# Bode Plot: Example 4

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 3.

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

The transfer function has 4 components:

- A constant of -10
- A pole at s=-10
- A doubly repeated pole at s=-1
- A zero at the origin

## 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 10 is equal to 20 dB). The phase is constant at -180
degrees (constant is negative).
- The pole at 10 rad/sec is the blue
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 then drops linearly down to -90 degrees at 10 times the break
frequency.
- The repeated pole at 1 rad/sec is
the green line. It is 0 dB up to the break frequency, then drops off
with a slope of -40 dB/dec. The phase is 0 degrees up to 1/10 the break
frequency then drops linearly down to -180 degrees at 10 times the break
frequency. The magnitude and phase drop twice as steeply as those
for a single pole.
- The zero at the origin is the red
line. It has a slope of +20 dB/dec and goes through 0 dB at 1 rad/sec.
The phase is 90 degrees.

## 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.