Frequency Response, Bode Plots, and Resonance

1
Electrical Engineering and Electronics II

• Chapter 6
• Frequency Response, Bode Plots, and Resonance

Scott
2008.10
2

• Main Contents

1. State the fundamental concepts of Fourier
analysis. 2. Determine the output of a filter for
a given input consisting of sinusoidal components
using the filters transfer function.
3. Use circuit analysis to determine the transfer
functions of simple circuits. 4. Draw first-order
lowpass or highpass filter circuits and sketch
their transfer functions.
8. Calculate parameters for series and parallel
resonant circuits.
3
(No Transcript)
4
6.1Fourier Analysis, Filters, and Transfer
Function

• Fourier Analysis

Examplesignal u is not sinusoidal, how to
determine the value of current i?
5

• Non-sinusoidal signals
• Such as electric pulse?sawtooth
  wave?triangle wave?square wave.

• Fourier Analysis

All real-world signals are sums of
sinusoidal components having various frequencies,
amplitudes and phases.
6
Fourier Analysis
??????????????????????????????????????????f
(t)?????????????
??????
?? ??
????
????
7
(No Transcript)
8
Filters
Filters process the sinusoid components of
an input signal differently depending of the
frequency of each component. Often, the goal of
the filter is to retain the components in certain
frequency ranges and to reject components in
other ranges.
9

• Filters

We use filters to retain components in a
given range of frequencies and discard the
components in another range.
10
Transfer Functions
The transfer function H(f ) of the two-port
filter is defined to be the ratio of the phasor
output voltage to the phasor input voltage as a
function of frequency
11

• Transfer Functions

• The magnitude of the transfer function shows how
  the amplitude of each frequency component is
  affected by the filter.
• Similarly, the phase of the transfer function
  shows how the phase of each frequency component
  is affected by the filter.

12
(No Transcript)
13
(No Transcript)
14
Determining the output of a filter for an input
with multiple components
1. Determine the frequency and phasor
representation for each input component. 2.
Determine the (complex) value of the transfer
function for each component.
3. Obtain the phasor for each output component by
multiplying the phasor for each input component
by the corresponding transfer-function value. 4.
Convert the phasors for the output components
into time functions of various frequencies. Add
these time functions to produce the output.
15
(No Transcript)
16

• Determining the Transfer Function

17
6.2 First-order lowpass filters

• This circuit tends to pass low-frequency
  components and reject high-frequency components.

18
6.2 First-order lowpass filters
19
6.2 First-order lowpass filters
20

• The low-frequency components are passed to
  the output almost unchanged in amplitude or phase.

• The high-frequency components are rejected to
  the output, the phase shifts nearly 900.

fB--Half-power frequency, break frequency,
corner frequency At such frequency point, the
magnitude of the transfer function is 0.707
times its maximum value.
21
(No Transcript)
22
6.5 First-order highpass filters

• This circuit tends to pass high-frequency
  components and reject low-frequency components.

23
6.5 First-order highpass filters
24
6.5 First-order highpass filters
25
6.5 First-order highpass filters
Lowpass filter or highpass filter??
It is a highpass circuit
26
6.6 SERIES RESONANCE

• Resonance is a phenomenon that can be observed in
  mechanical systems and
• electrical circuits.

27
6.6 SERIES RESONANCE
Series resonance happens.
28
6.6 SERIES RESONANCE
29
A bandpass circuit(?????)
30
Series Resonant Circuit as a Bandpass Filter
31

• Series Resonant Circuit as a Bandpass Filter

32

• Series Resonant Circuit as a Bandpass Filter

How to prove it?
33
Example6.6 Compute the resonant frequency, the
bandwidth, and the half-power frequencies.
Assuming that the frequency of source is the same
as the resonance frequency, find the phasor
voltages across the elements and draw a phasor
diagram.
34
(No Transcript)
35
Can you list the practical application of series
resonance? Which one takes use of its advantage
or disadvantage?
36
6.7 PARALLEL RESONANCE
37
6.7 PARALLEL RESONANCE
38

• Example6.7 Find the L and C values for a
  parallel resonant circuit that has R10kO,
  f01MHz, and B100kHz. If I10-3/00, draw the
  phasor diagram showing the currents through each
  of the elements in the circuit at resonance.

39
6.8 Ideal and Second-Order Filters
40
(No Transcript)
41
(No Transcript)