Bode Plot: Example 3

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 33.3
• A pole at s=-3
• A pole at s=0 
• A zero at s=-10

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 33.3 is equal to 30 dB).  The phase is constant at 0 degrees.
• The pole at 3 rad/sec is the green line.  It is 0 dB up to the break frequency, then drops off with a slope of -20 dB/dec.  The phase is 0 degrees up to 1/10 the break frequency (0.3 rad/sec) then drops linearly down to -90 degrees at 10 times the break frequency (30 rad/sec).
• The pole at the origin.  It is a straight line with a slope of -20 dB/dec.  It goes through 0 dB at 1 rad/sec.  The phase is -90 degrees.
• The zero at 10 rad/sec is the red line.  It is 0 dB up to the break frequency, then rises at 20 dB/dec.  The phase is 0 degrees up to 1/10 the break frequency (1 rad/sec) then rises  linearly to 90 degrees at 10 times the break frequency (100 rad/sec).

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

The overall asymptotic plot is the translucent pink line, the exact response is the black line.