Frequency Response
AC
+
-
Asin(ωt) L
R+
vL(t)-
What is the change of vL(t)when the frequency of thevoltage source change?
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)
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.
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.
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
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
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
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