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Sketching Bode Magnitude and Phase Plots

MEM 639 – Real-time Microcomputer Controls 1

What is a Bode Plot and why would I care?

Page 3: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

Characterizes if should lead or lag….

Page 4: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

Page 5: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

Bode Plots: Why Study Them?

Input: 0.1)( tVi

Output (dots): )(tVo

• Output reaches 63.6% of steady-state at 0.47 ms

• Note: 1/0.00047 = 2127 radians/sec

Recall: RC Low-pass filter time response plot

Page 6: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

Low Pass Filter Bode PlotDefinition: A Bode diagram consists of 2 plots. The first plots the output/input ratio[dB] versus frequency. The second plots the phase angle versus frequency.Typically a semi-log plot for frequency is used

Low Pass Filter Bode Plot Diagram:

-3 dB

2127 radians/sec

Thus the -3 dB point represents the frequency corresponding to about 1 time constant

Page 7: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

Phase Shift Significance

Observe: Apply a sine voltage input (338 Hz) into a low-pass RC filter

Hence see that this is approximately the 45 degree lag shown on Bode plot

Bode phase plot on previous slide says 45-degree lag at 2127 radians/sec [338 Hz]

Period sec003.00019.00049.0 T0.003 sec = 333.3 Hz

sec00042.000148.00019.0 t

deg 502

Page 8: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

Step 1: Semi-Log Paper

Page 9: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

Step 2: Label Axis

Note units

Page 10: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

Step 3: Calculate magnitude [dB] and phase angle [deg]

Page 11: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

Step 4: Plot magnitude [dB] versus frequency [Hz]

Page 12: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

Step 5: Sketch slope and -3 dB point, identify cutoff frequencies

Page 13: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

Step 6: Plot phase angle [deg] versus frequency [Hz]. Label inflection point

Page 14: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

System ID Given the Bode PlotProblem: Given the following Bode Plot, calculate the transfer function

Page 15: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

Step 1: Note that the magnitude is not zero at start and slope is -20 dB/dec

sKTF1

Step 2: Slope decreases -20 dB/dec, hence have another pole. with time constant

52.0

1Hence

15s1TF2

Step 3: Slope increase +20 dB/dec, hence a zero has been added.

2.0cThe cutoff frequency

8.0cThe cutoff frequency The time constant is

25.18.0

Hence

125.1TF3 s

Step 4: Slope decreases another 20 dB/dec. This means a simple pole was added

The cutoff frequency is 10c The time constant

1.0101

Hence

10.1s1TF4

Step 5: Take product of all sub transfer functions

)11.0)(15(1)K(1.25s)(TF

ssssG

Step 6: Determine the value of K

Take decibel log of each side and replace s with j

11.0log2

2015log2

20log2025.11log2

20log20)(log20 222222 KsG

(1)

Page 17: Sketching Bode Magnitude and Phase Plots - Drexel … · Sketching Bode Magnitude and Phase Plots ... Hence see that this is approximately the 45 degree lag shown on Bode plot Bode

From Bode magnitude plot, see that at 1.0 have dB 60)(log20 jG

Thus substituting this frequency into the (1)

4103.4969.0200673.0log20dB 60 K

90.40log20 K

9.110K

Hence

)11.0)(15()125.1(9.110)(

sss

ssG

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