02-01-2013, 10:00 AM
CREATING BODE PLOTS FROM A TRANSFER FUNCTION
1CREATING BODE.pdf (Size: 102.53 KB / Downloads: 156)
Determine the zeros and poles of the function:
We find the zeros and poles by observing the numerator and denominator respectively,
and determining the value of s that will make each term zero. The absolute value of that
term is the zero or pole. The power to which the expression is raised corresponds to the
order of the pole or zero.
Determining the slope of the Bode Amplitude Plot:
The order value of each zero and pole indicates the change in slope in multiples of
20 dB/decade. For example, an order of 2 means there is will be change in slope of
40 dB/decade at the frequency of the zero or pole. The slope is increased at zeros and
reduced at poles.
Beginning at the left of the graph, mark the top of each decade column with up or down
arrows indicating the slope at that decade. Each arrow stands for 20 dB/decade of slope.
In this case, since there is a 2nd order zero at w = 0, which is off the graph to the left, we
begin by marking the first decade with two up arrows.
Determining the slope of the Bode Phase Plot:
On the Bode Phase Plot, again use up and down arrows to mark the slope of the graph.
This time, each arrow represents a 45°/decade slope for each order of zero or pole.
Zeros cause an upward slope and poles cause a downward slope. Each pole or zero
exerts an influence over one decade on either side of the pole or zero frequency. For
example, a 2nd order pole causes a 90°/decade downward slope that extends from one
decade below to one decade above the pole frequency. This would be indicated on the
graph by two downward arrows on each side of the pole frequency. Some decades will
have both up and down arrows. These will be summed, with the result that some arrows
will cancel each other.
Determining the phase angles for the Bode Phase Plot:
Next, we mark the graph with the phase angle at each decade. The four up arrows due to
the 2nd order zero at w = 0 tell us that the plot begins at +180°. The phase angle remains
unchanged until we encounter the next two down arrows which cause a –90° shift to
+90°. The following decade has two up arrows and one down arrow, resulting in a net
-45° phase change, etc.