Of course, in a numerical engine like MATLAB, we can easily define our transfer functions directly on the s domain and call the desired built-in function to automatically perform this evaluation and create the appropriate frequency diagram, in this case, bode plot. To create a frequency response diagram, we need to evaluate both of these functions at different values of w in the frequency range of interest. And the phase angle is usually displayed in degrees. The magnitude is usually displayed in decibels, which is defined as 20 times the log of the amplitude ratio. Both of this will be functions of the frequency w.Īs a quick note, frequency diagrams are normally drawn on logarithmic scales. And the phase angle of that vector corresponds to the phase shift introduced by the system. The magnitude of that vector is the gain of the transfer function or, in other words, equivalent to the amplitude gain from the input to output sine waves. The resulting expression for G will be a vector in the complex plane- part real, part imaginary. Now, in general, if we need an analytic way to calculate this frequency responses directly from the dynamic equations of the system, in the Laplace domain, setting the operator s to a pure, imaginary number like jw is equivalent to exciting the system with a pure sinusoidal tone or frequency w. This is why when estimating responses empirically or experimentally people usually use random white noise or sinusoidal chirps with enough frequency content as excitations. Notice that in order to capture all the relevant dynamics, we need to make sure that we excite our system at enough frequency points to get a good trace. This type of frequency response diagram is what is normally called a bode plot. If each of these individual measurements is plotted on its own axis against the corresponding pure tone frequency of the sine wave, it will give us a single point on a frequency response diagram.īy repeating this process for a number of different pure tone frequencies, we can construct a trace for the amplitude variation, also known as the gain of the system, as well as a trace for the phase shift introduced by the system for any given frequency range. But it will not alter its fundamental frequency.Ĭomparing the input and the output sinusoidals, we can measure the change in amplitude and phase shift introduced by the system. Notice that a linear time-invariant system can affect the amplitude of the signal and can introduce a shift in the phase of the sine wave. By definition, if we fit in a pure sinusoidal tone into a generic linear time-invariant system, the output will also be a pure sinusoidal tone. = bode(FinalTF,freqMarkers) Īnd works great! Thanks to for the help.In this section, we're going to describe what a frequency response diagram is, as well as take a look at their primary characteristics. Now I managed to add markers to the specific frequencies I wanted like this: figure(4) Īxis() It just printed the bodeplot of the transfer function. Here is some sample code to illustrate the results. I'm using Matlab 2015, if it makes any difference.Īny help would be appreciated. Maybe because I'm using bodeplot instead of regular plot? I don't know how else to do it though. I tried using the function evalfr(), but tbh the values it returns seem a bit off.Ģ) Ignoring the previous point, even if I do the calculations by hand, I can't add them on the plot using this method, and I'm not sure what the problem is. I am currently running into two basic problems:ġ) I don't know how to get the specific dB at each frequency just by using the TF object. I know how to do it by clicking on the graph, but that will be too time consuming, as I have many plots to go through. What I want is to add markers on specific points in this plot (specifically I want to highlight the frequencies fp,fo,fs, you don't need to know what these are, they're just 3 different points on the x-axis, and the dB at each frequency) with code. Where FinalTF is the transfer function I'm talking about. Title('Butterworth LowPass Fifth Order') Setoptions(h,'FreqUnits','Hz','PhaseVisible','off') I have successfully calculated it and have plotted its bode response like this: % Butterworth Fifth Order Low Pass I am currently designing a 5th order Butterworth filter and looking at its transfer function response in Matlab.
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