize, and enforce the passivity of output from the rationalfit
function.
S-Parameter Data Passivity
Time-domain analysis and simulation depends critically on being able to convert frequency-domain S-parameter data into causal, stable, and passive time-domain representations. Because the rationalfit
function guarantees that all poles are in the left half plane, rationalfit
output is both stable and causal by construction. The problem is passivity.
N-port S-parameter data represents a frequency-dependent transfer function H(f). You can create an S-parameters object in RF Toolbox™ by reading a Touchstone® file, such as passive.s2p
, into the sparameters
function.
You can use the ispassive
function to check the passivity of the S-parameter data, and the passivity
function to plot the 2-norm of the N x N matrices H(f) at each data frequency.
S = sparameters('passive.s2p');
ispassive(S)
ans = logical
1
passivity(S)
Testing and Visualizing rationalfit
Output Passivity
The rationalfit
function converts N-port sparameter data, S
into an NxN matrix of rfmodel.rational
objects. Using the ispassive
function on the N x N fit output reports that even if input data S
is passive, the output fit is not passive. In other words, the norm H(f) is greater than one at some frequency in the range [0,Inf].
The passivity
function takes an N x N fit as input and plots its passivity. This is a plot of the upper bound of the norm(H(f)) on [0,Inf], also known as the H-infinity norm.
fit = rationalfit(S); ispassive(fit)
ans = logical
0
passivity(fit)
The makepassive
function takes as input an N x N array of fit objects and also the original S-parameter data, and produces a passive fit by using convex optimization techniques to optimally match the data of the S-parameter input S
while satisfying passivity constraints. The residues C and feedthrough matrix D of the output pfit
are modified, but the poles A of the output pfit are identical to the poles A of the input fit.
pfit = makepassive(fit,S,'Display','on');
ITER H-INFTY NORM FREQUENCY ERRDB CONSTRAINTS 0 1 + 1.791e-02 17.6816 GHz -40.4702 1 1 + 2.878e-04 275.337 MHz -40.9167 5 2 1 + 9.211e-05 365.993 MHz -40.9092 7 3 1 - 3.684e-07 368.036 MHz -40.906 9
ispassive(pfit)
ans = logical
1
passivity(pfit)
all(vertcat(pfit(:).A) == vertcat(fit(:).A))
ans = logical
1
Start makepassive
with Prescribed Poles and Zero C and D
To demonstrate that only C and D are modified by makepassive
, one can zero out C and D and re-run makepassive
. The output, pfit
still has the same poles as the input fit. The differences between pfit
and pfit2
arise because of the different starting points of the convex optimizations.
One can use this feature of the makepassive
function to produce a passive fit from a prescribed set of poles without any idea of starting C and D.
for k = 1:numel(fit) fit(k).C(:) = 0; fit(k).D(:) = 0; end pfit2 = makepassive(fit,S); passivity(pfit2)
all(vertcat(pfit2(:).A) == vertcat(fit(:).A))
ans = logical
1
Generate Equivalent SPICE Circuit from Passive Fit
The generateSPICE
function takes a passive fit and generates an equivalent circuit as a SPICE subckt file. The input fit is an N x N array of rfmodel.rational
objects as returned by rationalfit with an S-parameters object as input. The generated file is a SPICE model constructed solely of passive R, L, C elements and controlled source elements E, F, G, and H.
generateSPICE(pfit2,'mypassive.ckt') type mypassive.ckt
* Equivalent circuit model for mypassive.ckt .SUBCKT mypassive po1 po2 Vsp1 po1 p1 0 Vsr1 p1 pr1 0 Rp1 pr1 0 50 Ru1 u1 0 50 Fr1 u1 0 Vsr1 -1 Fu1 u1 0 Vsp1 -1 Ry1 y1 0 1 Gy1 p1 0 y1 0 -0.02 Vsp2 po2 p2 0 Vsr2 p2 pr2 0 Rp2 pr2 0 50 Ru2 u2 0 50 Fr2 u2 0 Vsr2 -1 Fu2 u2 0 Vsp2 -1 Ry2 y2 0 1 Gy2 p2 0 y2 0 -0.02 Rx1 x1 0 1 Fxc1_2 x1 0 Vx2 18.7469464276868 Cx1 x1 xm1 3.95175907242771e-09 Vx1 xm1 0 0 Gx1_1 x1 0 u1 0 -0.0922190094088541 Rx2 x2 0 1 Fxc2_1 x2 0 Vx1 -0.0837722394825499 Cx2 x2 xm2 3.95175907242771e-09 Vx2 xm2 0 0 Gx2_1 x2 0 u1 0 0.00772539294104206 Rx3 x3 0 1 Cx3 x3 0 2.73023891256077e-12 Gx3_1 x3 0 u1 0 -2.06042486944108 Rx4 x4 0 1 Cx4 x4 0 7.77758885464816e-12 Gx4_1 x4 0 u1 0 -2.91722728004894 Rx5 x5 0 1 Cx5 x5 0 2.29141629880011e-11 Gx5_1 x5 0 u1 0 -0.544081852880844 Rx6 x6 0 1 Cx6 x6 0 9.31845201582549e-11 Gx6_1 x6 0 u1 0 -0.654514144349138 Rx7 x7 0 1 Cx7 x7 0 4.89917765129955e-10 Gx7_1 x7 0 u1 0 -0.081150682957521 Rx8 x8 0 1 Cx8 x8 0 1.25490425576858e-08 Gx8_1 x8 0 u1 0 -0.947639642515798 Rx9 x9 0 1 Fxc9_10 x9 0 Vx10 18.3799951758361 Cx9 x9 xm9 3.95175907242771e-09 Vx9 xm9 0 0 Gx9_2 x9 0 u2 0 -0.0931995636552071 Rx10 x10 0 1 Fxc10_9 x10 0 Vx9 -0.0854447278512561 Cx10 x10 xm10 3.95175907242771e-09 Vx10 xm10 0 0 Gx10_2 x10 0 u2 0 0.00796341135237499 Rx11 x11 0 1 Cx11 x11 0 2.73023891256077e-12 Gx11_2 x11 0 u2 0 -2.08390040117714 Rx12 x12 0 1 Cx12 x12 0 7.77758885464816e-12 Gx12_2 x12 0 u2 0 -2.92728466103907 Rx13 x13 0 1 Cx13 x13 0 2.29141629880011e-11 Gx13_2 x13 0 u2 0 -0.60755498978755 Rx14 x14 0 1 Cx14 x14 0 9.31845201582549e-11 Gx14_2 x14 0 u2 0 -0.692661202952815 Rx15 x15 0 1 Cx15 x15 0 4.89917765129955e-10 Gx15_2 x15 0 u2 0 -0.0860909221892133 Rx16 x16 0 1 Cx16 x16 0 1.25490425576858e-08 Gx16_2 x16 0 u2 0 -0.948027270725434 Gyc1_1 y1 0 x1 0 -1 Gyc1_2 y1 0 x2 0 -1 Gyc1_3 y1 0 x3 0 -0.138997516772907 Gyc1_4 y1 0 x4 0 -0.0228656374371864 Gyc1_5 y1 0 x5 0 -1 Gyc1_6 y1 0 x6 0 -1 Gyc1_7 y1 0 x7 0 1 Gyc1_8 y1 0 x8 0 0.99981366678824 Gyc1_9 y1 0 x9 0 0.988833364887048 Gyc1_10 y1 0 x10 0 0.954427023481541 Gyc1_11 y1 0 x11 0 1 Gyc1_12 y1 0 x12 0 -1 Gyc1_13 y1 0 x13 0 0.809866454553765 Gyc1_14 y1 0 x14 0 0.941820890321495 Gyc1_15 y1 0 x15 0 -0.935047938274679 Gyc1_16 y1 0 x16 0 -1 Gyd1_1 y1 0 u1 0 0.603094947896403 Gyd1_2 y1 0 u2 0 -0.352309575151679 Gyc2_1 y2 0 x1 0 0.997602900366527 Gyc2_2 y2 0 x2 0 0.962184497756674 Gyc2_3 y2 0 x3 0 1 Gyc2_4 y2 0 x4 0 -1 Gyc2_5 y2 0 x5 0 0.900750606534717 Gyc2_6 y2 0 x6 0 0.996964239636478 Gyc2_7 y2 0 x7 0 -0.991552150259613 Gyc2_8 y2 0 x8 0 -1 Gyc2_9 y2 0 x9 0 -1 Gyc2_10 y2 0 x10 0 -1 Gyc2_11 y2 0 x11 0 -0.265688315029049 Gyc2_12 y2 0 x12 0 0.0684931208135682 Gyc2_13 y2 0 x13 0 -1 Gyc2_14 y2 0 x14 0 -1 Gyc2_15 y2 0 x15 0 1 Gyc2_16 y2 0 x16 0 0.999985365626095 Gyd2_1 y2 0 u1 0 -0.337215002653904 Gyd2_2 y2 0 u2 0 0.700223770278306 .ENDS