how to find the transfer function from LTspice

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francesco baldi el 23 de Dic. de 2021

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Comentada: Star Strider el 26 de Dic. de 2021

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hi there,

i have plotted the bode diagram of my transfer function from LTSpice to matlab using the following code:

filename = 'nameofthefile.txt';
fidi = fopen(filename, 'rt');
Dc = textscan(fidi, '%f(%fdB,%f°)', 'CollectOutput',1);
D = cell2mat(Dc);
figure
subplot(2,1,1)
semilogx(D(:,1), D(:,2))
title('Amplitude (dB)')
grid
subplot(2,1,2)
semilogx(D(:,1), D(:,3))
title('Phase (°)')
grid
xlabel('Frequency')

now i need to see the expression of the transfer function i plotted as a function of the frequency, but i don't know how to do it. Is there anyone who can help me to do it?

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Answer 1

Star Strider el 23 de Dic. de 2021

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Perhaps I am missing something, however ‘the expression of the transfer function i plotted as a function of the frequency’ is essentially the definition of the magnitude spectrum of the Bode plot.

If the desired result is a state-space (or other) realisation of system identified from the magnitude, phase and frequency, start with the idfrd function and follow the documentation to identify the model. Be certain that the units are the same as the System Identification Toolbox functions require, so it may be necessary to convert them approporiately.

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Star Strider el 24 de Dic. de 2021

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A second-order system provides a perfect fit —

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/842990/Draft1.txt', 'VariableNamingRule','preserve')

T1 = 401×2 table

Var1 Var2 ______ ______________________________________________________ 10 {'(-6.02060034191108e+000dB,-1.79999994078238e-002°)'} 10.233 {'(-6.02060036211185e+000dB,-1.84192732265253e-002°)'} 10.471 {'(-6.02060038326466e+000dB,-1.88483131850069e-002°)'} 10.715 {'(-6.02060040541437e+000dB,-1.92873467657410e-002°)'} 10.965 {'(-6.02060042860797e+000dB,-1.97366067499370e-002°)'} 11.22 {'(-6.02060045289464e+000dB,-2.01963313409642e-002°)'} 11.482 {'(-6.02060047832591e+000dB,-2.06667642906489e-002°)'} 11.749 {'(-6.02060050495572e+000dB,-2.11481550285142e-002°)'} 12.023 {'(-6.02060053284056e+000dB,-2.16407587940291e-002°)'} 12.303 {'(-6.02060056203956e+000dB,-2.21448367719392e-002°)'} 12.589 {'(-6.02060059261468e+000dB,-2.26606562307481e-002°)'} 12.882 {'(-6.02060062463075e+000dB,-2.31884906644261e-002°)'} 13.183 {'(-6.02060065815569e+000dB,-2.37286199374180e-002°)'} 13.49 {'(-6.02060069326061e+000dB,-2.42813304330296e-002°)'} 13.804 {'(-6.02060073001998e+000dB,-2.48469152052698e-002°)'} 14.125 {'(-6.02060076851176e+000dB,-2.54256741342303e-002°)'}

V2c = cellfun(@(x)sscanf(x, '(%fdB,%f°'), T1.Var2, 'Unif',0);

V2m = cell2mat(V2c')';

T2 = table('Size',[size(T1.Var1,1) 3],'VariableTypes',{'double','double','double'}, 'VariableNames',{'FreqHz','MagndB','PhasDg'});T2.FreqHz = T1.Var1;

T2.MagndB = V2m(:,1);

T2.PhasDg = V2m(:,2)

T2 = 401×3 table

FreqHz MagndB PhasDg ______ _______ _________ 10 -6.0206 -0.018 10.233 -6.0206 -0.018419 10.471 -6.0206 -0.018848 10.715 -6.0206 -0.019287 10.965 -6.0206 -0.019737 11.22 -6.0206 -0.020196 11.482 -6.0206 -0.020667 11.749 -6.0206 -0.021148 12.023 -6.0206 -0.021641 12.303 -6.0206 -0.022145 12.589 -6.0206 -0.022661 12.882 -6.0206 -0.023188 13.183 -6.0206 -0.023729 13.49 -6.0206 -0.024281 13.804 -6.0206 -0.024847 14.125 -6.0206 -0.025426

Mag = db2mag(T2.MagndB);

Phs = deg2rad(T2.PhasDg);

Rsp = Mag.*exp(1j*Phs)

Rsp =

0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0002i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0003i 0.5000 - 0.0004i 0.5000 - 0.0004i 0.5000 - 0.0004i 0.5000 - 0.0004i 0.5000 - 0.0004i 0.5000 - 0.0004i 0.5000 - 0.0004i 0.5000 - 0.0004i 0.5000 - 0.0004i 0.5000 - 0.0004i 0.5000 - 0.0004i 0.5000 - 0.0005i 0.5000 - 0.0005i 0.5000 - 0.0005i 0.5000 - 0.0005i 0.5000 - 0.0005i 0.5000 - 0.0005i 0.5000 - 0.0005i 0.5000 - 0.0005i 0.5000 - 0.0005i 0.5000 - 0.0006i 0.5000 - 0.0006i 0.5000 - 0.0006i 0.5000 - 0.0006i 0.5000 - 0.0006i 0.5000 - 0.0006i 0.5000 - 0.0006i 0.5000 - 0.0007i 0.5000 - 0.0007i 0.5000 - 0.0007i 0.5000 - 0.0007i 0.5000 - 0.0007i 0.5000 - 0.0007i 0.5000 - 0.0008i 0.5000 - 0.0008i 0.5000 - 0.0008i 0.5000 - 0.0008i 0.5000 - 0.0008i 0.5000 - 0.0008i 0.5000 - 0.0009i 0.5000 - 0.0009i 0.5000 - 0.0009i 0.5000 - 0.0009i 0.5000 - 0.0009i 0.5000 - 0.0010i 0.5000 - 0.0010i 0.5000 - 0.0010i 0.5000 - 0.0010i 0.5000 - 0.0011i 0.5000 - 0.0011i 0.5000 - 0.0011i 0.5000 - 0.0011i 0.5000 - 0.0012i 0.5000 - 0.0012i 0.5000 - 0.0012i 0.5000 - 0.0012i 0.5000 - 0.0013i 0.5000 - 0.0013i 0.5000 - 0.0013i 0.5000 - 0.0014i 0.5000 - 0.0014i 0.5000 - 0.0014i 0.5000 - 0.0015i 0.5000 - 0.0015i 0.5000 - 0.0015i 0.5000 - 0.0016i 0.5000 - 0.0016i 0.5000 - 0.0016i 0.5000 - 0.0017i 0.5000 - 0.0017i 0.5000 - 0.0018i 0.5000 - 0.0018i 0.5000 - 0.0018i 0.5000 - 0.0019i 0.5000 - 0.0019i 0.5000 - 0.0020i 0.5000 - 0.0020i 0.5000 - 0.0021i 0.5000 - 0.0021i 0.5000 - 0.0022i 0.5000 - 0.0022i 0.5000 - 0.0023i 0.5000 - 0.0023i 0.5000 - 0.0024i 0.5000 - 0.0024i 0.5000 - 0.0025i 0.5000 - 0.0025i 0.5000 - 0.0026i 0.5000 - 0.0027i 0.5000 - 0.0027i 0.5000 - 0.0028i 0.5000 - 0.0029i 0.5000 - 0.0029i 0.5000 - 0.0030i 0.5000 - 0.0031i 0.5000 - 0.0031i 0.5000 - 0.0032i 0.5000 - 0.0033i 0.5000 - 0.0034i 0.5000 - 0.0034i 0.5000 - 0.0035i 0.5000 - 0.0036i 0.5000 - 0.0037i 0.5000 - 0.0038i 0.5000 - 0.0039i 0.5000 - 0.0039i 0.5000 - 0.0040i 0.5000 - 0.0041i 0.5000 - 0.0042i 0.5000 - 0.0043i 0.5000 - 0.0044i 0.5000 - 0.0045i 0.5000 - 0.0046i 0.5000 - 0.0047i 0.5000 - 0.0049i 0.5000 - 0.0050i 0.4999 - 0.0051i 0.4999 - 0.0052i 0.4999 - 0.0053i 0.4999 - 0.0054i 0.4999 - 0.0056i 0.4999 - 0.0057i 0.4999 - 0.0058i 0.4999 - 0.0060i 0.4999 - 0.0061i 0.4999 - 0.0063i 0.4999 - 0.0064i 0.4999 - 0.0065i 0.4999 - 0.0067i 0.4999 - 0.0069i 0.4999 - 0.0070i 0.4999 - 0.0072i 0.4999 - 0.0073i 0.4999 - 0.0075i 0.4999 - 0.0077i 0.4999 - 0.0079i 0.4999 - 0.0081i 0.4999 - 0.0082i 0.4999 - 0.0084i 0.4999 - 0.0086i 0.4998 - 0.0088i 0.4998 - 0.0090i 0.4998 - 0.0092i 0.4998 - 0.0095i 0.4998 - 0.0097i 0.4998 - 0.0099i 0.4998 - 0.0101i 0.4998 - 0.0104i 0.4998 - 0.0106i 0.4998 - 0.0109i 0.4998 - 0.0111i 0.4997 - 0.0114i 0.4997 - 0.0116i 0.4997 - 0.0119i 0.4997 - 0.0122i 0.4997 - 0.0125i 0.4997 - 0.0128i 0.4997 - 0.0131i 0.4996 - 0.0134i 0.4996 - 0.0137i 0.4996 - 0.0140i 0.4996 - 0.0143i 0.4996 - 0.0146i 0.4996 - 0.0150i 0.4995 - 0.0153i 0.4995 - 0.0157i 0.4995 - 0.0161i 0.4995 - 0.0164i 0.4994 - 0.0168i 0.4994 - 0.0172i 0.4994 - 0.0176i 0.4994 - 0.0180i 0.4993 - 0.0184i 0.4993 - 0.0189i 0.4993 - 0.0193i 0.4992 - 0.0197i 0.4992 - 0.0202i 0.4991 - 0.0207i 0.4991 - 0.0212i 0.4991 - 0.0216i 0.4990 - 0.0221i 0.4990 - 0.0227i 0.4989 - 0.0232i 0.4989 - 0.0237i 0.4988 - 0.0243i 0.4988 - 0.0248i 0.4987 - 0.0254i 0.4986 - 0.0260i 0.4986 - 0.0266i 0.4985 - 0.0272i 0.4984 - 0.0278i 0.4984 - 0.0285i 0.4983 - 0.0291i 0.4982 - 0.0298i 0.4981 - 0.0305i 0.4980 - 0.0312i 0.4980 - 0.0319i 0.4979 - 0.0327i 0.4978 - 0.0334i 0.4976 - 0.0342i 0.4975 - 0.0350i 0.4974 - 0.0358i 0.4973 - 0.0366i 0.4972 - 0.0375i 0.4970 - 0.0383i 0.4969 - 0.0392i 0.4968 - 0.0401i 0.4966 - 0.0410i 0.4965 - 0.0420i 0.4963 - 0.0429i 0.4961 - 0.0439i 0.4959 - 0.0449i 0.4957 - 0.0460i 0.4955 - 0.0470i 0.4953 - 0.0481i 0.4951 - 0.0492i 0.4949 - 0.0503i 0.4946 - 0.0515i 0.4944 - 0.0526i 0.4941 - 0.0538i 0.4939 - 0.0550i 0.4936 - 0.0563i 0.4933 - 0.0576i 0.4930 - 0.0589i 0.4926 - 0.0602i 0.4923 - 0.0616i 0.4919 - 0.0630i 0.4916 - 0.0644i 0.4912 - 0.0658i 0.4908 - 0.0673i 0.4903 - 0.0688i 0.4899 - 0.0703i 0.4894 - 0.0719i 0.4889 - 0.0735i 0.4884 - 0.0752i 0.4879 - 0.0768i 0.4873 - 0.0785i 0.4868 - 0.0803i 0.4862 - 0.0820i 0.4855 - 0.0838i 0.4849 - 0.0857i 0.4842 - 0.0875i 0.4835 - 0.0894i 0.4827 - 0.0914i 0.4819 - 0.0934i 0.4811 - 0.0954i 0.4802 - 0.0974i 0.4793 - 0.0995i 0.4784 - 0.1016i 0.4774 - 0.1038i 0.4764 - 0.1060i 0.4754 - 0.1082i 0.4743 - 0.1105i 0.4731 - 0.1128i 0.4719 - 0.1151i 0.4707 - 0.1175i 0.4694 - 0.1199i 0.4680 - 0.1223i 0.4666 - 0.1248i 0.4652 - 0.1273i 0.4637 - 0.1298i 0.4621 - 0.1324i 0.4604 - 0.1350i 0.4587 - 0.1376i 0.4569 - 0.1403i 0.4551 - 0.1430i 0.4532 - 0.1457i 0.4512 - 0.1484i 0.4491 - 0.1512i 0.4470 - 0.1540i 0.4447 - 0.1568i 0.4424 - 0.1596i 0.4400 - 0.1624i 0.4376 - 0.1653i 0.4350 - 0.1681i 0.4324 - 0.1710i 0.4296 - 0.1739i 0.4268 - 0.1768i 0.4239 - 0.1796i 0.4209 - 0.1825i 0.4177 - 0.1854i 0.4145 - 0.1882i 0.4112 - 0.1911i 0.4078 - 0.1939i 0.4043 - 0.1967i 0.4007 - 0.1995i 0.3970 - 0.2022i 0.3931 - 0.2050i 0.3892 - 0.2077i 0.3852 - 0.2103i 0.3811 - 0.2129i 0.3768 - 0.2154i 0.3725 - 0.2179i 0.3681 - 0.2203i 0.3636 - 0.2227i 0.3590 - 0.2250i 0.3542 - 0.2272i 0.3494 - 0.2294i 0.3446 - 0.2314i 0.3396 - 0.2334i 0.3345 - 0.2353i 0.3294 - 0.2371i 0.3242 - 0.2387i 0.3189 - 0.2403i 0.3135 - 0.2418i 0.3081 - 0.2431i 0.3026 - 0.2444i 0.2971 - 0.2455i 0.2915 - 0.2465i 0.2859 - 0.2474i 0.2803 - 0.2482i 0.2746 - 0.2488i 0.2689 - 0.2493i 0.2631 - 0.2497i 0.2574 - 0.2499i 0.2516 - 0.2500i 0.2459 - 0.2500i 0.2401 - 0.2498i 0.2344 - 0.2495i 0.2287 - 0.2491i 0.2230 - 0.2485i 0.2173 - 0.2479i 0.2117 - 0.2470i 0.2061 - 0.2461i 0.2005 - 0.2450i 0.1950 - 0.2439i 0.1895 - 0.2426i 0.1842 - 0.2412i 0.1788 - 0.2397i 0.1736 - 0.2380i 0.1684 - 0.2363i 0.1633 - 0.2345i 0.1583 - 0.2326i 0.1533 - 0.2306i 0.1485 - 0.2285i 0.1437 - 0.2263i 0.1390 - 0.2240i 0.1345 - 0.2217i 0.1300 - 0.2193i 0.1256 - 0.2169i 0.1213 - 0.2143i 0.1171 - 0.2118i 0.1131 - 0.2092i 0.1091 - 0.2065i 0.1052 - 0.2038i 0.1014 - 0.2011i 0.0978 - 0.1983i 0.0942 - 0.1955i 0.0907 - 0.1927i 0.0874 - 0.1899i 0.0841 - 0.1870i 0.0809 - 0.1841i 0.0778 - 0.1813i 0.0749 - 0.1784i 0.0720 - 0.1755i 0.0692 - 0.1726i 0.0665 - 0.1698i 0.0639 - 0.1669i 0.0614 - 0.1640i 0.0589 - 0.1612i 0.0566 - 0.1584i 0.0543 - 0.1556i 0.0521 - 0.1528i 0.0500 - 0.1500i 0.0480 - 0.1472i 0.0460 - 0.1445i

Sizes = [size(T2.FreqHz); size(Rsp)]

Q3 = 2×2

401 1 401 1

sysfr = idfrd(Rsp,T2.FreqHz,0,'FrequencyUnit','Hz') % Create System Response Data Object

sysfr = IDFRD model. Contains Frequency Response Data for 1 output(s) and 1 input(s). Response data is available at 401 frequency points, ranging from 10 Hz to 1e+05 Hz. Status: Created by direct construction or transformation. Not estimated.

sys_ss = ssest(sysfr, 2) % State Space Realisation

sys_ss = Continuous-time identified state-space model: dx/dt = A x(t) + B u(t) + K e(t) y(t) = C x(t) + D u(t) + e(t) A = x1 x2 x1 -3919 1.652e-06 x2 1.32e-17 -2e+05 B = u1 x1 -2.096e-09 x2 256 C = x1 x2 y1 -0.0006452 390.6 D = u1 y1 0 K = y1 x1 0 x2 0 Parameterization: FREE form (all coefficients in A, B, C free). Feedthrough: none Disturbance component: none Number of free coefficients: 8 Use "idssdata", "getpvec", "getcov" for parameters and their uncertainties. Status: Estimated using SSEST on frequency response data "sysfr". Fit to estimation data: 100% FPE: 1.135e-31, MSE: 1.112e-31

figure

compare(sysfr, sys_ss)

sys_tf = tfest(sysfr, 2) % Transfer Function Realisation

sys_tf = 1e05 s + 3.919e08 --------------------------- s^2 + 2.039e05 s + 7.838e08 Continuous-time identified transfer function. Parameterization: Number of poles: 2 Number of zeros: 1 Number of free coefficients: 4 Use "tfdata", "getpvec", "getcov" for parameters and their uncertainties. Status: Estimated using TFEST on frequency response data "sysfr". Fit to estimation data: 100% FPE: 1.19e-29, MSE: 1.166e-29

figure

compare(sysfr, sys_tf)

figure

pzmap(sys_ss)

grid on

format long E

Poles = pole(sys_ss)

Poles = 2×1

1.0e+00 * -3.918846154562714e+03 -2.000000000000001e+05

Zeros = zero(sys_ss)

Zeros =

-3.918846154562714e+03

The phases are ‘off’ by 360° so exactly match.

.

Star Strider el 25 de Dic. de 2021

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That warning only occurs with tfest and it goes away when both the number of poles and the number of zeros are set specifically —

sys_tf = tfest(sysfr, 1,1)

I made that change here, and the system is identified correctly. Note that it has a highpass characteristic with a pole at infinity (with respect to floating-point precision).

The state space realisation continues to be a second-order system.

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/843515/Draft2.txt', 'VariableNamingRule','preserve')

T1 = 301×2 table

Var1 Var2 ______ _____________________________________________________ 1000 {'(-6.00777260984419e+000dB,1.79586560570654e+000°)'} 1023.3 {'(-6.00716963461470e+000dB,1.83749784854299e+000°)'} 1047.1 {'(-6.00653839179706e+000dB,1.88008566363902e+000°)'} 1071.5 {'(-6.00587756356241e+000dB,1.92365030242762e+000°)'} 1096.5 {'(-6.00518577135216e+000dB,1.96821344014452e+000°)'} 1122 {'(-6.00446157314733e+000dB,2.01379718070299e+000°)'} 1148.2 {'(-6.00370346062171e+000dB,2.06042406133642e+000°)'} 1174.9 {'(-6.00290985617443e+000dB,2.10811705697993e+000°)'} 1202.3 {'(-6.00207910983768e+000dB,2.15689958435995e+000°)'} 1230.3 {'(-6.00120949605494e+000dB,2.20679550575875e+000°)'} 1258.9 {'(-6.00029921032525e+000dB,2.25782913241795e+000°)'} 1288.2 {'(-5.99934636570885e+000dB,2.31002522754294e+000°)'} 1318.3 {'(-5.99834898918951e+000dB,2.36340900886699e+000°)'} 1349 {'(-5.99730501788862e+000dB,2.41800615073106e+000°)'} 1380.4 {'(-5.99621229512652e+000dB,2.47384278563210e+000°)'} 1412.5 {'(-5.99506856632595e+000dB,2.53094550518955e+000°)'}

V2c = cellfun(@(x)sscanf(x, '(%fdB,%f°'), T1.Var2, 'Unif',0);

V2m = cell2mat(V2c')';

T2 = table('Size',[size(T1.Var1,1) 3],'VariableTypes',{'double','double','double'}, 'VariableNames',{'FreqHz','MagndB','PhasDg'});T2.FreqHz = T1.Var1;

T2.MagndB = V2m(:,1);

T2.PhasDg = V2m(:,2)

T2 = 301×3 table

FreqHz MagndB PhasDg ______ _______ ______ 1000 -6.0078 1.7959 1023.3 -6.0072 1.8375 1047.1 -6.0065 1.8801 1071.5 -6.0059 1.9237 1096.5 -6.0052 1.9682 1122 -6.0045 2.0138 1148.2 -6.0037 2.0604 1174.9 -6.0029 2.1081 1202.3 -6.0021 2.1569 1230.3 -6.0012 2.2068 1258.9 -6.0003 2.2578 1288.2 -5.9993 2.31 1318.3 -5.9983 2.3634 1349 -5.9973 2.418 1380.4 -5.9962 2.4738 1412.5 -5.9951 2.5309

Mag = db2mag(T2.MagndB);

Phs = deg2rad(T2.PhasDg);

Rsp = Mag.*exp(1j*Phs)

Rsp =

0.5005 + 0.0157i 0.5005 + 0.0161i 0.5005 + 0.0164i 0.5006 + 0.0168i 0.5006 + 0.0172i 0.5006 + 0.0176i 0.5006 + 0.0180i 0.5007 + 0.0184i 0.5007 + 0.0189i 0.5007 + 0.0193i 0.5008 + 0.0197i 0.5008 + 0.0202i 0.5009 + 0.0207i 0.5009 + 0.0212i 0.5009 + 0.0216i 0.5010 + 0.0221i 0.5010 + 0.0227i 0.5011 + 0.0232i 0.5011 + 0.0237i 0.5012 + 0.0243i 0.5012 + 0.0248i 0.5013 + 0.0254i 0.5014 + 0.0260i 0.5014 + 0.0266i 0.5015 + 0.0272i 0.5016 + 0.0278i 0.5016 + 0.0285i 0.5017 + 0.0291i 0.5018 + 0.0298i 0.5019 + 0.0305i 0.5020 + 0.0312i 0.5020 + 0.0319i 0.5021 + 0.0327i 0.5022 + 0.0334i 0.5024 + 0.0342i 0.5025 + 0.0350i 0.5026 + 0.0358i 0.5027 + 0.0366i 0.5028 + 0.0375i 0.5030 + 0.0383i 0.5031 + 0.0392i 0.5032 + 0.0401i 0.5034 + 0.0410i 0.5035 + 0.0420i 0.5037 + 0.0429i 0.5039 + 0.0439i 0.5041 + 0.0449i 0.5043 + 0.0460i 0.5045 + 0.0470i 0.5047 + 0.0481i 0.5049 + 0.0492i 0.5051 + 0.0503i 0.5054 + 0.0515i 0.5056 + 0.0526i 0.5059 + 0.0538i 0.5061 + 0.0550i 0.5064 + 0.0563i 0.5067 + 0.0576i 0.5070 + 0.0589i 0.5074 + 0.0602i 0.5077 + 0.0616i 0.5081 + 0.0630i 0.5084 + 0.0644i 0.5088 + 0.0658i 0.5092 + 0.0673i 0.5097 + 0.0688i 0.5101 + 0.0703i 0.5106 + 0.0719i 0.5111 + 0.0735i 0.5116 + 0.0752i 0.5121 + 0.0768i 0.5127 + 0.0785i 0.5132 + 0.0803i 0.5138 + 0.0820i 0.5145 + 0.0838i 0.5151 + 0.0857i 0.5158 + 0.0875i 0.5165 + 0.0894i 0.5173 + 0.0914i 0.5181 + 0.0934i 0.5189 + 0.0954i 0.5198 + 0.0974i 0.5207 + 0.0995i 0.5216 + 0.1016i 0.5226 + 0.1038i 0.5236 + 0.1060i 0.5246 + 0.1082i 0.5257 + 0.1105i 0.5269 + 0.1128i 0.5281 + 0.1151i 0.5293 + 0.1175i 0.5306 + 0.1199i 0.5320 + 0.1223i 0.5334 + 0.1248i 0.5348 + 0.1273i 0.5363 + 0.1298i 0.5379 + 0.1324i 0.5396 + 0.1350i 0.5413 + 0.1376i 0.5431 + 0.1403i 0.5449 + 0.1430i 0.5468 + 0.1457i 0.5488 + 0.1484i 0.5509 + 0.1512i 0.5530 + 0.1540i 0.5553 + 0.1568i 0.5576 + 0.1596i 0.5600 + 0.1624i 0.5624 + 0.1653i 0.5650 + 0.1681i 0.5676 + 0.1710i 0.5704 + 0.1739i 0.5732 + 0.1768i 0.5761 + 0.1796i 0.5791 + 0.1825i 0.5823 + 0.1854i 0.5855 + 0.1882i 0.5888 + 0.1911i 0.5922 + 0.1939i 0.5957 + 0.1967i 0.5993 + 0.1995i 0.6030 + 0.2022i 0.6069 + 0.2050i 0.6108 + 0.2077i 0.6148 + 0.2103i 0.6189 + 0.2129i 0.6232 + 0.2154i 0.6275 + 0.2179i 0.6319 + 0.2203i 0.6364 + 0.2227i 0.6410 + 0.2250i 0.6458 + 0.2272i 0.6506 + 0.2294i 0.6554 + 0.2314i 0.6604 + 0.2334i 0.6655 + 0.2353i 0.6706 + 0.2371i 0.6758 + 0.2387i 0.6811 + 0.2403i 0.6865 + 0.2418i 0.6919 + 0.2431i 0.6974 + 0.2444i 0.7029 + 0.2455i 0.7085 + 0.2465i 0.7141 + 0.2474i 0.7197 + 0.2482i 0.7254 + 0.2488i 0.7311 + 0.2493i 0.7369 + 0.2497i 0.7426 + 0.2499i 0.7484 + 0.2500i 0.7541 + 0.2500i 0.7599 + 0.2498i 0.7656 + 0.2495i 0.7713 + 0.2491i 0.7770 + 0.2485i 0.7827 + 0.2479i 0.7883 + 0.2470i 0.7939 + 0.2461i 0.7995 + 0.2450i 0.8050 + 0.2439i 0.8105 + 0.2426i 0.8158 + 0.2412i 0.8212 + 0.2397i 0.8264 + 0.2380i 0.8316 + 0.2363i 0.8367 + 0.2345i 0.8417 + 0.2326i 0.8467 + 0.2306i 0.8515 + 0.2285i 0.8563 + 0.2263i 0.8610 + 0.2240i 0.8655 + 0.2217i 0.8700 + 0.2193i 0.8744 + 0.2169i 0.8787 + 0.2143i 0.8829 + 0.2118i 0.8869 + 0.2092i 0.8909 + 0.2065i 0.8948 + 0.2038i 0.8986 + 0.2011i 0.9022 + 0.1983i 0.9058 + 0.1955i 0.9093 + 0.1927i 0.9126 + 0.1899i 0.9159 + 0.1870i 0.9191 + 0.1841i 0.9222 + 0.1813i 0.9251 + 0.1784i 0.9280 + 0.1755i 0.9308 + 0.1726i 0.9335 + 0.1698i 0.9361 + 0.1669i 0.9386 + 0.1640i 0.9411 + 0.1612i 0.9434 + 0.1584i 0.9457 + 0.1556i 0.9479 + 0.1528i 0.9500 + 0.1500i 0.9520 + 0.1472i 0.9540 + 0.1445i 0.9559 + 0.1418i 0.9577 + 0.1391i 0.9595 + 0.1365i 0.9611 + 0.1339i 0.9628 + 0.1313i 0.9643 + 0.1287i 0.9658 + 0.1262i 0.9672 + 0.1237i 0.9686 + 0.1212i 0.9700 + 0.1188i 0.9712 + 0.1164i 0.9725 + 0.1141i 0.9736 + 0.1118i 0.9748 + 0.1095i 0.9758 + 0.1072i 0.9769 + 0.1050i 0.9779 + 0.1028i 0.9788 + 0.1007i 0.9797 + 0.0986i 0.9806 + 0.0965i 0.9815 + 0.0945i 0.9823 + 0.0925i 0.9830 + 0.0905i 0.9838 + 0.0886i 0.9845 + 0.0867i 0.9852 + 0.0849i 0.9858 + 0.0830i 0.9864 + 0.0813i 0.9870 + 0.0795i 0.9876 + 0.0778i 0.9881 + 0.0761i 0.9887 + 0.0744i 0.9892 + 0.0728i 0.9896 + 0.0712i 0.9901 + 0.0697i 0.9905 + 0.0682i 0.9909 + 0.0667i 0.9913 + 0.0652i 0.9917 + 0.0638i 0.9921 + 0.0624i 0.9924 + 0.0610i 0.9928 + 0.0596i 0.9931 + 0.0583i 0.9934 + 0.0570i 0.9937 + 0.0558i 0.9940 + 0.0545i 0.9943 + 0.0533i 0.9945 + 0.0521i 0.9948 + 0.0510i 0.9950 + 0.0498i 0.9952 + 0.0487i 0.9954 + 0.0476i 0.9956 + 0.0466i 0.9958 + 0.0455i 0.9960 + 0.0445i 0.9962 + 0.0435i 0.9964 + 0.0425i 0.9965 + 0.0416i 0.9967 + 0.0406i 0.9968 + 0.0397i 0.9970 + 0.0388i 0.9971 + 0.0380i 0.9972 + 0.0371i 0.9974 + 0.0363i 0.9975 + 0.0355i 0.9976 + 0.0347i 0.9977 + 0.0339i 0.9978 + 0.0331i 0.9979 + 0.0324i 0.9980 + 0.0316i 0.9981 + 0.0309i 0.9982 + 0.0302i 0.9982 + 0.0295i 0.9983 + 0.0289i 0.9984 + 0.0282i 0.9985 + 0.0276i 0.9985 + 0.0269i 0.9986 + 0.0263i 0.9987 + 0.0257i 0.9987 + 0.0252i 0.9988 + 0.0246i 0.9988 + 0.0240i 0.9989 + 0.0235i 0.9989 + 0.0230i 0.9990 + 0.0224i 0.9990 + 0.0219i 0.9991 + 0.0214i 0.9991 + 0.0209i 0.9992 + 0.0205i 0.9992 + 0.0200i 0.9992 + 0.0196i 0.9993 + 0.0191i 0.9993 + 0.0187i 0.9993 + 0.0182i 0.9994 + 0.0178i 0.9994 + 0.0174i 0.9994 + 0.0170i 0.9994 + 0.0166i 0.9995 + 0.0163i 0.9995 + 0.0159i

Sizes = [size(T2.FreqHz); size(Rsp)]

Sizes = 2×2

301 1 301 1

sysfr = idfrd(Rsp,T2.FreqHz,0,'FrequencyUnit','Hz') % Create System Response Data Object

sysfr = IDFRD model. Contains Frequency Response Data for 1 output(s) and 1 input(s). Response data is available at 301 frequency points, ranging from 1000 Hz to 1e+06 Hz. Status: Created by direct construction or transformation. Not estimated.

sys_ss = ssest(sysfr, 2) % State Space Realisation

sys_ss = Continuous-time identified state-space model: dx/dt = A x(t) + B u(t) + K e(t) y(t) = C x(t) + D u(t) + e(t) A = x1 x2 x1 -2e+05 1.087e+13 x2 -1.526e-18 -1.79e+21 B = u1 x1 -6.066e-15 x2 3.436e+10 C = x1 x2 y1 -479.5 5.21e+10 D = u1 y1 0 K = y1 x1 0 x2 0 Parameterization: FREE form (all coefficients in A, B, C free). Feedthrough: none Disturbance component: none Number of free coefficients: 8 Use "idssdata", "getpvec", "getcov" for parameters and their uncertainties. Status: Estimated using SSEST on frequency response data "sysfr". Fit to estimation data: 100% FPE: 1.01e-30, MSE: 9.839e-31

figure

compare(sysfr, sys_ss)

sys_tf = tfest(sysfr, 1,1) % Transfer Function Realisation

sys_tf = s + 1e05 ---------- s + 200000 Continuous-time identified transfer function. Parameterization: Number of poles: 1 Number of zeros: 1 Number of free coefficients: 3 Use "tfdata", "getpvec", "getcov" for parameters and their uncertainties. Status: Estimated using TFEST on frequency response data "sysfr". Fit to estimation data: 100% FPE: 1.251e-31, MSE: 1.226e-31

figure

compare(sysfr, sys_tf)

figure

pzmap(sys_ss)

grid on

format long E

Poles = pole(sys_ss)

Poles = 2×1

1.0e+00 * -2.000000000000003e+05 -1.790281097801373e+21

Zeros = zero(sys_ss)

Zeros =

-9.999999933194378e+04

figure

nyquist(sys_ss)

figure

impulse(sys_ss)

figure

step(sys_ss)

The state space realisation had no problem with the order, however the transfer function realisation does.

This is interesting!

.

francesco baldi el 26 de Dic. de 2021

i'm sorry for the number of questions i'm asking you, i hope it is the last one:

let's assume that i succesfully exported the .txt file of my transfer function (H) from spice to Matlab, and i can see the Bode diagrams. Now, i need to use the values of H to calculate other parameters (G). For example, i need to compute this operation: G = H*100/(1 - H). Do i need to estimate the state space reasilation and find the transfer function of H (as we did), or there was a way to cumpute this operation without writing all this code but only with the Bode diagram exported from Spice?

Star Strider el 26 de Dic. de 2021

Abrir en MATLAB Online

I remember something like that from classical control. (I have done very little with classical control, and mostly use modern control with what I do.)

Using the transfer function realisation for what I believe to be ‘H’ here —

s + 1e05

----------

s + 200000

the Symbolic Math Toolbox makes this relatively straightforward —

syms s

H = (s + 1e05 ) / (s + 200000)

H =

G = H*100/(1 - H)

G =

G = simplifyFraction(G)

G =

GdB = vpa(20*log10(abs(G)))

GdB =

figure

hfp = fplot(G, [0 1E+5]);

Xv = hfp.XData

Xv = 1×45

1.0e+05 * 0 0.0209 0.0455 0.0692 0.0909 0.1132 0.1364 0.1614 0.1818 0.2071 0.2273 0.2492 0.2727 0.2946 0.3182 0.3435 0.3636 0.3880 0.4091 0.4330 0.4545 0.4771 0.5000 0.5227 0.5455 0.5691 0.5909 0.6155 0.6364 0.6587

Yv = hfp.YData

Yv = 1×45

100.0000 102.0855 104.5455 106.9249 109.0909 111.3208 113.6364 116.1441 118.1818 120.7148 122.7273 124.9198 127.2727 129.4575 131.8182 134.3534 136.3636 138.8011 140.9091 143.3013 145.4545 147.7062 150.0000 152.2733 154.5455 156.9085 159.0909 161.5458 163.6364 165.8701

grid

xlabel('Frequency (Hz)')

ylabel('Absolute Amplitude')

figure

semilogx(Xv, Yv, 'LineWidth',2)

grid

xlabel('Frequency (Hz)')

ylabel('Amplitude (dB)')

(I had problems with fplot and the logarithmic x-axis, so I extracted the data and plotted it using semilogx.)

I am not exactly certain what the problem is, since the Symbolic Math Toolbox will do all the ‘heavy lifting’ here to calculate the desired result. That of course will work with other transfer functions as well.

.

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