1

BJT ampplifier-cutoff frequencies

Basic –cutoff frequencies

High frequency limits

Low frequency limits

Basic – low/high cutoff frequencies

2

RCf

π21

1 =

f1=100kkHz

AV [dB]

AV=1

=0dB +20dB/decade

RC high pass filterlow cuoff frequency

Low input cutoff frequencies

( ) 11 2

1CrR

finG

in +=

π

Input BJThigh frequencies

RCf

π21

1 =

inG

inbe rR

rUU

+=

3

Low input cutoff frequencies

( ) 1211 ||||2

1CrRRR

fbeBBG

in +=

π

Low input cutoff frequencies

( ) ( ) 221 2

1||2

1CRrCRrR

fLoutCELceC

out +=

+=

ππ

C2

CE

RL

EG ~

RG

RE

+ EC

RB1WY

C1

RB2

WE

RC

mE

GBBbeEinE g

RRRRr

Rr1

||||||

|| 21 ≈

+=β

CE amp BJTlow frequencies

inEEE

rCf

=121

π

EGBBbe

E

E

CRRRr

R

f

+=

βπ ||||

||2

1

211

4

Low frequencies of CE - sum up

EGBBbe

E

E

CRRRr

R

f

+=

βπ ||||

||2

1

211

( ) 1211 ||||2

1CrRRR

fbeBBG

in +=

π ( ) 21 ||2

1CRrR

fLceC

out +=

π

C2

CE

RL

EG ~

RG

RE

+ EC

RB1WY

C1

RB2

WE

RC

( ) ( ) ( )21

21

211 Eoutin ffff ++≈

RLRE

+ EC

C2

RB1

RB2

EG ~

RG

C1WE

WY

( )( ) 121

1

||||||2

1

CRRrRRR

f

inTr

LEbeBBG

in

++

=

44 344 21βπ 2

211 ||||

||||2

1

CRRRRr

rR

f

LGBBbe

ceE

out

++=

βπ

( ) ( )21

211 outin fff +≈

Low frequencies of CC - sum up

( )( ) BGEbeBBB CRRrRR

f||||||2

1

211 βπ +

=

( ) 21 ||2

1CRrR

fLceC

out +=

π

( ) ( ) ( )21

21

211 Boutin ffff ++≈

121

1 ||||2

1

CRRr

RR

fBBbe

EG

in

++=

βπ

Low frequencies of CB - sum up

5

Low frequencies - sum up

f CE CC CB

f1in

X X

f1out

X

f1E(B) NA

f1

EGBBbe

E CRRRr

R

+β

π ||||||2

1

21

( ) 121 ||||21

CrRRR beBBG+π

( ) 2||21

CRrR LceC +π

( )( )( ) 121 ||||||21

CRRrRRR LEbeBBG βπ ++

221 ||||

||2

1

CRRRRr

R LGBBbe

E

++β

π ( ) 2||21

CRrR LceC +π

1||2

1

Cr

RR beEG

+

βπ

( ) ( ) ( )2)(1

21

211 BEoutin ffff ++≈

( )( ) BGEbeBB CRRrRR ||||||21

21 βπ +

Low frequencies - sum up

f CE CC CB

f1in

X X X

f1out

f1E(B) -------( ) EoutCCE CrR ||2

1π

( ) 121

CrR inCEG +π

( ) 221

CRr LoutCE +π

( ) 121

CrR inCCG +π

( ) 221

CRr LoutCC +π ( ) 221

CRr LoutCB +π

( ) 121

CrR inCBG +π

( ) ( ) ( )2)(1

21

211 BEoutin ffff ++≈

( ) BRRinCC CrGL )(2

1

→π

High frequency limits

Low frequency limits

Basic – low/high cutoff frequencies

6

RCf

π21

2 =f2=10Hz

AV [dB]

AV=1

=0dB -20dB/decade

RC low pass filter

High input cutoff frequencies

inG

inin rR

rU

+=

( ) ininGin CrR

f||21

2 π=

Input BJThigh frequencies

7

High input cutoff frequencies

CceL

Lin RrR

RU

||+=

( ) ( ) outLoutoutLCceout CRrCRRr

f||21

||||21

2 ππ==

Output BJThigh frequencies

rin

rout

( ) ininGin CrR

f||21

2 π= ( ) outLout

out CRrf

||21

2 π=

Output & Inputcutoff frequencies

8

The Miller effect

( ) in

in

v

in

vininCCin

sC

V

AsC

VsC

AVV

sC

VII

1||1

1

1||

1

=+

=

=+===

( )1|| += vin ACC

The Miller effect(inverting amp !!!!!!)

( )1|| += vin ACC

+=||1||

v

vout A

ACC

The Miller effect – an example

f – [Hz]

frequency

f2=10Hz

AV [dB]

AV=100dB=

=100000V/V

-20dB/decade

9

C2

CE

RL

EG ~

RG

RE

+ EC

RB1WY

C1

RB2

WE

RC

outrinr beinT rr =

Gin

in

V

outLC

Rr

r

V

k

rRR

LOADmVeff Rgk

+

⋅⋅−= γ

4434421

321||||

be

R

BBin rRRr

B

|||| 21 43421= C

RrCceout RRrr

Cce>>≈= ||

CQ

CEQAce

mbe

T

CQm

I

UVr

gr

Ig

+=

=

=

βϕ

ceoutT rr =

DCAC

CQCEQ

A

T

poIU

VV

mV

ββ

ϕ

≈

−−÷≈

≈

intQ,

30050

26

Summary of CE amp BJTmedium frequencies

( )||1 vbcbeinCE ACCC ++=

be

R

BBin rRRr

B

|||| 21 43421=

Summary of CE BJT ampinput characteristic

( )||1 vbcbeinCE ACCC ++=

be

R

BBinCE rRRr

B

|||| 21 43421=

Summary of CE amp BJTupper cutoff frequency

( ) inCEinCEGin CrR

f||2

12 π

=

10

T

CQm

T

mbcbe

Ig

f

gCC

ϕ

π

=

⋅⋅=+

2

be

R

BBin rRRr

B

|||| 21 43421=

( ) ininGin CrR

f||21

2 π=

( ) ||2

||1 vbcT

mvbcbeinCE AC

f

gACCC +

⋅⋅≈++=

π

Sumary of CE amp BJThigh frequencies

….taking rbb’ into account

( )( ) inbebbBGin CrrRR

f||||2

1

'2 +

=π

….very important for v.h.f.

…..when RG is small and commeasurable with rbb’

parasiticbcoutCE CCC +=

CceoutCE Rrr ||=

Summary of CE BJT ampoutput characteristic

( )( )parabcceCLout CCrRR

f+

=||||2

12 π

11

RLRE

+ EC

C2

RB1

RB2

EG ~

RG

C1WE

WY

⋅+⋅⋅⋅

=

LEcem

bebcBG

in

RRrg

ccRR

f

π2

12

bcT

mbe

CQ

CEQEYce

T

CQm

cf

gc

I

UUr

Ig

−⋅⋅

=

+=

=

π

ϕ

2

0m.cz.dla

kataloguz

pkt.pracy,

30050

26

=

−÷≈

≈

bb'

bc

T

CQCEQ

EY

T

r

c

f

IU

VU

mV

β

ϕ

Sumary of CC amp BJThigh frequencies

inout ff 22 >>

( )( )parabcceLCout CCrRR

f+

=||||2

12 π

Sumary of CB amp BJThigh frequencies

bebe

EG

in

Cr

RR

f

=

βπ ||||2

12

High frequencies - sum up

f CE CC CB

f2in

X X

f2out

X

Just

about

~fT/β <fT ~fT

( ) ( ) 21

21

11

−−− +≈ outin fff

Uwaga: tabela nie uwzględnia rbb’ istotną przy dużych częstotliwościach

( )( ) inbeBGin CrRR

f||||2

12 π

=

( )( )( )parabcbcCLout CCrRR

f+

=||||2

12 π

⋅+⋅⋅

=

LEcem

bebcinCCG

in

RRrg

ccrR

f

π2

12

inout ff 22 >>( )( )( )parabcceCL

out CCrRRf

+=

||||21

2 π

bebe

EG

in

Cr

RR

f

=

βπ ||||2

12

( ) ininGin CrR

f||21

2 π=

( ) outLoutout CRr

f||21

2 π=

( )||1 vbcbein ACCC ++=

T

CQm

T

mbcbe

Ig

f

gCC

ϕ

π

=

⋅⋅=+

2

12

High frequencies - sum up

f CE CC CB

Cin

X X

Cout

X

Just

about

~fT/β <fT ~fT

( ) ( ) 21

21

11

−−− +≈ outin fff

Uwaga: tabela nie uwzględnia rbb’ istotną przy dużych częstotliwościach

parabc CC +

LEcem

bebc RRrg

cc

⋅+

inout ff 22 >> parabc CC +

beC

( ) ininGin CrR

f||21

2 π=

( ) outLoutout CRr

f||21

2 π=

( )||1 Vbcbein ACCC ++=

T

CQm

T

mbcbe

Ig

f

gCC

ϕ

π

=

⋅⋅=+

2

paraC

CE-CC-CB comparison

Para-

meter

configuration

CE CC CB

mbeBBB grRRR /1/|| 21 == β

be

ceLC

r

rRR ||||β−β

beceLE

ceLE

rrRR

rRR

+||||

||||

L

beV u

uA =

L

bI i

iA = β

LceC

ceC

RrR

rR

+−

||||

LceC

ceC

RrR

rR

+−

||||

)(eb

bein i

ur =

)(ec

outout i

ur =

βLE

E

RR

R

+

beB rR ||

ceC rR ||

( )( ) BbeLE RrRR |||| +β Ebe Rr

||

β

( )E

beGB RrRR

||||

+β

(e) – for CB

ceC rR ||

be

ceLC

r

rRR ||||β−

CE-CC-CB general comparison

Para-

meter

configuration

CE CC CB

High(10-200)

<1 High(10-200)

High(10-200)

High(10-200)

<1

Medium(0.5k-5k)

High(10k-1M)

Low(10Ω-500Ω)

Medium(0.5k-5k)

Low(10Ω-500Ω)

Medium(0.5k-5k)

L

beV u

uA =

L

bI i

iA =

)(eb

bein i

ur =

)(ec

outout i

ur =

(e) – for CB

13

C2

RL

EG ~

RG

RE

+ EC

RB1WY

C1

RB2

WE

RC

( )Gininin RrC

fπ2

12 =

0m.cz.dla

kataloguz

pkt.pracy,

30050

26

=

−÷≈

≈

bb'

bc

T

CQCEQ

EY

T

r

c

f

IU

VU

mV

β

ϕ

( ) ( )

E

Cu

ubcEbe

bebein

bcT

mbe

T

CQm

R

Rk

kcRr

rcc

cf

gc

Ig

≈

−+++

=

−⋅⋅

=

=

11

2

β

π

ϕ

( )[ ]121 ++= βEbe

R

BBin RrRRr

B

43421

Sumary of BJT with feedbackhigh frequencies

Sumary cutoff frequencies

RC circuits for high and low cutoff frequencies

( ) ininGin CrR

f||21

2 π=( ) 1

1 21

CrRf

inGin +

=π

Sumary –cutoff frequencies

•RC circuits for high and low cutoff frequencies

•Miller effect

( ) ininGin CrR

f||21

2 π=( ) 1

1 21

CrRf

inGin +

=π

( ) 21 2

1CRr

fLoutCE

out +=

π ( ) outLoutout CRr

f||21

2 π=

14

Problems

• Draw schematic diagram of BJT (transistor as model) amplifier showing cut-off frequencies elements

• Describe Miller effect.• Estimate low- and high-cut off

frequencies for given RC diagram.• Compare high-cut off frequencies for

BJT in CE, CC, CB configurations.