Transistor h-parameter analysis.ppt

1

CHAPTER-7 TRANSISTOR AT LOW

FREQUENCY

2

7.1 Transistor Amplifier Circuit:-Transistor equivalent ckt are divided in two

types (i) D.C. equivalent ckt. (ii) A.C. equivalent ckt.

Fig.7.1(a) Transistor Amplifier using Self Bias

3

4

Fig.7.1(b) D.C. Equivalent Ckt.

Fig.7.1(c) A.C. Equivalent ckt.

5

The capacitors CC1 & CC2 are called the coupling capacitors. Capacitors CC1 is used to couple the a.c. input signal to the base of the transistor. A coupling capacitor is also called a blocking capacitor because it blocks d.c.

Another capacitor CE is called bypass capacitor because it bypasses the all a.c. current from the emitter to ground.

6

7.2 Hybrid Parameter (h-Parameter):- h-parameter is widely used because they gives

accurate results & can be measured very easily. The transistor is a three terminal device but if one

terminal is grounded, then transistor can be used as a two port network.

The h-parameters are

V1=h11I1+h12V2

I2=h21I1+h22V2

The parameter h11, h12, h21 & h22 are called h-parameters.

7

Fig.7.2 (a) General h-parameter Equivalent Circuit

Fig.2.2(b) Transistor Two Port Network

8o22

1-

2

222

r12

2

112

f21

1

221

i11

1

111

hh as, drepresente also isit

mho.or ohm isunit & ckt.open I/P with admittance O/Ph


unit. no has & circuitedopen I/Pgain with voltageReverseV

Vh

hh as drepresente also isit

none. isunit & shorted O/Pgain with current forwardI

Ih


ohm isunit & shorted O/P with impedance I/PI

Vh

as, summarized isparameter -h the

V

I

9

7.3 h-Parameter Representation for Transistor:-Sr. No.

h-Parameter Common Emitter

Common Base

Common Collector

1. h11 hie hib hic

2. h21 hfe hfb hfc

3. h12 hre hrb hrc

4. h22 hoe hob hoc

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7.4 Analysis of Transistor Amplifier by h-Parameter:-

Fig 7.4(a) General Amplifier Circuit with Source & Load Resistance

Fig 7.4(b) h-Parameter Equivalent Circuit of above General Amplifier

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1. The Current Gain (Ai):- The current gain for the transistor amplifier is defined as the ratio of O/P current to the I/P current. Mathematically,

Ih)hR1(I

h.RI-IhI

get, weeq.(4)in V of value theputting Now

...eq.(4) VhIhI

...eq.(3) VhIhV

are, equations Parameters-h theNow

...eq.(2) .R-I.RIV

,V is minaloutput ter theacross voltage thefigure above from

...eq.(1) I

I-

I

IA

1foL2

oL21f2

2

2o1f2

2r1i1

L2LL2

2

1

2

1

Li

12

hR1

h-

I

I

I

I- A

hR1

h

I

I So

oL

f

1

L

1

2i

oL

f

1

2

13

2. The Input Resistance (Ri):- The I/P resistance Ri is defined as the resistance we see looking into the amplifier I/P terminals (1-1’). Mathematically,

i1

1rL

1

2i

1

1

1

rL21i1

2r1i1

L22

1

1i

RI

V But h.R

I

I-h

I

V

have, we.Iby sideboth on eq. above thedividing Now

h.RI-IhV

VhIhV

parameter -h of eq.in .R-IV of value theputting Now

I

VR So

14

Admittance Load R

1Y where

Yh

hhh

R1h

hhhR

Rh1

hRhhh.R

Rh1

h-hR so

Rh1

hA that know weh.RAh R

AI

I-but h.R

I

I-h R thereforeSo

LL

o

rfi

Lo

rfii

Lo

rLfirL

Lo

fii

Lo

firLiii

i1

2rL

1

2ii

L

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3. The Voltage gain (Av):- The voltage gain is defined as the ratio of the O/P voltage V2 to I/P voltage V1.

Mathematically,

oL

frii

Lo

fi

i

Livi

1

1

1

1Li

1

L1iv

1i21

2i

1

L2

1

2v

hR1

hhhR &

Rh1

hA that,know Again we

..eq.(2) R

RAA So, R

I

V But

V

IRA

V

RIAA Therefore

IAIor I

IA that,Know weSince

eq.(1) ... V

RI

V

VA

16

hh-hhΔh where

R.Δhh

RhA

R.Δhh

Rh

Rhh-hhh

RhA

hR1

hhh

Rh1Rh-

A

have, then weeq.(2)in value theseputting now

froi

Li

Lfv

Li

Lf

Lfroii

Lfv

oL

fri

Lo

Lf

v

17

4. Output Resistance (Ro) :- The O/P resistance may be calculated by reducing the source voltage Vs to source & load resistance RL to infinity & driving the O/P terminals by a voltage generator V2. as shown below,

Fig.7.4(c) h-equivalent ckt. to calculate the O/P resistance

O/P resistance Ro is the ratio of the voltage V2 & the current drawn from the voltage source I2

So Ro=V2/I2

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2ois

2rf

2

2ois

2rf

2o

1

is

2r1

2r1is

2r1i1s

2o1f

2o

2o1f2

VhhRVhhV

VhhR

Vhh

VR

get, weeq.(1)in I of value theputting Now

...eq.(2) hR

VhI

VhIhR or

0VhIhIR

fig.7.4(c)in shown as ckt. theof side I/P the toKVL Applying

...eq.(1) VhIh

VR hence

VhIhI eq.parameter -h from

19

Δh

hR

be, willresistance O/P then 0R resistance source if

hhhhΔh where ΔhRh

hRR ,

hhhhRh

hR

hhhRh

hRR

get, wearrangingRe

io

s

rfioso

iso

rfioso

is

rfiso

iso

So

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5. The Overall Voltage Gain (Avs):- The overall voltage gain of the transistor amplifier is the ratio of O/P voltage V2 to the source voltage Vs . It is denoted by Avs.

Fig 7.4(d) Equivalent I/P ckt.

...eq.(1) .AA fore thereV

VA but,

V

V

V

VA gain, voltageoverallally Mathematic

1vvs

1

2v

1

1

2

s

2vs

s

s

V

V

V

V

21

0)(R source

voltageidealan gain with voltage theis A therefore

AAen th0R if

RZ

ZA.AA

get, weeq.(1)in /VV of value theputting

RZ

Z

V

Vor

RZ

.ZVV

have, wefigure from resistance I/P

amplifier therepresents Zhere ckt. equivalent from now

s

v

vvss

si

iv

1vvs

s1

si

i

s

1

si

is1

i

sV

V

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6. Overall Current Gain (Ais):- overall current gain of the transistor amplifier is the ratio of the O/P current (IL) to the current delivered by the source (Is)

Fig 7.4(e) Modified I/P Equivalent ckt.

1

2i

s

1

1

2is

s

2

s

Lis

I

IAbut ...eq.(1)

I

I

I

IA but,

have, weexpression above themodifying

I

I

I

IA gain,Current overallally Mathematic

23)(R sourcecurrent idealan gain with current

theis A thereforeAA then R if Now

ZR

RA

I

I.AA

get, weeq.(1)in I

I of value theputting now

...eq.(2) ZR

R

I

I then

ZR

RII

have wefig.7.4(e) from ,resistance I/Pamplifier is Zhere

ckt., equivalent I/P modified use weA determine To

...eq.(1) I

I.AA So

s

iiiss

is

si

s

1iis

s

1

is

s

s

1

is

ss1

i

is

s

1iis

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7.5 h-Parameter Expression for CE amplifier:-

Fig. 7.5 h-parameter equivalent circuit for CE amplifier

E

CB

EE

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1. Current gain (Ai):-

hR1

h- A

Amplifier,Emitter Common for Gain Current

)Expression (General hR1

h- A

oeL

fei

oL

fi

R then Zresistance biasing

nofor & RR Zckt. bias fixed for the

R1h

hhhR

Amplifier, E-Cfor resistance I/P The

)Expression (General

R1h

hhhR

ii

Bii

Loe

refeiei

Lo

rfii

2. Input Resistance (Ri):-

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hh-hhΔh where

R.Δhh

RhA amplifier, CEfor gain Voltage

)Expression (General R.Δhh

RhA

fereoeie

Lie

Lfev

Li

Lfv

3. Voltage Gain (Av):-

Loo

srefeieoe

soe

ieso

so

iso

RR Z

be willstageamplifier theof resistance O/P The

resistance source theis R & hhhhΔh where

amplifier) CE(for ΔhRh

hRR

)Expression (General ΔhRh

hRR

4. Output Resistance (Ro):-

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fereoeie

si

i

Lie

Lfe

si

ivvs

si

iv

1vvs

hhhhΔh here

amplifier) CE(for RZ

Z

ΔhRh

Rh-

RZ

ZAA

)expression (general RZ

ZA.AA

sV

V

amplifier) CE(For ZR

R

Rh1

hA

)expression (General ZR

R

Rh1

h

ZR

RAA

is

s

Loe

feis

is

s

Lo

f

is

siis

5. Overall Voltage Gain (Avs):-

6. Overall Current Gain (Ais):-

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Properties of Common Emitter Amplifier:-

1. Large current gain (Ai=100).

2. Large voltage gain (Av=500).

3. Large power gain (Ap=Av.Ai)

4. Moderate I/P impedance (50KΩ).

5. Moderate O/P impedance (10KΩ).

6. Phase shift is 180º bet I/P & O/P voltage.

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hR1

h- A

Amplifier, BaseCommon for Gain Current

obL

fbi

R Z

then,biasing no is theret.ifarrangemen biasing

upon the depends stageamplifier theof resistance i/p The

R1h

hhhR

Amplifier, B-Cfor resistance I/P The

ii

Lob

rbfbibi


7.6 h-Parameter Expression for CB amplifier:-

30

hh-hhΔh where

R.Δhh

RhA amplifier, CBfor gain Voltage

fbrbobib

Lib

Lfbv


Loo

srbfbibob

sob

ibso

RR Z

be willstageamplifier theof resistance O/P The

resistance source theis R & hhhhΔh where

ΔhRh

hRR


31

rbfbibob

si

i

Lib

Lfb

si

ivvs

hhhhΔh here

RZ

Z

ΔhRh

Rh-

RZ

ZAA

ZR

R

Rh1

hA

is

s

Lob

fbis



The overall current gain for the CB amplifier is,

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Properties of Common base Amplifier:-

1. current gain is less than 1(Ai<1).

2. Large voltage gain (Av=150).

3. Power gain is less than CE configuration (Ap=Av.Ai)4. Small I/P impedance (40Ω).5. Large O/P impedance (1MΩ).6. No voltage & current Phase shift.

33


hR1

h- A

Amplifier,collector Common for Gain Current

ocL

fci

R Z

then,biasing no is theret.ifarrangemen biasing

upon the depends stageamplifier theof resistance i/p The

R1h

hhhR

Amplifier, C-Cfor resistance I/P The

ii

Loc

rcfcici


7.7 h-Parameter Expression for CC amplifier:-

34

hh-hhΔh where

R.Δhh

RhA amplifier, CCfor gain Voltage

fcrcocic

Lic

Lfcv


resistance source theis R

hhhhΔh where

ΔhRh

hRR

is,amplifier CC theof resistance O/P The

s

rcfcicoc

soc

icso


35

rcfcicoc

si

i

Lic

Lfc

si

ivvs

hhhhΔh here

RZ

Z

ΔhRh

Rh-

RZ

ZAA

ZR

R

Rh1

hA

is

s

Loc

fcis



The overall current gain for the CC amplifier is,

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Properties of Common Collector Amplifier:-

1. current gain is Very high (Ai=100).

2. Voltage gain is less than unity (Av<1).

3. Power gain is less than CE configuration (Ap=Av.Ai)

4. Large I/P impedance (750KΩ).

5. Small O/P impedance (50Ω).

6. No voltage & current Phase shift.

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7.8 Simplified or Approximate model:- ..Simplified model are used to reduce the ckt complexity.

…If the load resistance RL is small it is possible to neglect the parameter hre & hoe and obtain the approx. equivalent ckt. as shown in fig.7.8 below. By using hoe.RL<=0.1 the error in calculating Ai, Av, Ri & Ro is less than 10%

Fig.7.8 h-parameter Approximate CE model

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Parameter Symbol CE Approx.

CB Approx.

CC Approx.

Current Gain

Ai -hfe hfb=1 hfc

I/P Resistance

Ri hie hib hic+hfcRL

Voltage Gain

Av 1

O/P Resistance

Ro

ie

Lfe

h

Rh

oeh

1

obh

1

ib

Lfb

h

Rh

fc

icS

h

hR

39

7.9 Typical h-Parameter values for Transistor:-Sr. No.

h-Parameter Common Emitter

Common Base

Common Collector

1. hi 1100Ω 1100Ω 22Ω

2. hr 1

3. hf 50 -51 -0.98

4. ho 25μA/V 25μA/V 0.49μA/V

-410 2.5 4103

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7.10 Conversion Expression for h-parameter:-

Sr. No. Common Base Common Collector

1. hic=hie

2. hrc=(1-hre)≈1

3. hfc=-(1+hfe)

4. hoc=hoe

fe

ieib h1

hh

refe

oeierb h

h1

hhh

fe

fefb h1

h-h

fe

oeob h1

hh

41

re model of Transistor:- re model of transistor is an alternate approach which

employs transistor beta & resistance values is gaining importance.

Advantage of using these models are:-

(1) Required parameters are easily available.

(2) Simple & easy procedure.

(3) Results obtained have a fairly good accuracy for the study of amplifier circuit.

Note:- In CE re-model hie=βre & hfe=β

In CB re-model hib=re & hfb=-1

Rest of the analysis is very similar to approx. analysis.

42

7.11 Giacoletto or hybrid π-Model:-

Fig. 7.11(a) Giacoletto or hybrid-π Model of a CE transistor

43

Fig. 7.11(b) Diagram showing virtual base B’ & ohmic base spreading resistance rbb’

44

7.12 Hybrid-π Parameter Values:-The typical magnitude for the element of the hybrid π Parameter Values at room temperature & for IC=1.3mA are,

gm=50mA/V, rbb’=100Ω, rb’e=1K Ω

rb’c=4MΩ, rce=80K Ω Cb’c=3pF

Cb’e=100pF

45

7.13 Relationship bet low frequency h-parameter & high frequency or π- Parameters :-

cb'feoece

ce

re

eb'

cb'cb'

eb'iebb'

fe

meb'

m

feeb'

C

T

Cm

)gh(1hr

1g (V)

h

r

g

1r (IV)

r-hr (III)

h

ggor

g

hr (II)

26

)mAin (I

V

Ig (I)

46

unity. todropsgain current

ckt.short CE heat which trequency theis f

CCCC

f2

gC (VI)

T

DeTeDeeb'

T

meb'

47

7.14 Frequency Response of an Amplifier:-

Fig. 7.14(a) Typical R-C Coupled Amplifier Frequency Response

48

If the I/P voltage of an amplifier is kept constant but its frequency is varied, it is found that the amplifier gain,

remains practically constant over a sizable range of the mid frequency.

Decrease at low as well as high frequencies.

thus in frequency response curve three values of frequency are important,

(i) Mid frequency range.

(ii) Lower cutoff frequency, fL.

(iii) Upper cutoff frequency, fH

49

7.15 Frequency Response Parameter:- The β cut off frequency fβ is the CE short ckt small signal

forward current transfer ratio cut off frequency. It is given by,

fα is the cut off frequency at which the CB short ckt small signal forward current ratio drops 3dB from its value at low frequency.

b'eb'cb'eβ )rcCπf

(2

1

b'eb'e

fe

b'efbb'e rπC

h

)rhπCf

21(2

1

50

fT is the frequency at which the short ckt. Common emitter current gain attains unit magnitude.

cbeb

mT CC

gf

''2

51

7.16 Cascaded Amplifier:-

Fig. 7.16(a) Cascaded Amplifier

When the amplification of a single stage transistor is not sufficient for a particular purpose then two or more stages are connected in cascaded Then the required level of amplification is achieved.

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Transistor h-parameter analysis.ppt