BwEE2601-13_BJT and FET Frequency Response

8/4/2019 BwEE2601-13_BJT and FET Frequency Response

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13. BJT and FET FrequencyResponse

13.1 Decibel Unit (dB)

13.2 High-pass Filter (Amplifier lower cutoff frequency=f L)

13.3 Low-pass Filter (Amplifier higher cutoff frequency=f H)

13.4 Pass-band of BJT Amplifier

13.5 Pass-band of FET Amplifier



2

13.1 Decibel Unit (dB)dB is an electrical unit used in Electronic engineering. They provide a lot of

easiness in understanding on the performance of the systems.

dB is the 10 times logarithm of a power ratio dB = 10 log(P1/P2)

Since P= V2/R then dB=10log(P1/P2)=10log(V12/R)/(V2

2/R)=10log(V12/V2

2)=20log(V1/V2)

Since P= I2 R then dB=10log(P1/P2)=10log(I12R/I2

2R)=10log(I1/I2)2= 20log(I1/I2)

Then dB is the 20 times logarithm of a voltage ratio or current ratio.

AV=10

Amplifier1mV 10mV

Voltage ratio

Amplifier1mV 10mV

(AV)dB=20log10=20dB

dB

(AV)dB=20 log (10mV/1mV)=20 log10=20dB

Voltage Gain of the amplifier is 10 or 20dB

Amplifier1mV 10mV

AV=10mV/1mV=10

Vin Vo



3

AP=200

Amplifier1mW 200mW

Power ratio

Amplifier

1mW 200mW

(AP)dB=10log200=23dB

dB

(AP)dB=10 log (100mW/1mW)=10 log100=20dB

Power Gain of the amplifier is 200 or 23dB



4

Total Voltage Gain of the system is 100 or 40dB

Amplifier 20mV

(AV2)dB=20log2=6dB AV2=2 AV1=10

Amplifier 1mV 10mV

Voltage ratio (AV1)dB=20log10=20dB dB

Amplifier AV3=5

100mV

(AV3)dB=20log5=14dB

AVT =10x2x5=100 Multiply the ratio for total Voltage Gain

(AVT )dB=20+6+14=40dB Add the dB for total Voltage Gain in dB

(AVT )dB=20log100=40dB

Or find dB from the ratio for total Voltage Gain in dB



5

decreasesfCandincreasesfas)f(Vequalwill)f(VffWhen.

dB.log.)f(V)f(VCfRwhenorRCffWhen.

increasedisfwhenincreasewill)f(V.

fCR

R)f(V

XR

R)f(V

jXR

R)f(V)f(V

SL

SL

L

S

C

SC

S

213

3707020707022

12

12

1

21

2222

13.2 High-pass Filter(Amplifier lower cutoff frequency)

RCfL

2

1

f

V

R

C ~VS(f)

fLLower cutoff frequency fL

V (f)

0dB

-3dB



6

•All types of BJT amplifier circuits have a high pass filter at the place where coupling andbypass capacitors are used

VCC

RL

Ri

CC

CB

vi

R2

R1

RE

vo

RoRin

vin

iin

iL

Emitter Follower

VCC

RC

RL

CE

Ri CCCB

vi

R2

R1 RE

vo

Common Emitter

At lower frequencies, Reactance of bypass capacitor becomes higher (open) and the CE

amplifier behave as CE with RE whose voltage gain becomes smaller

RCfL 2

1

f

V

R

C ~VS(f)


V (f)

0dB

-3dB



7

1CL1L CRR2

1f

6dB/octave

12dB/octave

18dB/octave

fL1= fL2= fLE

Overall Lower frequency response of Common Emitter amplifier

If fL1= fL2= fLE

18dB/octave

at Mid-frequencies

fL1

fL2fLE

CE amplifier at Low frequencies

RLbre

Rs

Rin

C1C2

RTE

= RE

//(re

+(Rs

//RB

)/b)

CE

~

RB

RC

E TE LE

C R 2 1 f

2 2 T 2 L

C R 2

1 f

RT2=Rs+(RB//(bre))

Assume all capacitorsshort when consideringone capacitor

f

V

fLEfL2fL1



8

13.3 Low-pass Filter(Amplifier higher cutoff frequency)

123

3707020707022

12

12

1

21

1

1

1

1

1

2

22

fCRas)f(Vequalwill)f(VffWhen.

dB.log.)f(V)f(VCfRwhenorRCffWhen.

increasedisfwhendecreasewill)f(V.

fCR)f(V

XR

)f(V

XR j

)f(V jXR

jX)f(V)f(V

SH

SH

H

S

C

S

C

SC

CS

RCfH

2

1

Higher cutoff frequency fH

f fHC

R

V V (f)

0dB -3dB ~VS(f)



9

Although inter-electrode capacitances of BJT are very small, at very highfrequency, their reactances become lower which make the voltage gain ofthe amplifier decreases. This constitute an equivalent low pass filter

RLbre

Rs CCE

Cb’e~

RB

RC

Cb’c

At high frequencies, reactance of coupling

and bypass capacitors become smaller (short)

Miller’

stheorem

VCC

RC

RL

CE

Ri CCCB

vi

R2

R1

RE

vo

Common Emitter

Cb’e

CCE

Cb’c Cob

Overall Higher frequency response of Common Emitter amplifier



10

fH2fH1 CE amplifier at High frequencies

RLbre

Rs CCE

Cb’e

~

RB

RC

CM1

CM2

Cb’c

e'b1MeBS1H CCr//R//R2

1f

b

CE2MLC2H CCR//R2

1f

Miller’s theorem v1M

v1Mv1M A1CC

A1C j

1

C j

1

A1

ZZ

vc'b1M A1CC

vc'b2M A

11CC

e

LCv

r

R//RA

CE amplifier at Highfrequencies

RLbre

Rs CCE

Cb’e

~

RB

RC

CM1

CM2

Cb’

c

f

V

fH1f

V

fH2



11

f

V

fL fH

CE amplifier at High frequencies

RLbre

Rs CCE

Cb’e

~

RB

RC

CM1

CM2Cb’

c


RLbre

Rs

Rin

C1C2

RTE=RE//(re+(Rs//RB)/b)

CE

~

RB

RC

f

V

fH

13.4 Pass-band of BJT Amplifier

f

V

fL



12

f

V

fL fH

CE amplifier at High frequencies

RLbre

Rs CCE

Cb’

e

~

RB

RC

CM1

CM2Cb’

c


RLbre

Rs

Rin

C1C2

RTE=RE//(re+(Rs//RB)/b)

CE

~

RB

RC

ETELE

CR

f

2

1

22

22

1

CRf

T L

1CL1L

CRR2

1f

e'beT Crf

2

1

vc'b2M A

11CC

e

LCv

r

R//RA

vc'b1M A1CC

CEMLCH CCR//Rf

22

2

1

e'b1MeBS1H CCr//R//R2 1f b

Pass-band of Common Emitter amplifier



13

13.5 Pass-band of FET Amplifier

•All types of FET amplifier circuits have a high pass filter at the place where coupling andbypass capacitors are used

VDD

RD

RL

CS

Ri CCCG

vi

RG RS

vo

Common Source Amplifier

RC 2 1 f L

f

V

R C ~f


At lower frequencies, Reactance of bypass capacitor becomes higher (open) and the CS

amplifier behave as CS with RS whose voltage gain becomes smaller

Overall Lower frequency response of Common Source amplifier

STSLS CR

f

2

1

GiGL

CRRf 2

12

CDLL CRR

f

2

11

CS amplifier at Low frequencies

RL

Ri

Rin

CCCG

RTS = RS//(1/gm)CS

RG RD



14

RL

Ri Cds

Cgs~

RG

RD

Cgd

At high frequencies, reactance of couplingand bypass capacitors become smaller (short)

Miller’stheorem

VDD

RD

RL

CS

Ri CCCG

vi RG

RS

vo

Common Source Amplifier

Cgs

Ccs

Ccd

Overall Higher frequency response of Common Source amplifier

CS amplifier at High frequencies

RL

Ri Ccs

Cgs

~

RG

RD

CM1

CM2Cgd

c

fH1

fH2

vgdM A

CC 112 LDmv R//RgA vgdM ACC 1

1

gsMiGH CCR//Rf

11

2

1

dsMLD

H CCR//Rf

22

2

1

RC

fH

2

1

Higher cutoff frequency fHf fHC

R

V V (f)

0dB -3dB ~VS(f)



15

f

V

fL fH

Pass-band of Common Source amplifier

vgdM A

CC1

12 LDmv R//RgA

vgdM ACC 11

gsMiGH CCR//Rf

11

2

1

dsMLDH CCR//Rf

22

2

1

CS amplifier at High frequencies

RL

Ri Ccs

Cgs

~

RG

RD

CM1

CM2Cgdc

STS

LS

CR

f

2

1

GiGL

CRRf

2

12

CDL

L

CRR

f

2

11

CS amplifier at Low frequencies

RL

Ri

Rin

CCCG

RTS = RS//(1/gm)

CS

RG RD

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BwEE2601-13_BJT and FET Frequency Response