Frequency Response

1
Frequency Response

• Instructor Chia-Ming Tsai
• Dept. of Electronics Engineering
• National Chiao Tung University

2
Contents

• Introduction
• Transfer Function
• The Decibel Scale
• Bode Plots
• Series Resonance
• Parallel Rosonance
• Passive Filters
• Active Filters
• Applications

3
Introduction

• Analysis with a constant frequency is already
  learned.
• To obtain the frequency response
• Keep the amplitude and the phase of the
  sinusoidal source constant. (amplitude 1, phase
  0)
• Sweep the frequency from a starting frequency to
  a stop frequency.
• Plot the amplitude and the phase of the desired
  voltage or current versus frequency.

4
Transfer Function

• The transfer function H(?)
• can be expressed as
• Zeros the roots of N(?)0
• Poles the roots of D(?)0

5
Example 1
Time domain
Phasor domain
6
Example 2
7
Example 3
8
The Thought of Bode Plots

• It is quite difficult to handle the plotting of
  the transfer function in a linear scale.
• If the transfer function is transformed to a
  logarithmic scale, then the plotting becomes much
  more easy.

9
The Decibel (dB) Scale
10
Bode Plots
11
Bode Plots

• Steps to construct a Bode plot
• Plot each factor separately.
• Additively combine all of them graphically
  because of the logarithms involved.
• The mathematical convenience of the logarithm
  makes the Bode plots a powerful tool.
• Straight-line plots used instead of actual plots.

12
Bode Plots A Gain K
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Bode Plots Zero/Pole at Origin
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Bode Plots Simple Zero
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Bode Plots Simple Pole
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Bode Plots Quadratic Pole
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Bode Plots Quadratic Zero
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Summary
19
Summary
20
Summary
21
Example 1
22
Example 1 (Contd)
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Example 2
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Example 2 (Contd)
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Example 3
26
Example 3 (Contd)
27
Series Resonance
28
When Resonance Occurs

• The impedance is purely resistive. The LC series
  combination acts like a short circuit.
• The voltage and the current are in phase, so the
  power factor is unity.
• The impedance Z(?) is minimum.
• The voltage across L and C can be much larger
  than the source voltage.

29
Half-Power Frequencies
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Quality Factor Q
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Summary
32
Parallel Resonance
33
When Resonance Occurs

• The impedance is purely resistive. The LC
  parallel combination acts like an open circuit.
• The voltage and the current are in phase, so the
  power factor is unity.
• The admittance Y(?) is minimum.
• The current flowing through L and C can be much
  larger than the source current.

34
Comparisons
Parallel circuit
Series circuit
35
Passive Filters
Lowpass
Bandpass
Highpass
Bandstop
36
Lowpass Filter
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Highpass Filter
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Bandpass Filter
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Bandstop Filter
rejection frequency
40
Active Filters
A general 1st-order active filter
Active 1st-order lowpass filter
41
Active 1st-Order Highpass Filter
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Active Bandpass Filter
(gain)
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Active Bandpass Filter
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Bandreject (or Notch) Filter
45
Bandreject (or Notch) Filter