How can I find the Transfer Function having Magnitude(dB), Phase(de... (2024)

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Liang Kar Yan on 10 Dec 2021

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Commented: Liang Kar Yan on 14 Dec 2021

Accepted Answer: Mathieu NOE

  • TF.m

I have 3 individual files which are Magnitude(dB), Phase(degrees) and Frequency(Hz) in excel. I need to find the transfer function with these data. After getting the transfer function, I need to plot back the graph (magnitude and phase) from transfer function to compare with my data.

I wish to get something like the picture attached below.

How can I find the Transfer Function having Magnitude(dB), Phase(de... (2)

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Mathieu NOE on 13 Dec 2021

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hello

can you also provide the 3 exel files ?

Liang Kar Yan on 13 Dec 2021

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  • Frequency.xlsx
  • Magnitude.xlsx
  • Phase.xlsx

Hi sure,

Thank you so much.

Star Strider on 13 Dec 2021

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Open in MATLAB Online

Something is definitely wrong with these data!

They do not describe a frequency-response function —

Freq = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/833095/Frequency.xlsx')

Freq = 2001×1

100.0000 100.1000 100.2000 100.3000 100.4000 100.5000 100.6000 100.7000 100.8000 100.9000

Magn = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/833100/Magnitude.xlsx')

Magn = 2001×1

-43.9413 -43.8619 -43.7825 -43.7031 -43.6236 -43.5442 -43.4648 -43.3853 -43.3059 -43.2265

Phse = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/833105/Phase.xlsx')

Phse = 2001×1

111.3686 105.0197 98.6691 92.3168 85.9627 79.6068 73.2493 66.8899 60.5289 54.1661

cplxv = Magn .* exp(1j*deg2rad(Phse))

cplxv =

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figure

subplot(2,1,1)

plot(Freq, Magn)

grid

subplot(2,1,2)

plot(Freq, Phse)

grid

How can I find the Transfer Function having Magnitude(dB), Phase(de... (6)

frd = idfrd(cplxv, Freq, 1/(2*Freq(end)))

frd =IDFRD model.Contains Frequency Response Data for 1 output(s) and 1 input(s).Response data is available at 2001 frequency points, ranging from 100 rad/s to 300 rad/s. Sample time: 0.0016667 secondsStatus: Created by direct construction or transformation. Not estimated.

figure

plot(Freq, imag(cplxv))

How can I find the Transfer Function having Magnitude(dB), Phase(de... (7)

NrPoles = nnz(islocalmax(imag(cplxv)))

NrPoles = 44

sys_tf = tfest(frd, 2, 1)

sys_tf = -19.56 s - 3578 ------------------------- s^2 + 0.9124 s + 1.296e04 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 "frd".Fit to estimation data: 2.943% FPE: 188.8, MSE: 188.1

figure

compare(frd, sys_tf)

grid

How can I find the Transfer Function having Magnitude(dB), Phase(de... (8)

.

Mathieu NOE on 14 Dec 2021

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Control Tutorials for MATLAB and SimulinkControl Tutorials for MATLAB and SimulinkMagnitude-only Bode plot of frequency responseFFT Magnitude and Phase Spectrum using MATLAB

hello @Star Strider

I believe Magn is given in dB (like in the plot)

so first think is to convert back to linear magnitude

Magn = 10.^(Magn/20) , and then

cplxv = Magn .* exp(1j*deg2rad(Phse))

Liang Kar Yan on 14 Dec 2021

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Hi @Star Strider, thank you for your help.

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Accepted Answer

Mathieu NOE on 14 Dec 2021

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hello

I tried a few options , IIR or FIR filters fit.

As the phase plot shows , there is a quite significant phase roll rate, idicating the presence of a huge delay in the system.

I assumed a sampling rate of Fs = 1000 hz and found out that more or less we can fit either a FIR or a IIr high pass filter in series with almost 200 samples of delay (hudge !!)

maybe there are more powerful tools then the simple invfreqz (not giving any good results here) or the manual fit I am doing here

FIR fit plot :

How can I find the Transfer Function having Magnitude(dB), Phase(de... (12)

IIR fit plot :

How can I find the Transfer Function having Magnitude(dB), Phase(de... (13)

clc

clearvars

Freq = readmatrix('Frequency.xlsx');

Magn_dB = readmatrix('Magnitude.xlsx');

Phse = readmatrix('Phase.xlsx');

figure(1)

subplot(211),plot(Freq,Magn_dB);

subplot(212),plot(Freq,Phse);

Magn = 10.^(Magn_dB/20) ;

%% high pass filter model (IIR)

Fs = 1000; % ? to be confirmed

N = 8; % filter order

dc_gain = Magn(end); % asymptotic value

[val,ind] = min(abs(Magn_dB - Magn_dB(end) + 5)); % - 5dB (vs dc_gain) cut off frequency index search

fc = Freq(ind); % - 5dB (vs dc_gain) cut off frequency

[b,a] = butter(N,2*fc/Fs,'high');

b = b*dc_gain; % apply dc gain on numerator

[g,p] = dbode(b,a,1/Fs,2*pi*Freq);

% adding delay due to sampling

nd = 200; % delay (samples)

rpd = -360*nd*Freq/Fs;

p = p+rpd; % adding filter phase to samples delay phase

p = mod(p,360);

p = p -180; % polarity correction

figure(1)

subplot(211),plot(Freq,Magn_dB,Freq,20*log10(g));

title('IIR model fit')

ylabel('Modulus (dB)');

subplot(212),plot(Freq,Phse,Freq,p);

xlabel('Frequency (Hz)');

ylabel('Phase (°)');% return

%% high pass filter model (FIR)

Fs = 1000; % ? to be confirmed

N = 20;

dc_gain = Magn(end); % asymptotic value

[val,ind] = min(abs(Magn_dB - Magn_dB(end) + 3)); % - 3dB (vs dc_gain) cut off frequency index search

fc = Freq(ind); % - 3dB (vs dc_gain) cut off frequency

[b,a] = fir1(N,2*fc/Fs,'high');

b = b*dc_gain; % apply dc gain on numerator

[g,p] = dbode(b,a,1/Fs,2*pi*Freq);

% adding delay due to sampling

Fs = 1000; % ? to be confirmed

nd = 200; % delay (samples)

rpd = -360*nd*Freq/Fs;

p = p+rpd; % adding filter phase to samples delay phase

p = mod(p,360);

p = p -180; % polarity correction

figure(2)

subplot(211),plot(Freq,Magn_dB,Freq,20*log10(g));

title('FIR model fit')

ylabel('Modulus (dB)');

subplot(212),plot(Freq,Phse,Freq,p);

xlabel('Frequency (Hz)');

ylabel('Phase (°)');

%% Id with invfreqz (FIR)

h = Magn .* exp(1j*180/pi*(Phse));

nb = 40+nd;

na = 1;

iter = 1000;

[bb,aa] = invfreqz(h,pi*Freq/Fs,nb,na,[],iter); % stable approximation to system

[g,p] = dbode(bb,aa,1/Fs,2*pi*Freq);

p = mod(p,360);

figure(3)

subplot(211),plot(Freq,Magn_dB,Freq,20*log10(g));

subplot(212),plot(Freq,Phse,Freq,p);

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Liang Kar Yan on 14 Dec 2021

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Hi @Mathieu NOE, thank you for your help. Is there any method to get the transfer function equation from the graph?

Mathieu NOE on 14 Dec 2021

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hello again

this is a method using ifft to fit a FIR model to a given complex FRF- it works on some examples like the one below

clc

clearvars

%

Fs = 1e3;

Freq = linspace(0,Fs/2,100);

b = fir1(48,[0.3 0.5]); % Window-based FIR filter design

frf = freqz(b,1,Freq,Fs);

if mod(length(frf),2)==0 % iseven

frf_sym = conj(frf(end:-1:2));

else

frf_sym = conj(frf(end-1:-1:2));

end

fir = real(ifft([frf frf_sym]));

frfid = freqz(fir,1,Freq,Fs);

figure(1)

subplot(211),plot(Freq,20*log10(abs(frf)),Freq,20*log10(abs(frfid)));

legend('FIR input model','identified FIR model');

subplot(212),plot(Freq,180/pi*angle(frf),Freq,180/pi*angle(frfid));

legend('FIR input model','identified FIR model');

but when I try to use it on your data , it fails ... ugh !

clc

clearvars

Fs = 1e3;

Freq = readmatrix('Frequency.xlsx');

Magn_dB = readmatrix('Magnitude.xlsx');

Phse = readmatrix('Phase.xlsx');

figure(1)

subplot(211),plot(Freq,Magn_dB);

subplot(212),plot(Freq,Phse);

Magn = 10.^(Magn_dB/20) ;

frf = Magn .* exp(1j*pi/180*(Phse)); % FRF complex

if mod(length(frf),2)==0 % iseven

frf_sym = conj(frf(end:-1:2));

else

frf_sym = conj(frf(end-1:-1:2));

end

fir = real(ifft([frf; frf_sym]));

frfid = freqz(fir,1,Freq,Fs);

figure(1)

subplot(211),plot(Freq,20*log10(abs(frf)),Freq,20*log10(abs(frfid)));

subplot(212),plot(Freq,180/pi*angle(frf),Freq,180/pi*angle(frfid));

Mathieu NOE on 14 Dec 2021

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I think we could get a better result if your data was available on broader frequency range (from 0 to Fs/2) is Fs = sampling rate

Liang Kar Yan on 14 Dec 2021

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Hi, thank you so much for your help. The frequency is actually at 100GHz to 300GHz.

Mathieu NOE on 14 Dec 2021

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are you measuring an analog or digital filter / circuit ?

seems very high frequency range for anything digital ....

Mathieu NOE on 14 Dec 2021

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converting my code from 'Hz' to GHz by factor 10^9 is just making a new scale factor on the frequency axis , but not any impact on the FIR model output by itself

clc

clearvars

Freq = readmatrix('Frequency.xlsx'); % in Hz

Freq = Freq*1e9;% now in GHz

Fs = 2.56*max(Freq);

Magn_dB = readmatrix('Magnitude.xlsx');

Phse = readmatrix('Phase.xlsx');

figure(1)

subplot(211),plot(Freq,Magn_dB);

subplot(212),plot(Freq,Phse);

Magn = 10.^(Magn_dB/20) ;

frf = Magn .* exp(1j*pi/180*(Phse)); % FRF complex

if mod(length(frf),2)==0 % iseven

frf_sym = conj(frf(end:-1:2));

else

frf_sym = conj(frf(end-1:-1:2));

end

fir = real(ifft([frf; frf_sym]));

% fir = fir(1:end/4);

frfid = freqz(fir,1,Freq,Fs);

figure(1)

subplot(211),plot(Freq,20*log10(abs(frf)),Freq,20*log10(abs(frfid)));

subplot(212),plot(Freq,180/pi*angle(frf),Freq,180/pi*angle(frfid));

Liang Kar Yan on 14 Dec 2021

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I'm actually designing a terahertz waveguide at 100GHz to 300GHz and want to observe the s parameters (for this data set is actually the s21 graph).

Liang Kar Yan on 14 Dec 2021

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I think the first code is what I want and I manage to get the transfer function as well, thank you so much.

Mathieu NOE on 14 Dec 2021

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this is maybe something for you

but beyong my limited time possibilities right now

all the best for the future

Liang Kar Yan on 14 Dec 2021

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Thanks for the useful information.

Thank you.

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How can I find the Transfer Function having Magnitude(dB), Phase(de... (2024)

FAQs

How do you find the magnitude of a transfer function in DB? ›

To calculate the magnitude of the transfer function, square the real part of the transfer function and the imaginary part of the transfer function. Add these two results together and then take the square root of the sum. The result is the magnitude of the transfer function, often expressed in decibels.

Know More ›
How do you find the magnitude and phase angle of a transfer function? ›

The magnitude of the transfer function can be found by replacing s with jω and then taking the magnitude and phase of the transfer function.

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How do you find the magnitude and phase response? ›

A geometric way to obtain approximate magnitude and phase frequency responses is using the effects of zeros and poles on the frequency response of an LTI system. G ( s ) | s = j Ω 0 = K j Ω 0 − z j Ω 0 − p = K Z → ( Ω 0 ) P → ( Ω 0 ) .

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How to find the phase response of a transfer function? ›

To obtain the phase response, we take the arctan of the numerator, and subtract from it the arctan of the denominator. (Angle of a complex number expressed as a vector is something you may not be familiar with.

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How do you convert dB to magnitude? ›

Description. y = db2mag( ydb ) returns the magnitude measurements, y , that correspond to the decibel (dB) values specified in ydb . The relationship between magnitude and decibels is ydb = 20 log10( y ).

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How to find the magnitude of a function? ›

Thus, the formula to determine the magnitude of a vector (in two-dimensional space) v = (x, y) is: |v| =√(x2 + y2). This formula is derived from the Pythagorean theorem. the formula to determine the magnitude of a vector (in three-dimensional space) V = (x, y, z) is: |V| = √(x2 + y2 + z2)

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What is the magnitude of the transfer function? ›

The magnitude of the transfer function is proportional to the product of the geometric distances on the s-plane from each zero to the point s divided by the product of the distances from each pole to the point.

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What is the magnitude and phase of a function? ›

The magnitude describes the strength of each frequency in the signal. The phase describes the sine/cosine phase of each frequency. The phase can also be thought of as the relative proportion of sines and cosines in the signal (i.e., a phase of zero contains only cosines and a phase of 90 degrees contains only sines).

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What is the magnitude gain of the transfer function? ›

Transfer function gain=Yssr(t), where Yss represents output y(t) at steady-state and r(t) is the input. The transfer function gain is the magnitude of the transfer function, putting s=0. Otherwise, it is also called the DC gain of the system, as s=0 when the input is constant DC.

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How do you calculate transfer function? ›

To find the transfer function, first take the Laplace Transform of the differential equation (with zero initial conditions). Recall that differentiation in the time domain is equivalent to multiplication by "s" in the Laplace domain. The transfer function is then the ratio of output to input and is often called H(s).

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What is magnitude response in dB? ›

Magnitude response is a measure of how the amplitude of a system's output signal varies with frequency. It is often expressed in decibels (dB) and is used to characterize the frequency response of electronic filters, amplifiers, and other signal processing devices.

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How to get magnitude of frequency response? ›

The frequency response of a system is defined as the steady-state response of the system to a sinusoidal input. H(jω) is called the sinusoidal transfer function. css = X|H(jω)|sin(ωt + Φ), where |H(jω)| is the magnitude of H(jω) and Φ = 6 H(jω) is the argument of H(jω).

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How do you find the magnitude of a charge transfer? ›

Using Coulomb's law, F = k q1 q2/r2 , its magnitude is given by the equation F = k q Q /r2 , for a point charge (a particle having a charge Q) acting on a test charge q at a distance r (see the image below).

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What is the meaning of magnitude of transfer function? ›

The magnitude of the transfer function is proportional to the product of the geometric distances on the s-plane from each zero to the point s divided by the product of the distances from each pole to the point.

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How do you find the magnitude of a translation? ›

We can find the magnitude and direction of a translation by finding a point and its image under the translation and determining the distance between these points and the direction of the ray from the point to its image.

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