### 3336 Lect 10-Frequency response

```ECE 3336
Introduction to Circuits & Electronics
Lecture Set #10
Signal Analysis & Processing –
Frequency Response & Filters
Dr. Han Le
ECE Dept.
Outline
• Review
• Signal analysis
– Power spectral density
• Frequency response of a system (circuit)
– Transfer function
– Bode plot
• Filters
– Analog
– Digital
Concept Review: Signal Processing
• All electronics around us involve signal
processing.
• Signal represents information. That information
can be something we generate (e.g. texts,
sounds, music, images) or from sensors.
(discussion: examples of sensors)
• Electronics deal with signals: signal processing is
to transform the signal and extract the desired
information.
Concept Review: Signal Processing
(cont.)
• Signal processing is a general concept, not a single
specific thing. It includes:
– signal synthesis or signal acquisition
– signal conditioning (transforming): shaping, filtering,
amplifying
– signal transmitting
– signal receiving and analysis: transforming the signal,
converting into information
• Signal processing is mathematical operation;
electronics are simply tools.
• Computation is high-level signal processing: dealing
directly with information rather than signal.
Applications of mathematical
techniques
Signal and AC circuit
problems
Harmonic
function
Fourier
transform
• RLC or any time-varying linear
circuits. Applicable to linear
portion of circuits that include
nonlinear elements
• Signal processing
Complex
number
&analysis
Phasors
• signal analysis (spectral
decomposition)
• filtering, conditioning (inc
amplification)
• synthesizing
Note: The main lecture material is in the Mathematica file –
this
is only for concept summary
Homework (to be seen in HW 8)
Choose an electronic system around you (e. g. a TV, DVD
player, phone,…); show a functional block diagram and
describe the signal processing sequence (end to end).
Example
Antenna
Inductor
Variable Capacitor
Diode
(1N34A)
High-Impedance Earphone
Ground
Schematic
Carrier wave
(sound) signal
Antenna
50
40
30
20
1.5
1
10
0.5
5
-0.
-1
5
-1.
Ante
nna
Inductor
Variable
Capacitor
Diode
(1N34A)
Resonance circuit
High-Impedance
Earphone
1.5
Grou
nd
1
0.5
-0.5
-1
-1.5
Soundwave
10
20
30
40
50
Electrical signal
(voltage or current)
Link to Mathematica file: AM FM
Outline
• Review
• Signal analysis
– Power spectral density
• Frequency response of a system (circuit)
– Transfer function
– Bode plot
• Filters
– Analog
– Digital
Signal Fourier (or harmonic)
Analysis
• Treat each time-finite signal as if it is composed of
many harmonics, using Fourier series
xt
a0
n 1 an
Cos n
m
Xm
xt
t
m
n 1 bn
Sin n
t
t
 In complex (or Euler) representation, Fourier
series coefficients Xm are phasor components,
Xm
Xm
m
Signal Fourier (or harmonic)
Analysis (cont)
• If the signal is real (all cases involving real physical
quantity), then:
X
Xm
Xm
m
m
Xm
Xm
Xm
 Hence, we need to keep only positive frequencies
 A signal can be represented by a plot of | Xm | vs.
m
frequency, or usually | Xm |2 if x(t) is voltage or current,
known as the signal magnitude spectrum, or its power
spectral density.
 Equally important is the phase spectrum: plot of fm vs.
frequency
Do not be confused between the word
“spectrum” in the general English sense vs.
specific definition of “spectrum” in power spectral
density, or phase spectrum.
The Electromagnetic Spectrum
UV & solar
blind
Visible
Example of Spectra
0.89 s
11 025 Hz
3
60
2
80
1
100
0
1
120
140
0
2
3
1000 2000 3000 4000 5000
0
1000
2000
3000
4000
5000
Example of Spectra
0.79 s
11 025 Hz
3
60
2
80
1
100
0
1
120
2
3
0
1000 2000 3000 4000 5000
0
1000
2000
3000
4000
5000
Outline
• Review
• Signal analysis
– Power spectral density
• Frequency response of a circuit
– Transfer function
– Bode plot
• Filters
– Analog
– Digital
Example
R
t
input vin[t]
C
i(t)
output vout[t]
Frequency Response
1
t
1
1
H
1
or, Frequency Transfer Function
C
t
input vin[t]
i(t)
t
R
output vout[t]
1
H
1
Frequency Transfer Function
(Frequency Response Function)
For many linear RLC circuits, the frequency
response function usually has the form:
H
P
Q
a0 a1
b0 b1
a2 2
b2 2
am m
bn n
Example: Test 1
H
1 C2 L2 2
R1 L1
C1 R1
C2 L2 R3 2
R3 1
C1 R1 C2 R1
L1 L2
C1 R1
Bode Plot for Vout in Test 1
3
2
0.1
AmplitudeResponse
1
0.01
0.001
1
0
1
2
10
4
1000
104
105
Frequency Hz
106
3
1000
104
105
Frequency Hz
106
Applications of Frequency
Transfer Function
• Any signal can be decomposed as a sum of
many phasors (Fourier components)
• For a linear system, each component can be
multiplied by H[w] to obtain the output
phasor
• The signal output is simply the sum of all the
individual phasor (Fourier component)
outputs.
R
Example
C
input vin[t] i(t)
8
8
6
6
4
4
2
output vout[t]
2
0
0
2
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.4
0.2
0.0
0.2
0.4
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Outline
• Review
• Signal analysis
– Power spectral density
• Frequency response of a circuit
– Transfer function
– Bode plot
• Filters
– Analog
– Digital
General Filter Concept Review
Power SpectralDensity
This is a filter
This is also filter
60
80
100
120
140
0
This is another filter
1000 2000 3000 4000 5000
Frequency Hz
General Filter Concept
• A system (electronic circuit) can be
designed such that its transfer function
H[w] has preference (let through) certain
ranges of frequencies while attenuating
(blocking) other frequencies
• Such a circuit is called a filter. Filter is a
concept about the function of a circuit, not
the circuit itself.
• Filter includes both amplitude response
and phase shift. Usually, only amplitude is
plotted.
Common Types of Filters
Band pass
filter
Power SpectralDensity
Low pass
filter
High pass
filter
60
80
100
120
140
0
Band stop
(notch) filter
1000 2000 3000 4000 5000
Frequency Hz
Design of Filters
• A circuit designed to perform filtering
function on an analog signal is called an
analog filter.
• If a signal is digital (converted into a
sequence of number), a filter can be
realized as a mathematical operation, this is
called digital filter.
• Digital filter can be done with any
computing device: from a DSP chip to a
computer.
Example of Simple Analog Filters
 RC band stop filter.
 RC bandpass filters
Example of Simple Analog Filters
RLC resonant filter
Example of Simple Analog Filters
Notch filter application: rejection line 60-Hz signal
AmplitudeResponse
Example: Test 1 Notch Filter
0.100
0.050
0.010
0.005
10 000
15000 20000 30 000
50 000 70 000 100 000
Frequency Hz
1.0
0.5
0.0
0.5
1.0
1.5
2.0
2.5
10 000
15 000 20 000 30 000
50 000 70000 100 000
Frequency Hz
Example: Test 1: Bandpass Filter
AmplitudeResponse
1
0.1
0.01
0.001
10
4
1000
104
105
Frequency Hz
104
105
Frequency Hz
106
3
2
1
0
1
2
3
1000
106
Digital Filter
• Any filter function can be achieved with digital filter
Signal input
Microprocessor
(DSP)
User input
Filtered
signal
output
Digital Filter
• Digital filter can also be designed with sharp cut-off edge
that is difficult with analog filter.
This is another filter
This is a filter