Bode Plots Lecture

Objective: 

Today's lecture covered the process in creating Bode plots. The first step is to transform a circuit to its transfer function in terms of the given four possible transformation function gains. A transfer function is written in therms of factors that have real and imaginary parts. So we rewrite it by dividing out the zeros and poles. Thus, placing it in standard form. We then find the magnitude and phase by taking the natural log in terms of decibel values. The plot is created by sketching the asymptote lines and adding them or subtracting them to plot the actual lines.  

Group Practice Problems: 

1. The problem below shows a transfer function and are told to create a bode plot. The first step is to change the transfer function to its standard form and then take to the log of it in order to find its magnitude and phase. We then plot them by recording the corner frequencies, sketch the factors and then combine them by adding or subtracting to sketch the actual lines. 

Figure 1. The Bode plot of a transfer function.

2. We now have a new transfer function where one of our factors is squared. Similarly, to figure 1, we change the transfer function to its standard form and take the log and find the phase. Though we must point out that since one of the values is squared the log is multiplied by 40 instead of 20 when finding the gain or Hdb. 

Figure 2. Plotting the transfer function when one of the poles is squared.

3.  Figure 3 shows the calculation of resonance frequency, upper half and lower half frequencies. We also also calculate the bandwidth and quality factor from an RLC circuit. 

Figure 3.  Finding the resonance frequency and other values for an RLC circuit. 

Learning Outcome: 

We learned to create Bode plot for transfer functions by following some steps. The first step is to change the transfer function to standard form by taking out or dividing out the poles and zeros. We then find the magnitude by taking the log and then finding the phase. With this information, we are then able to create a bode plot by noticing the corner frequencies. We sketch the terms in dotted line and then add them together to obtain the over plot. Also, the phase plot in plotted based on the phase. We then consider resonant circuits in which in an RLC, the capacitive and inductive reactance are equal. From this, we can calculate the resonance frequency, quality factor, bandwidth, upper and lower power frequencies.