Reading Material 2 Frequency Response

7/27/2019 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


7/45

Common Source with Source Resistance


8/45

Midband Gain

Midband Gain =


9/45

Open Circuit Time Constant

Req for Cgs

IX

+

1

2

Vs

Vg


10/45


1

2

3

Vg

Vgs

Vo

4 Ix


11/45

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


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


22/45


sec/0

0)(@

1

11

rad

CctopenCsV

z

coz

krRRCforR

HzradRC

BsigCeq

eqC

p

24.5||

30sec/1911

11

1

1



23/45


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



24/45

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




25/45

CB pole & Zero : Short Cct Time Constant



26/45

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


Low frequency magnitude response of a CS amplifier


28/45

Low-frequency magnitude response of a CS amplifier



29/45




30/45


H h F R


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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


32/45


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


33/45

Normalized high-frequency response of the amplifier


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Complete Frequency Response : CE CB Configuration


35/45

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


36/45

Frequency Response

Common Collector

&

Common Emitter Circuit


37/45

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


39/45

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


40/45

CC-CE Configuration


41/45

Midband Gain

VVV

VA

sig

oM /6.70

High Frequency equivalent circuit


42/45




43/45


Open Circuit Time Constant :C R


44/45

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


45/45

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

Reading Material 2 Frequency Response

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