# 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 s
^{2}+3s+50 = s^{2}+2ζω_{0}s+ω_{0}^{2},

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.