# Bode plot and cutoff frequency

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Aaron Connell
on 25 Nov 2016

Commented: suketu vaidya
on 25 Dec 2020

below I am creating a bode plot of the specified transfer function. I want to know if there is an option using bode plot options to mark the corner frequency on the plot and determine the magnitude and phase at that frequency. How would I go about doing this on the plot

% code

num=[1]; %set the numerator in a matrix

den=[1 1.5]; %set the denominator in a matrix

Transfer_Function=tf(num,den) % use the tf function to set the transfer function

bodeplot(Transfer_Function) %create a bode plot

grid

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### Accepted Answer

Star Strider
on 26 Nov 2016

Edited: Star Strider
on 26 Nov 2016

Unfortunately, while bodeplot can do much, for whatever reason, it’s not possible to overplot anything on it. A somewhat more primitive approach is necessary:

num=[1]; %set the numerator in a matrix

den=[1 1.5]; %set the denominator in a matrix

Transfer_Function=tf(num,den) % use the tf function to set the transfer function

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

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

phase= squeeze(phase);

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

dB3 = interp1(magr2, [wout phase mag], 0.5, 'spline'); % Find Frequency & Phase & Amplitude of Half-Power (-3 dB) Point

figure(1)

subplot(2,1,1)

semilogx(wout, 20*log10(mag), '-b', dB3(1), 20*log10(dB3(3)), '+r', 'MarkerSize',10)

grid

subplot(2,1,2)

semilogx(wout, phase, '-b', dB3(1), dB3(2), '+r', 'MarkerSize',10)

grid

EDIT —

The code I added takes the data created by the bode function (magnitude, phase and radian frequency respectively) and first uses interpolation to calculate the half-power point values of all three variables. The half-power point (or -3 dB point) is defined as half the value of the square of the normalised ratio of the magnitude. This is the ‘magr2’ (magnitude ratio squared) vector.

Since the ‘breakpoint’ or the ‘passband’ is defined as the half-power point, the interp1 call uses ‘magr2’ as the independent variable for the spline interpolation to approximate the value corresponding to the half-power value for the frequency, phase, and magnitude matrix [wout phase mag]. (There’s nothing magic about using the spline interpolation, and here a linear interpolation would likely be as accurate.) This magickally returns those corresponding values in the ‘dB3’ vector (corresponding to the -3 dB point). These are the radian frequency, phase, and magnitude for the half-power point, respectively, as requested. These interpolated values are then overplotted as ‘+’ on the transfer function magnitude and phase plots.

The plots are then straightforward to understand. In order to make them compatible with the bode plot format, I plotted the magnitude and marker as a decibel 20*log10() values. (For magnitudes, the 20 multiplier is used, for power a 10 multiplier is used.)

Parenthetically, the Signal Processing Toolbox freqz and freqs create regular subplots that it is possible to address directly. The Control System Toolbox (and related Toolboxes) apparently have their own formats, so it is necessary to take the ‘long way round’ here.

##### 3 Comments

### More Answers (1)

zahypeti
on 11 May 2017

If you have the Control System Tlbx you can also try the bandwidth function.

fb = bandwidth(sys)

##### 1 Comment

Star Strider
on 11 May 2017

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