Reading Material 2 Frequency Response
Transcript of Reading Material 2 Frequency Response
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Problems Solution
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What can you do in One Minute?
In one minute you can recite Soorat al-Fatihah7 times, reciting rapidlyand silently. Some scholars said that the reward for reading al-Fatihah is
more than 1400 hasanahs, so if you read it 7 times you will, by the
permission of Allah, gain more than 9800 hasanahs - all of that in one minute.
In one minute you can recite Soorat al-Ikhlas (Qul Huwa Allahu Ahad) 20 times,reciting rapidly and silently. Reciting it once is equivalent to one-third of the
Qur'an. If you read it 20 times it is equivalent to reading the Qur'an 7 times.
If you read it 20 times in one minute each day, you will have read it 600 times
in one month, and 7200 times in one year, which will be equal in reward to
reading the Qur'an 2400 times.
In one minute you can say
20 times. The reward for saying this is like freeing 8 slaves for the sake of
-Allah from among the sons of Isma'il.
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What can you do in One Minute?
In one minute you can say Subhan Allahi wa bi hamdihi (Glory and praise be
to Allah) 100 times. Whoever says that in one day will be forgiven for his sins
even if they are like the foam of the sea.
In one minute you can say Subhan Allahi wa bi hamdihi Subhan Allah
il-Adheem (Glory and praise be to Allaah, glory be to Allah the Almighty)
50 times. These are two phrases which are light on the lips, heavy in the
balance and beloved to the Most Merciful, as was narrated by al-Bukhari and
Muslim.
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Miller Theorem
4
gm= -21.6mA/V. r
=4.63 k
C =4.93 pF, C = 0.8 pF
47 K
1 K
1 K
1 K
AM = Vo/Vsig= -7.2 V/V
Vo/Vb=10.8 V/V , , Ri = 4k
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Midband Gain
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High Frequency Response
MHzRC
f
rRRR
eqCininH
insigeqCin
6.166671037.142
1
2
1
667||||
12
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Common Source with Source Resistance
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Midband Gain
Midband Gain =
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Open Circuit Time Constant
Req for Cgs
IX
+
1
2
Vs
Vg
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Common Source with Source Resistance
1
2
3
Vg
Vgs
Vo
4 Ix
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Mid-band Gain =
Rs()
AMV/V
Rgs
(k)
Rgd
(k)
H(k Rad/s)
Gain BW
M Rad/s
0 -20 100 2105 453.5 9.07100 -14.3 71.5 1534 623 8.91
250 -10 50.1 1105 865.7 8.66
Common Source with Source Resistance
OBSERVATIONS CE C fi ti
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OBSERVATIONS : CE Configuration
Cgd determines the high frequency response (H) of CE/CS.
To increase the upper 3-dB or cutoff frequency (H)
Reduce gmRL which reduces the mid-band gainor
Reduce the sourse resistance which might not always be possible.Alternatively One can use circuit that do not suffer from the Miller Multiplication
use Cascode configuration (CE-CB) wideband amplifier One can use circuit that isolates the source resistance
use Cascade configuration (CC-CE) wideband amplifier
Bsigx
Lm
sigB
B
sig
o
RRrr
Rgr
RR
R
V
V
||
'
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Solution for Wide Band Amplifier
Cascoded CE-CB Configuration
CE for voltage gain
CB provides wider bandwidth (Higher fH) throughminimizing the effect of Miller Multiplication Effect.
This is achieved by isolating the load resistance from the
collector of the CE stage by a low input resistance of CBstage.
Cascaded CC CE Configuration
CE for voltage gain
Although Miller multiplication occurs, but the resistanceseen by the capacitance is small because oflow outputresistance of the CC thus resulting large capacitance is
isolated from the source resistance by the CC.
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Frequency Response
Common Emitter
&
Common Base
Circuit
E f l
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CE-CB Configuration : Complete Frequency Response
3
3
2
2
1
1
4
4
3
3
2
2
1
1
1
1
1
1
1
1
)(
p
z
p
z
p
z
p
z
p
z
p
z
p
z
M s
s
s
s
s
s
s
s
s
s
s
s
s
sAsA
CE CB C fi ti
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CE-CB Configuration
Large input resistance to the signal source
Load resistance seen by Q1 is simply the input resistance re of Q2.
Low load resistance of Q1 considerably reduces the Miller multiplier effectof C, thus extends the upper cut-off frequency (fH). This is achievedwithout reducing the mid-band gain AM, since collector of Q2 carries equalcurrent to the collector of Q
1
.
The CB configuration Q2 does not suffer from the Miller effect, hence doesnot limit the high frequency response.
Q2 simply acts as a Current Buffer 0r an impedance transformer faithfullypassing on the signal current to the load while presenting a low loadresistance to the amplifying device Q1.
High frequency response being carried out omits rx2 & ro2 forsimplification.
CE CB C fi ti
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CE-CB Configuration
DC analysis
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CE-CB Configuration
DC analysis
mAI
I
E
E
1
101
44.43.37.04
1
1
mAIII ECE 1211
25
5.2
/40
21
21
m
ee
m
t
Cm
grr
kg
rr
VmAV
Ig
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Mid-band Gain
VVV
V
A
VVRrR
Rr
V
V
VVrgV
V
VVRgVV
sig
o
M
Bs
B
sig
be
em
be
be
Lm
be
o
/4.23
/24.0||
||
/1
/96'
1
11
2
1
2
2
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Low Frequency Response Model
Cc1 pole & Zero Short Cct Time Constant
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Cc1 pole & Zero : Short Cct Time Constant
C pole & Zero : Short Cct Time Constant
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Cc1 pole & Zero : Short Cct Time Constant
sec/0
0)(@
1
11
rad
CctopenCsV
z
coz
krRRCforR
HzradRC
BsigCeq
eqC
p
24.5||
30sec/1911
11
1
1
C pole & Zero : Short Cct Time Constant
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Cc2 pole & Zero : Short Cct Time Constant
Apply Test Voltage to find Req for CC2Signal Voltage Source is suppressed
sec/0
0)(@
1
21
rad
CctopenCsV
z
coz
kRRCforR
HzradRC
LCeq
eqC
p
C 10
9.15sec/1001
2
2
2
C pole & Zero : Short Cct Time Constant
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CE pole & Zero : Short Cct Time Constant
HzradRC
CctopenCsV
EE
z
Eoz
8.4sec/301
R||0)(@
3
E3
5.408.1525||33001
||||
||
393sec/24701
32
1
3
sig
eEeq
eqE
p
RRR
rRCforR
HzradRC
E
Apply Test Voltage to find Req for CC2Signal Voltage Source is suppressed
C pole & Zero : Short Cct Time Constant
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CB pole & Zero : Short Cct Time Constant
C pole & Zero : Short Cct Time Constant
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CB pole & Zero : Short Cct Time Constant
C pole : Short Cct Time Constant
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CB pole : Short Cct Time Constant
kRRrRRCforR
VgVgVVgrV
HzradRC
sigeq
bembembebemebe
eqB
p
B 08.4||||||
9.3sec/5.241
3121
112211122
4
Apply Test Voltage to find Req for CC2Signal Voltage Source is suppressed
Low frequency magnitude response of a CS amplifier
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Low-frequency magnitude response of a CS amplifier
High Frequency Response
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High Frequency Response
High Frequency Response
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High Frequency Response
H h F R
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High Frequency Response
1221
2 em rgV
V
111 211 CCCi
111 211 CCCo
sxsigsigsig
RRRrr
r
RRR
RR
VV ||||||
||
'3211
1
32
32
sxsigsig RRRrrVR ||||||' 3211
Hi h F R
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High Frequency Response
Mhz
RCC sigipCin 95.8
'
1
11
MHzMrad
rCC epCoutH 356sec/6.2234
2
1
212
1
MHzMrad
RRCC LCLpCout 33sec/208
||
1
2
2
CLNegelectpFCCpFCC ,2,9.13 2121
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Normalized high-frequency response of the amplifier
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Complete Frequency Response : CE CB Configuration
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Comparison CE & CE-CB Configurations
Parameters CE CE-CB
Mid-band Gain V/V -22.5 -23.5
Lower cut-off Freq 439.5 Hz 439.5 Hz
Total input Capacitance 203.4 pF 17.9 pF
High cut-off frequency 787 k Hz 8.95 M Hz
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Frequency Response
Common Collector
&
Common Emitter Circuit
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CC-CE Configuration
Common Collector (Emitter Follower) provides excellent highfrequency response due to absence of Miller multiplication
effect
CC has no voltage gain.
To obtain voltage Gain & wide bandwidth use cascaded CC-CEConfiguration
Collector of Q1 is at signal ground so C1does not getmultiplied with the stage gain. Thus the pole caused by the
interaction of the source resistance Rsig and the inputresistance C1 will be at a high frequency.
Q2 suffers MillerMultiplication Effect. But the resistanceseen by this capacitance will be small because of the low
output resistance of Q1.
CC CE C fi i
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CC-CE Configuration
CC-CE Configuration
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CC-CE Configuration
DC Analysis
krrVmAg
mAImAI
VVVVVV
em
EE
EEB
5.2,25,/40
1,1
6.3,3.4,5
21
211
pFCpFC 9.13,2
CC CE C fi ti
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CC-CE Configuration
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Midband Gain
VVV
VA
sig
oM /6.70
High Frequency equivalent circuit
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High Frequency equivalent circuit
High Frequency equivalent circuit
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High Frequency equivalent circuit
Open Circuit Time Constant :C R
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Vb
Is
Open Circuit Time Constant :CReq
IbI1
LsmE RIVgV '1
LsmsEsb
RIVgVVVV '1
LLmssig RIRgVRI ''1' 11
LmsLsig RgVRRI '1''1
ZRg
RR
I
V
Lm
Lsigs
'1
''
1
rV
Ir
VIIII ss
e
ssbs
11
rZ
rZVIr
VIIZ
Vss
ss
s1
Lm
Lsig
s
s
eq Rg
RRrZr
I
VR
C '1
''||||
gmVs-I1
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Comparison CE, CE-CB, CC-CE
Parameters CE CE-CB CC-CE
Mid-band Gain V/V -22.5 -23.5
Lower cut-off Freq 439.5 Hz 439.5 Hz
Total input Capacitance 203.4 pF 17.9 pF
High cut-off frequency 787 k hZ 8.95 M Hz 7 M Hz