cmpe306 lecture24 frequency response 2 101201
TRANSCRIPT
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
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Find the load impedance that maximizes the powertransfer.
n e max mum power n e oa mpe ance
1-1
UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 1
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
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!"
Chapter 14.1Frequency Response
Fundamentals of Electric Circuits 3nded.,
2007) 14.1-4
1-2
UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 1
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
3/17
Example (Synthesis)- - .
What is the gain at 2 90 Hz? at 2 150 Hz?
C
Single pole filter, two options: or .
filter, take the output voltage to be across t
RL RC
RL he inductor.
0
1 260 sec but 10 mH is 2.2" 1.2", and the smalle
10 mH
R
L
we make , the smaller we have to make . Not a good answer.L R
0
er, a e e ou pu vo age across e res s or
1
160 sec , 0.1 is 2mm 1.25mmF
1-3UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 1
.
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
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0( j RC
V
H
rps / 31.8( )
1 r s 1 / 31.8
s
j jff
H
2
/ 31.8( )
1 ( / 31.8)
ff
H
90 Hz, ( ) 0.9428
150 Hz 0.9782
f f
H
H
50 k , 0.1 FC
1
f)|
0 50 100 1500
.|H
1-4UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 1
f in Hz
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
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Series Resonance (1)
and inductive reactances are equal in magnitude, thereby resultingin a purely resistive impedance (at a specific frequency)
1( ) s R j L
j C
V
Z HI
Resonance occurs at when
R j LC
Z
0 0
0
Im( ) 1 0
resonance frequency
L C
Z
1. is purely resistiveRZ2. and are in phase, pf 1s V I
0
1 rad/s
LC
. e magn u e o smaximum
4. The voltage of the inductor and
1-5UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 15 of 20
0 0 2 Hz2
fLC
Chapter 14.5
the capacitor can be more than that
of the source
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
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Series Resonance (2) 1L
Z
Z
C
Z
L
1
R ( 1/ ) ,
1tanZ
Z L C
L C
1 0LC R Z
Cv
s
I V Z0
0
( ),R R( )
s sL Cj L
j C
V VV V
m V Z
II 0m
L m
VL QV
R V
2 2R ( 1/ )
m mIZ L C
I
0( )
mC m
VQV
R C V
1-6UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 16 of 20
( ),( )
s sL Cj L
j C
V V
Z Z
Chapter 14.5
0 0
R Q
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
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Series Resonance (3)
221
2 2
1( ) m
VP I R R
1 2
2
Half maximum power dissipation at ,
1 1voltage or current power
22
1 2 0
22
( ) ( ) ( )2 2 2mP P R
.
2 2
m m
R
1 2
2 2
1,2 ( ) R ( 1/ ) 2Z L C R
1-7UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 17 of 20Chapter 14.5
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
8/17
Series resonance (3a)
2 2
1,2( ) R ( 1/ ) 2Z L C R 1 1
vo tage or current power22
1
1
2 2
R
L L LC
1 1voltage or current power
22
2
2
1
2 2
R R
L L LC
0 1 2
0 1 2 0
2 1 bandwidthB
1-8UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 1
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
9/17
Series Resonance (4)
max stored in the circuitQuality factor Q 2dissipated in one period at resonance
E
E
210 02
In a series RLC circuit
2 f L LLI
212 00
(1/ )
1
R RRI f
L Resonant circuit
0
20
R CR
R
characterized by five
related parameters:
For a hig
L Q
h- circuit ( 10)Q Q
1 2 0, , , ,
1-9UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 19 of 20Chapter 14.5
1 0 2 0,
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
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Practice 14.7
A series-connected circuit has 4 , L 25 mH, and 50R Q
300 3
(50)(4)(a) 8 10 rad/s
25 10
L QRQ
R L
0 2 6 3
0
3
1 1 10.625 F
(64 10 )(25 10 )
8 10o
CLLC
1 0
50Since Q 10
/ 2 8000 80 7920 rad/s
Q
B
2 0
2
0
/ 2 8000 80 8080 rad/s
100(c) At ,
2
m
B
VP
R
2
1.25 kW
8
2
1
2
At , 0.5 0.625 kW2
At 0.5 0.625 kW
m
m
VP
R
VP
1-10UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 110 of 20
2R
Chapter 14.5
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
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Parallel Resonance (1)
11
)( LjCjR V
I
HY
)(atwhenoccursResonance 0
LCj
R
Y
frequencyResonance
01)Im(
0
00 LC
Y 0At1 R
H
rad/s
1
0LC
m
mL m
I Rj jQI
V
I
LjCj
RIm
V
HYV
0 0
0 0( )C m mC jI R C jQI I V
1-11UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 111 of 20
Lj CL
Chapter 14.6
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
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Parallel Resonance (2)
2
1
Ha - requency
1 1 1
0 1 2
20 1 2 0
2
1 1 1
2 2RC RC LC
2 1
1B
RC
0
0
2
01
Q RCB L
1 0
1 0
2
0 2 0
2 2 21
1
Q QQ
B
1-12UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 112 of 20Chapter 14.5
2 2Q Q
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
13/17
Practice 14.8
0 1 2
A parallel resonant circuit has 100k , 20mH, and 5nF
Calculate , , , , and
L C
Q B
5
0-3 -9
10 rad/s(20 10 )(5 10 )LC
5 -3
0
100 10 50(10 )(20 10 )
QL
0B 2000rad/s50Q
5
1 0
5
/ 2 10 -1000 99 krad/sB
1-13UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 1
13 of 20Chapter 14.5
2 0
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
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Practice 14.9fre uencresonanttheCalculate
AT RESONANCE, THE
10 / 0.2j
REACTANCE IS ZERO!
.10 1/ 0.2j
2 2
10 1 2 10(1 2 ) 10 20j j jj j j
20 0 00 1 (2 ) 2020Im ( ) 0 0
j jj
H
0 0
0
1-14UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 1
14 of 20Chapter 14.5
2 2
0 0 01 4 20 2.179 rad/s4 2
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
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Decibels: Definition
210
1
log , with a unit is ,P belsP
210
1
more commonly 10log expressed in (dB).P
decibelsP
210
number of bels log P
G Some special cases:
0.1 ; the quantity corresponds to the factor expressed in dB10 x yy
1
2dB 10
1
10log (1/10 of bels)P
GP
2 1
2 1
( / ) 1 0 dB
( / ) 10 10 dB
P P y x
P P y x
1 2 dB 10
1 2 dB 10
10log 1 0 dB
2 10log 2 3 dB
P P G
P P G
2 1
2 1
( / ) 0.1
/ 2 3.010...
10 dB
3 dB
y x
P P
P P y x
x
1-15UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 1
1 2 dB 10
15 of 23
When engineers refer to 3 dB gain or 3 dB loss, they mean a factor of 2!
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
16/17
Decibels: Absolute units
Engineers will often normalize with respect to a fixed value
EXAMPLE: dBm = power relative to 1 mW
=
0 dBm 1 mW 30 dBW
10 dBm 10 mW 20 dBW
30 dBm 1 W 0 dBW
10 dBm 0.1 mW 40 dBW
3 dBm 2 mW 27 dBW
Many different normalizations are used in different fields!
1-16UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 1
16 of 23Chapter 14.3
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7/27/2019 CMPE306 Lecture24 Frequency Response 2 101201
17/17
The Decibel Scale in Circuit Theory
.
20log is used for voltage or current
2. dB is logarithmic measurement of the
ratio of one variable to another of the
same kind
. ,
negative signs and angles are handled
separately.2
11
1input power
VP
1
2
22
2
1output power
2
VP
R
2
2 2 1dB 10 10 10
1 1 2
10log 10log 10logP V R
GP V R
1-17UMBC ENEE423 Communication Systems
Course Notes E F C LaBerge, 2008 All rights reserved.Portions Copyright Prentice, Hall, Inc. All rights reserved
Week 1
17 of 23Chapter 14.3
2 21 2 dB 10 10
1 1
If 10log 20logV V
R R GV V