Transistor Equivalent Circuits and Models

TRANSISTORTRANSISTORTRANSISTORTRANSISTORTRANSISTOREQUIVALENTEQUIVALENTEQUIVALENTEQUIVALENTEQUIVALENTCIRCUITS ANDCIRCUITS ANDCIRCUITS ANDCIRCUITS ANDCIRCUITS ANDMODELSMODELSMODELSMODELSMODELS

Learning ObjectivesLearning ObjectivesLearning ObjectivesLearning ObjectivesLearning Objectives General DC Equivalent Circuit AC Equivalent Circuit Equivalent Circuit of a

CB Amplifier Effect of Source Resistance

Rs on Voltage Gain Equivalent Circuit of a

CE Amplifier Equivalent Circuit of a

CC Amplifier Small-signal Low-frequency

Model or Representation T-Model Formulas for T-Equivalent of

a CC Circuit What are h-parameters ? Input Impedance of a Two

Port Network Voltage Gain of a Two Port

Network The h-parameters of an

Ideal CB Transistor The h-parameters of an

ideal CE Transistor Approximate Hybrid

Equivalent Circuits Transistor Amplifier

Formulae Usingh-parameters

Typical Values of Transistorh-parameters

Approximate HybridFormulas

Common Emitterh- parameter Analysis

Common Collectorh-parameter Analysis

Conversion ofh-parameters

2238 Electrical Technology

Fig. 59.2

Fig. 59.1

59.1. General59.1. General59.1. General59.1. General59.1. General

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2239Transistor Equivalent Circuits and Models 2239

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59.3. AC Equivalent Circuit59.3. AC Equivalent Circuit59.3. AC Equivalent Circuit59.3. AC Equivalent Circuit59.3. AC Equivalent Circuit

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6.:02

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Fig. 59.9

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∴ # $

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2. >8

) 7

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)'2

+,-#$

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7

2

2

1

45

)

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)

0>

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∴

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)0>8E,)20-5)3'-(

+,)-#!$ % &'((*+,$

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!

!

))2

1# #)#0;:$9/D)82.( 7

)0,982)/-Ω

) 7 @@

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)

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2/-

.

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)

)2.(

)

)2ED)25

7 7

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/-

)3

B" 0, 8 25

3'(

59.5. Effect of Source Resistance R59.5. Effect of Source Resistance R59.5. Effect of Source Resistance R59.5. Effect of Source Resistance R59.5. Effect of Source Resistance Rs s s s s on Voltage Gainon Voltage Gainon Voltage Gainon Voltage Gainon Voltage Gain

3

3

3

3

+,-0

3

+

,-/#$*"3#7@@A$

3

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+"

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R C

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)/D

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7

7

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7"

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≅

7

Fig. 59.13

∴7

7

7

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7"

39

7!

J""

34

799

≅

34

7 ∴

7# $

33

6

3II

7

J!3

7!

7

7

+,)-#!$ $ &'(4,$

! $# ! $##

5#!$

#. 0

1# #

7# $

3 3

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)D@@0J

≅ D()0,90,D).

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D

#D 08 $

3

Fig. 59.14

+20 V-25 V

RS

in out

Vs

2 mV(rms)

1K

25 K 10 K

2 MV V


B"

)99

7)0,D@@0,Ω≅ 0,Ω ∴

0,

3

1

400400400400400

'

.A#$")

2

" B"A#$"

Fig. 59.15

))E0)05 ∴ /0

2

)3µµµµµ(

.#+,-,$"

3

7#!

7@@

$

∴7

7

0,0

0,

)3µµµµµ(

59.6. Equivalent Circuit of a CE Amplifier59.6. Equivalent Circuit of a CE Amplifier59.6. Equivalent Circuit of a CE Amplifier59.6. Equivalent Circuit of a CE Amplifier59.6. Equivalent Circuit of a CE Amplifier

K+,-8#$

Fig. 59.16

+".,-0%

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(

≅

≅ β

iS

IB

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IC VCCVCC

RB

RL

RL

IE

RCRC

ib

C1

C2

in

out

Vs

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(a) (b)

B

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V


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7

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7

)

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)*+

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@@

&

' (#

B" 7

∴ 7 7

6

IIβ

7

) #*&)

)

+,)-'$ $ &'(6*+,

/7),/()1,

/(8,

/(

8,/7#β/&),$

##,670--

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)β

),E0.).

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*+)β

7),E0)0,Ω

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# $

05

0,

5µµµµµ(

)β

),E8)43µµµµµ

)

99β

7)J@@0,Ω ≅ )3ΩΩΩΩΩ

)

@@

)J@@D≅ 32


7 7

D

0,

'33

)

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)

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.+,--

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88: D

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)

08":)''$

When Emitter Bypass Capacitor is RemovedWhen Emitter Bypass Capacitor is RemovedWhen Emitter Bypass Capacitor is RemovedWhen Emitter Bypass Capacitor is RemovedWhen Emitter Bypass Capacitor is Removed"B"

.β .,:02"

#4β$#74

$ ≅ β

#74

$

7

+

,-0#$

B"

+,-0#$

)

@@β

#4

$ ≅

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7

Fig. 59.19

Fig. 59.18

Fig. 59.20


Fig. 59.22

Fig. 59.21

7)0,Ω 6

∴ β #74

$≅ β

)ED)J

∴ )

@@β

)0J@@J

)0

J/

)55592 6

)5592 6

)

β#

74

$(

)

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∴ # 7 $ # 7 $

88: D

D3559 6

)

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+,)-5 % &'7(, #*+

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Fig. 59.23

Fig. 59.24

20V

C1RS

C2

C3

VoutVs

20 K

20 K

2mV(rms)

40 K10 K

20 V

R1

RL

RC

RE

C1

R2

C2

C3

2

Vs

45 K 5 K

5 K

5 K1 K

+

_


59.7. Effect of Source Resistance R59.7. Effect of Source Resistance R59.7. Effect of Source Resistance R59.7. Effect of Source Resistance R59.7. Effect of Source Resistance Rsssss

N

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)

;

3

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$ $ &'72,$# "

!! %3())Ω=1;:/&)

1# #

+,-0/3

.A->"7),Ω"

β7)0,Ω

∴ @@β

7 )D@@00,Ω )0Ω

;!1<33ΩΩΩΩΩ

% "05

Ω0Ω1Ω

0Ω*"

)

)05

)0

∴

)E

)0E0)'33,(,

;!1<2

%"@@β

7)0D

7

7

@@ 00 >5

/ 0# @@ $

∴

)0E>)53,(

F"3"

59.8. Equivalent Circuit of a CC Amplifier59.8. Equivalent Circuit of a CC Amplifier59.8. Equivalent Circuit of a CC Amplifier59.8. Equivalent Circuit of a CC Amplifier59.8. Equivalent Circuit of a CC Amplifier

+,-0>#$

#$

!,=##*

Fig. 59.25

Fig. 59.26

Fig. 59.27

RS

RL

RC

VCC

RE

RBC

Vs


%%

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9

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!

3

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*+

!

%#4β$

#74

$≅ β

β

∴

* +

)O&@@

*+

)@@β#

74

$ ≅ β#

74

$

6

≅ β

67PP

) β

6)

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& # $

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)

)

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74

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Fig. 59.29


Fig. 59.32

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)

@@

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*+

)β#74

$≅ β

),E2)0D

∴ #70,Ω

2D$

* +

)

@@

*+

)2D@@0D

)2

)0D@@,D)'2

≅

7

%"

)

βE)β),(

)

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+,)-"!A#$!!% $ &'=(,$

*+ * + !β)

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*+)β#74$

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),D@@,D))2

)

≅ Eβ)100 (

)

)3$

+,)- $ &'=7,$

* +

!

β)0

1# #)090). 7)0,9)0,Ω

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*+

) β#74

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* +

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*+

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7

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,7 0, ,

3559

Fig. 59.31

Fig. 59.30

RL

RBRE

-20

+20

rinVoutVs 5 K20 K

400 K

20V

R1

V2R2

VCC

RLREVout

Vs

30 K

10 K5 K5 K

+

_


)

)88:E0)

59.9. Small-signal Low-frequency Model or Representation59.9. Small-signal Low-frequency Model or Representation59.9. Small-signal Low-frequency Model or Representation59.9. Small-signal Low-frequency Model or Representation59.9. Small-signal Low-frequency Model or Representation."

; ""

!

59.10. T-Model59.10. T-Model59.10. T-Model59.10. T-Model59.10. T-Model !

%+,-// ;

% ; .

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3%

0,5

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6

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Fig. 59.33 Fig. 59.34

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Q

+,-/,#$%"

;

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α )

)α

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)0,,Ω(

)Ω(

)JΩ

rb

re rc

I/P O/P

E C

B

Fig. 59.35

rbrb ib

ie

rere re

rc

rc

ie

I/P O/P

EE

C

C

B B

(a) (b)


; +,-/8

+,-/8 +,-/:

; +,-/>

Fig. 59.36 Fig. 59.37 Fig. 59.38

59.11. Formulas for T-Equivalent of a CB Circuit59.11. Formulas for T-Equivalent of a CB Circuit59.11. Formulas for T-Equivalent of a CB Circuit59.11. Formulas for T-Equivalent of a CB Circuit59.11. Formulas for T-Equivalent of a CB Circuit

%+,-/-

;

3

F"

1

'

# $

# $# $

3

)α

'# $

$# $ # $ #

) )

0

# # $

6

0

# $ # $

6

)

Fig. 59.39

RS

Vin

rinVsrorb

rcre

ieib

ic

rinie

r L=

RL

+_

Transistor

B

E C

Vout


59.12. Formulas for T-Equivalent of a CE Circuit59.12. Formulas for T-Equivalent of a CE Circuit59.12. Formulas for T-Equivalent of a CE Circuit59.12. Formulas for T-Equivalent of a CE Circuit59.12. Formulas for T-Equivalent of a CE Circuit

;

+,-2

1

'

# # $

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# $

3

)β # $

'# $

# $ # $

) )

0

# $=# # $?

0

# $=# # $ # $?

3

59.13. Formulas for T-Equivalent of a CC Circuit59.13. Formulas for T-Equivalent of a CC Circuit59.13. Formulas for T-Equivalent of a CC Circuit59.13. Formulas for T-Equivalent of a CC Circuit59.13. Formulas for T-Equivalent of a CC Circuit

; +,-2

'

# $

)

4#;α$#

4

3$

# $

# $

3

# $# $

' )

)

# $# $

).

&

+,)-'B /&)Ω,/(1, /(8α/)'0 ##" %! $()1! ! ,! %

$# :60--$

1# #)α)->

-> "

# $ , #; ->$

'3

).ν

)2E->)/:

)

4

#;α$),4#;->$)93ΩΩΩΩΩ

+,)-)""B ! #!$ "

%! =))1! $ !

7))Ω

C5$! $#!$ ! !# $

;"%:#')>Ω"

):Ω"

)J

#)-:8D

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Fig. 59.40

Fig. 59.41

RS

rin

Vs

ro

reie

rcrb

ib

ic

Vout

rmie

r L=

RL

+_B

E

C

Vin


1# #*"#)α#

4

$≅ α

∴ α )

#9

)-:8D9D)-:8

/0

-:8 /

# $ > : #; -:8$

4'3

/0 -:8 /

# $ 0 > : #; -:8$

'9

+,)-5! ! ,!! ,! %

$ $!!% "#'

/=)Ω,

/4))Ω,

/)2&8, α/)'&,

/()1

3/4))Ω

!, ! !% !

#@##7#0---

1# #2

/#; $ #; -,$

433ΩΩΩΩΩ

# $

3

-, :," 2

:," #; -,$ />">:#/ 2 2$

34/

-,

- # -,$

/

-,EE

# $ # $ 24 #/ 4 2$E,

< )

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20:,)5$

59.14. What are h-parameters ?59.14. What are h-parameters ?59.14. What are h-parameters ?59.14. What are h-parameters ?59.14. What are h-parameters ?

!.

!"

K!!

!+,-20.

" !

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% "

0 RQ

F " 0 0

A$$=#,1#. @

.+,-2/" 0)"

%

Fig. 59.42


0

5

6

00

6

!=#*$

0

!

?

)

4

0

0

0)

04

00

0

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A$

$

=#,. @

.+,-22" )

0

0

0

0

6

000

0

6

."0

#09

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00

#$

"3%!

N"

)

0

)

0

)

00

)

59.15. Input Impedance of a Two Port Network59.15. Input Impedance of a Two Port Network59.15. Input Impedance of a Two Port Network59.15. Input Impedance of a Two Port Network59.15. Input Impedance of a Two Port Network

K !

+,-2,

."D

)

9

A#$.

,-2"

0 0

D

0 0

Fig. 59.43

Fig. 59.44

Fig. 59.45


.+,-2,0);ν09

!0A#$.,-2"

000 00 0

;

0 0

00 9

A#$"

0 0

00

9

D

59.16. Voltage Gain of a Two Port Network59.16. Voltage Gain of a Two Port Network59.16. Voltage Gain of a Two Port Network59.16. Voltage Gain of a Two Port Network59.16. Voltage Gain of a Two Port Network

#+ ,-2,$ )ν

09ν

Bν

)

D

*"

)ν

09

D

ν09

.,-,"

0

00# 9 $

D

+,)-9"#$ % &'46*+

1# #+"0

+"

+,-28#$

Fig. 59.46

!

)042@@2)'ΩΩΩΩΩ .+-28#$"

.

0);

90#

!

$

∴ 0 0

; 9 0

0

? 3)

B""

!0+,-2:%

02Ω

2Ω

.*")

090

∴ 0

00 0

9 0

0.50.50.50.50.5

Fig. 59.47


!

)242)>Ω

∴ 00

)9>)3)1,,#

*"!+,-28#$" '

)2Ω 0);, 0), 00)0,

59.17. The h-parameter Notation for Transistors59.17. The h-parameter Notation for Transistors59.17. The h-parameter Notation for Transistors59.17. The h-parameter Notation for Transistors59.17. The h-parameter Notation for Transistors "

)

)

0

)$

)

0

)

)

00

))

)

.

+""'

$

"""

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$ "

59.18. The h-parameters of an Ideal Transistor59.18. The h-parameters of an Ideal Transistor59.18. The h-parameters of an Ideal Transistor59.18. The h-parameters of an Ideal Transistor59.18. The h-parameters of an Ideal Transistor.""

"!

*""

' )

$

)

59.19.59.19.59.19.59.19.59.19. The h-parameters of an Ideal CB TransistorThe h-parameters of an Ideal CB TransistorThe h-parameters of an Ideal CB TransistorThe h-parameters of an Ideal CB TransistorThe h-parameters of an Ideal CB Transistor

%+,-2>#$" !+"

,-2>#$%

A#*$,

+,-2-#$

∴ )

"

!

;

$

#%α$

!,

+,-2-#$

"%#$

Fig. 59.48


RQ& "

""0*"

ν)

∴

0 0

""!

K"

#)9∞$

∴

)

SummarySummarySummarySummarySummary

)

(

$);"

)(

)

+,-,%#%"

#

;

;8$

%"

"

!#$

*"

59.20. The 59.20. The 59.20. The 59.20. The 59.20. The hhhhh-parameters of an ideal CE Transistor-parameters of an ideal CE Transistor-parameters of an ideal CE Transistor-parameters of an ideal CE Transistor-parameters of an ideal CE Transistor

+,-,#$

!

,-,#$

β

A#*$,

+ ,-,0 #$

F"β

∴ )β

0

$

#%

$

!,

+,-,0#$

7

")%

)"

!!*"(

Fig. 59.50

Fig. 59.51

hib

ie ic

hfbie

C

B

E

B

Fig. 59.49

Fig. 59.52


∴

0 0

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∴

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(

$)β"

)(

)

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B.,--

59.21. Approximate Hybrid Equivalent Circuits59.21. Approximate Hybrid Equivalent Circuits59.21. Approximate Hybrid Equivalent Circuits59.21. Approximate Hybrid Equivalent Circuits59.21. Approximate Hybrid Equivalent Circuits"!

#$

Q " R!Q

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4

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Fig. 59.53


B76$

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ν

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) $4

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59.22. Transistor Amplifier Formulae Using 59.22. Transistor Amplifier Formulae Using 59.22. Transistor Amplifier Formulae Using 59.22. Transistor Amplifier Formulae Using 59.22. Transistor Amplifier Formulae Using hhhhh-parameters-parameters-parameters-parameters-parameters

.+,-,:"

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) $4

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Fig. 59.56

hf i1hrv2

rinvS

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ie

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+_

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1

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iLv2

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2b

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);0LA#$"

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∴ 00

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4

3$;

7)

9

0);

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3 3

∴

3

3

%

3

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00 0 0

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3 3

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( # $

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9 3 3

3 3

59.23. Typical Values of Transistor 59.23. Typical Values of Transistor 59.23. Typical Values of Transistor 59.23. Typical Values of Transistor 59.23. Typical Values of Transistor hhhhh-parameters-parameters-parameters-parameters-parameters

%

#

0,Ω D D

/E;2

0,E;2 ≅

$

;-> , ;,

,E;8

0,E;8

0,E;8

59.24. Approximate Hybrid Formulas59.24. Approximate Hybrid Formulas59.24. Approximate Hybrid Formulas59.24. Approximate Hybrid Formulas59.24. Approximate Hybrid Formulas

3

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4$

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≅ β

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59.25. Common Emitter 59.25. Common Emitter 59.25. Common Emitter 59.25. Common Emitter 59.25. Common Emitter hhhhh-parameter Analysis-parameter Analysis-parameter Analysis-parameter Analysis-parameter Analysis

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Fig. 59.59

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∴ $

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)

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)"

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3 3

# @@ $

$

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3

)

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0


∴ 0# @@ @@ $ 3

$

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@@

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0

B" )

)

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∴9

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8 2

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$/()),

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Fig. 59.64

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vs

C1 C2

RB

RS

RE

+VCC

vo

RC

=100

250 K 5 K

0.5 K

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Fig. 59.70

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∴ );/2>8E8->)?',(

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∴ ,

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Tutorial Problems No. 59.1Tutorial Problems No. 59.1Tutorial Problems No. 59.1Tutorial Problems No. 59.1Tutorial Problems No. 59.1

G +,-:"

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α );-!=#$)ΩΩΩΩΩ#$)2#$33#$-5?

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OBJECTIVE TESTS – 59

ROUGH WORK

Engineering

Transistor Equivalent Circuits and Models