However, we still need to take the Bode plot of the plant of our power supply and with the addition of some extra circuitry change its shape so that the final Bode plot meets the stability criteria. The extra circuitry that allows us to change the shape of the Bode plot to what we desire is our compensator. Typically in analog PSUs this is just an inverting op-amp with a few capacitors and resistors. The compensator circuit is usually very simple; the hard part is calculating the correct values of the capacitors and the resistors to get the correct shape of the overall Bode Plot. How do we calculate these? Do we randomly pick a bunch of components, solder them on and hope that the power supply magically becomes stable? No, we clearly need a mathematical method of linking our capacitors and resistors to the shape of the Bode plot; this is the job of our transfer function. A transfer function is simply a mathematical model of our circuit that relates it input to its output. It follows therefore that if we have the transfer function of our system and I use a known sine wave as my input (say 1V amplitude at 10Hz), I can then calculate the amplitude and phase of the sine wave that comes out. Et voilà; we have a way of mathematically plotting the Bode plot of our system before building it. ## Plotting Bode Plots from Transfer FunctionsThe transfer function relates the input to the output and by definition it is: Please register or login to download the complete version of this resourceConsider the simple low pass filter shown in Figure 1. Please register or login to download the complete version of this resourceUsing, the potential divider equation we have: Please register or login to download the complete version of this resourcePlease note that we only use the Laplace operate “s” to simplify the algebra. There is nothing to fear about Laplace; it is just another mathematical tool to help us analyse circuits. Substituting Xc and a little bit of algebra results in my transfer function H(s): Please register or login to download the complete version of this resourceYou can see from the previous equation the transfer function is a complex number. This is great news because it means that now as I vary the frequency f, I can plot my gain and my phase; i.e. I have a way of relating the component values R and C to the shape of the Bode plot. I have achieved my objective! Moreover, if I am not happy with the shape of the Bode plot I can influence its shape by changing the values of R and C. We know from our mathematics classes how to get the gain a complex number: Please register or login to download the complete version of this resourceNote that the result is not complex and therefore I can plot my gain vs. frequency which is usually done in decibels as shown in Figure 2. This is my gain plot of my Bode plot. Please register or login to download the complete version of this resourceI can now do the same thing for my phase. I know from school mathematics, how to work out the phase of the complex number. In my case this will be: Please register or login to download the complete version of this resourceAgain this equation is not complex and therefore I can plot my phase vs. frequency to get the phase plot of my Bode plot. This is shown in Figure 3. Please register or login to download the complete version of this resource |