find x or y at given point for f_cutoff, 0.1*f_cutoff and 10*f_cutoff

% %Need to replace so it looks the same but  with calculation of x at given y= -3.02 in magnitude plot
% and y at -45.01 deg, -84.28 deg, -5,7 deg 
% cut-off frequency atbandwidth from datatip  -3.02 dB 
clc;
clear all; close all; %%matlab
np = tf(0.999, [9.99e-4, 1])

np =
 
      0.999
  --------------
  0.000999 s + 1
 
Continuous-time transfer function.

% [mag,phase,w] = bode(np,w);
%plotting av teoretisk vs eksperimentell data
figure (1)
subplot(2,1,1)
bodemag(np,'k-.'); hold on
grid on
% cutoff frekvensen at -3.02 dB found with datatip
yline(-3.02000000267966,'r-','-3.02 dB', 'LabelHorizontalAlignment','left',  'Linewidth', 1.5)
xline(1001.21694896018,'r-','\omega_c = 1001.22 rad/s ','LabelVerticalAlignment','middle',  'Linewidth', 1.5)
title('1. ordens frekvens amplitude respons')
legend ('Simulated 1. order')
subplot(2,1,2)
h = bodeplot(np, 'k-.');
setoptions(h,'MagVisible','off'); hold on, grid on
% %Need to replace so it looks the same but  with calculation of x at given y= -3.02 in magnitude plot
% and y at -45.01 deg, -84.28 deg, -5,7 deg 
% cut-off frequency atbandwidth from datatip  -3.02 dB 
%calculate f at mag equal -3.02 dB
xline(1001.21694896018,'r-','\omega_c ','LabelVerticalAlignment','top', 'Linewidth', 1.5)
yline(  -45.0100,'r-','-45.01', 'LabelHorizontalAlignment','left','Linewidth', 1.5)
%data avlest fra datatip at 10_w_c [1.001216948960180e+04,-84.276493287076900]
xline(1001.21694896018*10,'b-','10*\omega_c ','LabelVerticalAlignment','t')
yline(-84.276493287076900,'b-','-84.28 deg', 'LabelHorizontalAlignment','left')
% data avlest fra datatip at 0.1_w_c [100.121694895791,-5.72603838444467]
xline(1001.21694896018*0.1,'m-','0.1*\omega_c','LabelVerticalAlignment','b')
yline(-5.72603838444467,'m-','-5.7 deg', 'LabelHorizontalAlignment','left')
% phase_shift[1001.21694882189,-45.0061545314931];
title('')
round(-84.276493287076900, 2)

ans = -84.2800

grid on

Answer 1

[Star Strider]

Use the interp1 funciton.

I wrote a short utility program that does exactly that —

% %Need to replace so it looks the same but  with calculation of x at given y= -3.02 in magnitude plot
% and y at -45.01 deg, -84.28 deg, -5,7 deg 
% cut-off frequency atbandwidth from datatip  -3.02 dB 
% clc;
% clear all; close all; %%matlab
np = tf(0.999, [9.99e-4, 1])

np =
 
      0.999
  --------------
  0.000999 s + 1
 
Continuous-time transfer function.

% [mag,phase,w] = bode(np,w);
%plotting av teoretisk vs eksperimentell data

[mag,phase,wout] = bode(np);
mags = squeeze(mag);
magsdB = mag2db(mags);
phases = squeeze(phase);

ydB = -3.02;
[wi,dBi] = intsx(wout,magsdB,ydB)

wi = 1.0012e+03

dBi = -3.0200

ydeg = [-45.01, -84.28, -5,-7];
for k = 1:numel(ydeg)
    [wdegi,phdgi] = intsx(wout,phases,ydeg(k));
    wdeg(k,:) = wdegi;
    phdg(k,:) = phdgi;
end

wdeg

wdeg = 4×1

1.0e+03 * 1.0014 9.9941 0.0876 0.1229

phdg

phdg = 4×1

-45.0100 -84.2800 -5.0000 -7.0000

function [xi,yi] = intsx(x,y,c)
% ARGUMENTS: (x,y): Vectors, c: Constant
    zci = find(diff(sign(y-c)));
    for k = 1:numel(zci)
        idxrng = max(1,zci(k)-1) : min(numel(x),zci(k)+1);
        xi(k,:) = interp1(y(idxrng)-c,x(idxrng),0);
        yi(k,:) = interp1(x(idxrng), y(idxrng), xi(k));
    end
end

I use bode here because it calculates and returns the requisite results.

This finds the appropriate radian frequency values for the chosen dependent variable values. I am sure you can take it from here.

.

[Olga Rakvag]

Thank you! Now it works :-)

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

.

[Olga Rakvag]

Here is the code, I just didn't used the function though, could be better if I would also calculated phase shift (degrees -5,7 deg and -84.28 deg ) at 0.1 w_cutoff and 10*w_cutoff, have you any suggestions?

clc;

clear all; close all; %%simulation of 1 order system

%variables given in oppgave 2-a

R=1e3;

RL=1e6;

C=1e-6;

%gain and time constant

tau=(C*R*RL)/(R+RL)

K=RL/(R+RL)

% calculation of 1. irder system

np = tf(K, [tau, 1])

[mag,phase,wout] = bode(np); % Get Plot Data

mag = squeeze(mag); % Reduce (1x1xN) Matrix To (1xN)

phase= squeeze(phase);

magr2 = (mag/max(mag)).^2; % Calculate Power Of Ratio Of 2mag/max(mag)’

% calculates cutoff frequency, phase shift and magnitude at -3 dB

% gir svar 1001.09989407495 -45.0028587822727 0.706365134034749]=

%[1001,1009 −45,0029 0,7064]= [1001.10 −45,00 0.71]

dB3 = interp1(magr2, [wout phase mag], 0.5, 'spline');

%calculates cutoff frequensy same answer as from formula 20*log(K)-3=-3.02 dB

%på s. 10 lab 2a

w_c=20*log10(dB3(3));

%plotting

figure (1)

subplot(2,1,1)

bodemag(np,'k-.'); hold on

grid on

% cutoff frekvensen at w_c=-3.0194 dB

yline(w_c,'r-',['' num2str(w_c) 'dB'], 'LabelHorizontalAlignment','left', 'Linewidth', 1.5)

xline(dB3(1),'r-', ['\omega_c =' num2str(dB3(1)) ' rad/s '],'LabelVerticalAlignment','middle', 'Linewidth', 1.5)

title('1. ordens frekvens amplitude respons')

legend ('Simulated 1. order')

subplot(2,1,2)

h = bodeplot(np, 'k-.');

setoptions(h,'MagVisible','off'); hold on, grid on

% visualisation of cutoff

xline(dB3(1),'r-','\omega_c ','LabelVerticalAlignment','top', 'Linewidth', 1.5)

yline( dB3(2),'r-',['' num2str(dB3(2)) 'deg'], 'LabelHorizontalAlignment','left','Linewidth', 1.5)

%data need to be calculated for 10_w_cso it will be apprx -84.276493287076900 deg

xline(dB3(1)*10,'b-','10*\omega_c ','LabelVerticalAlignment','t')

yline(-84.276493287076900,'b-','-84.28 deg', 'LabelHorizontalAlignment','left')

% data need to be calculated for 10_w_cso it will be apprx at 0.1_w_c -5.72603838444467 deg

xline(dB3(1)*0.1,'m-','0.1*\omega_c','LabelVerticalAlignment','b')

yline(-5.72603838444467,'m-','-5.7 deg', 'LabelHorizontalAlignment','left')

% phase_shift[1001.21694882189,-45.0061545314931];

title('')

grid on

[Star Strider]

I do not understand what you want to do.

If you want to calculate the system response at specific frequencies, use the freqresp function. (The function I posted does the opposite of that, returning the frequency for a specific magnitude or phase value.)

[Olga Rakvag]

I primarily want to calculate phase shifts at 0.1 of cutoff frequency and 10 of cut off frequency so I can then display them on bode phase shift plot. But never mind, it is already good :-)

[Star Strider]

Thank you!