Bode Plot: Example 5

Draw the Bode Diagram for the transfer function:

Step 1: Rewrite the transfer function in proper form.

Make both the lowest order term in the numerator and denominator unity.  The numerator is an order 1 polynomial, the denominator is order 2.

Step 2: Separate the transfer function into its constituent parts.

The transfer function has 4 components:

• A constant of 6
• A zero at s = -10
• Complex conjugate poles at the roots of s²+3s+50 = s²+2ζω₀s+ω₀², 
  so

Step 3: Draw the Bode diagram for each part.

This is done in the diagram below.

• The constant is the cyan line (A quantity of 6 is equal to 15.5 dB).  The phase is constant at 0 degrees.
• The zero at 10 rad/sec is the green line.  It is 0 dB up to the break frequency, then rises with a slope of +20 dB/dec.  The phase is 0 degrees up to 1/10 the break frequency then rises linearly to +90 degrees at 10 times the break frequency.
• The plots for the complex conjugate poles are shown in blue.  They cause a peak of:
                              
  at a frequency of
                  
  This is shown by the blue circle.  The phase goes from the low frequency asymptote (0 degrees) at
               
  to the high frequency asymptote at
               

Step 4:  Draw the overall Bode diagram by adding up the results from step 3.

The exact response is the black line.