Post on 13-Dec-2015
INC 111 Basic Circuit Analysis
Week 13
Frequency Response
Frequency Response
AC
+
-
Asin(ωt) L
R+
vL(t)-
What is the change of vL(t)when the frequency of thevoltage source change?
Frequency response is a study of how the change of frequency affect the voltage or current.
AC
+
-
Asin(ωt) L
R+
vL(t)-
AC
+
-
A∟0 jωL
R+
vL(t)-
Change to phasor
ALjR
LjvL
To sketch graph, we look at 3 points
1. When RL R
LjAA
LjR
LjvL
2. When RL 45707.01
AAj
jA
jRR
jRA
LjR
LjvL
3. When RL AALj
LjA
LjR
LjvL
AC
+
-
Asin(ωt) L
R+
vL(t)-
ω
|vL| (magnitude)
A
Linear Scale & Log Scale
1 2 3 4 5 6
0.1 1 10 100 1000 1000
Linear Scale
Log Scale
Log ω
|vL| (magnitude)
Log scale of frequency
A
AC
+
-
Asin(ωt)
R+
vC(t)-
CWhat is the frequency responseof vc(t)
Change to phasor
ARCj
A
CjR
CjvC
1
11
1
To sketch graph, we look at 3 points
1. When 1RC AAARCj
vC
1
1
1
1
2. When
3. When
AC
+
-
Asin(ωt)
R+
vC(t)-
C AC
+
-
A∟0
R+
vC(t)-
1/jωC
1RC
1RC
45707.01
1
1
1
AA
jA
RCjvC
RCj
AA
RCjA
RCjvC
1
1
1
AC
+
-
Asin(ωt)
R+
vC(t)-
CWhat is the frequency responseof vc(t)
Log ω
|vc| (magnitude)
A
Input & Output
SystemInput Output
Input is usually what we can control.
Output is usually what we are interested in.
AC
+
-
Asin(ωt)
R+
vC(t)-
CWhat is the frequency responseof vc(t)
Input = voltage source
Output = vc(t)
System = RC circuit
Measure Frequency Response
SystemInput Output
Freq 10HzAmplitude = 1 Phase = 0
Freq 100HzAmplitude = 1 Phase = 0
Freq 800HzAmplitude = 1 Phase = 0
Freq 10HzAmplitude = 0.96 Phase = 12
Freq 100HzAmplitude = 0.82 Phase = 44
Freq 800HzAmplitude = 0.53 Phase = 56
Frequency Response Plot
Note: log frequency and log magnitude
Magnitude
Phase
The HP 35670A Dynamic Signal Analyzer obtains
frequency responsedata from a
physicalsystem.
Frequency Domain
Frequency domain is another point of view of things in the world.
Some analysis are easier done in frequency domain than time domain.
Metaphor of Frequency Domain
(1,1,1)
(2,-3,0)
Time Domain
Frequency Domain
4
22sin
2 s
tTime Domain Frequency Domain
R L C R sL 1/sC
Transfer Function
Transfer function = ratio of output and input in frequency domain
System
H(s)
System
H(s)
Input Output
U(s) Y(s)
)(
)()(
sU
sYsH Transfer function
Note: Transfer function describes characteristic of a system.
Example: Obtaining Transfer Function
input is v(t)output is vc(t)
Change all components to Phasor(frequency domain)
Kirchoff’s Voltage Law
CssIsV
sV
CsRLs
sI
Cs
sIsRIsLsIsV
C
1)()(
)(1
1)(
)()()()(
LCs
LR
s
LCsV
sVC1
1
)(
)(
2 Transfer
function
Fourier Series
“Any periodic signal can be written in the sum of sine wave signalsat different frequency.”
Filter
AC
+
-2sin(t)+3sin(9t)
R +vC(t)
-C
Log ω
|vc| (magnitude)
We want to get rid of the signal 3sin(9t)
AC
+
-
2sin(t)+3sin(9t)
ω=5
Cut-off frequency
Example
AC
+
-2sin(t)+2sin(9t)
1Ω +vC(t)
-0.2f
Find vc(t)
Use superposition to consider the effect of two different frequencies
AC
+
-
2sin(t)
1Ω +vC(t)
-0.2f AC
+
-
2sin(9t)
1Ω +vC(t)
-0.2f
AC
+
-
2∟0
1 +vC(t)
--j5
For 2sin(t)
55
2.01
11j
jjCj
31.1196.1
0269.781.5
90502
15
5
j
jVc
)31.11sin(96.1)( ttvC
AC
+
-
2∟0
1 +vC(t)
--j0.556
For 3sin(9t)
556.0556.0
2.09
11j
jjCj
93.60972.0
0207.29144.1
90556.002
1556.0
556.0
j
jVc
)93.609sin(972.0)( ttvC
Finally, we add vc(t) from both frequencies
)93.609sin(972.0)31.11sin(96.1)( tttvC
AC
+
-2sin(t)+2sin(9t)
1Ω +vC(t)
-0.2f
Other topics
• Three-phase circuits
• Magnetically Coupled circuits• Transformer
Power Line Systems
3 phases systems have three wire called “line” which aresine wave with phase shift 120 from each other
AC
AC
AC
Power Plant
Line 1
Line 2
Line 3
02220
2402220
1202220
3 phases, 3 wires
AC
AC
AC
Power Plant
Line 1
Line 2
Line 3
02220
2402220
1202220
3 phases, 4 wires
Neutral
L1-N = 220Vrms, L2-N = 220Vrms L3-N = 220Vrms
L1-L2 = 381Vrms, L2-L3 = 381Vrms, L1-L3 = 381Vrms
Star Connection ( Y-connection)
AC
AC
AC
Z
Load
Each load get 220 Vrms
Delta Connection ( Δ-connection)
AC
AC
AC Z
Load
Each load get 381 Vrms