Chapter 3 small signal midfrequency BJT

INTRODUCTION For sufficiently small emitter-collector voltage and current excursions about the quiescent point small signals, the BJT is considered linear; it may then be replaced with

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Val de Loire Program p.40

CHAPTER 3:

SMALL-SIGNAL MIDFREQUENCY BJT

Table of Contents

3.1 INTRODUCTION 42

3.2 HYBRID-PARAMETER MODELS 43

3.2.1 Common-Emitter Transistor Connection 43

3.2.2 Common-Base Transistor Connection 45

3.2.3 Common-Collector Amplifier 46

3.3 MEASURES OF AMPLIFIER CHARACTERISTIC 48

3.3.1 CE amplifier analysis 49

3.3.2 CB amplifier analysis 51

3.3.3 CC amplifier analysis 54

Table of Figures Fig 3-1 Common-emitter characteristics (npn, Si device) 43

Fig 3-2 CE small-signal equivalent circuit 44

Fig 3-4 CB small-signal equivalent circuit 46

Fig 3-5 CC small-signal equivalent circuit 47

Fig 3-6 Amplifier circuit 48

Fig 3-7 CE amplifier 49

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Val de Loire Program p.41 Fig 3-8 CB amplifier 52

Fig 3-9 CC amplifier 54

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CHAPTER 3:

SMALL-SIGNAL MIDFREQUENCY BJT

3.1 INTRODUCTION

For sufficiently small emitter-collector voltage and current

excursions about the quiescent point (small signals), the BJT is considered linear; it may then be replaced with small-signal

equivalent-circuit models

There is a range of signal frequencies which are large enough so that coupling or bypass capacitors can be considered short circuits, yet low enough so that inherent capacitive reactances associated with BJTs can be considered open circuits In this chapter, all BJT voltage and current

signals are assumed to be in this midfrequency range

In practice, the design of small-signal amplifiers is divided into two parts:

(1) setting the dc bias or Q point

(2) determining voltage- or current-gain ratios and impedance values

at signal frequencies

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3.2 HYBRID-PARAMETER MODELS

3.2.1 Common-Emitter Transistor Connection

Fig 3-1 Common-emitter characteristics (npn, Si device)











1 2

, ,

If the total emitter-to-base voltage v goes through only small BE

excursions (ac signals) about the Q point, then v BE v be,i C i , and so c

on Therefore,

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The four partial derivatives, evaluated at the Q point, are called CE

hybrid parameters and are denoted as follows:

Input resistance:   

ie

h

Reverse voltage ratio:   

re

h

Forward current gain:   

fe

h

Output admittance:    

oe

h

Therefore:







be ie b re ce

c fe b oe ce

v h i h v

i h i h v

The equivalent circuit is shown :

Fig 3-2 CE small-signal equivalent circuit

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The circuit is valid for use with signals whose excursion about the Q

point is sufficiently small so that the h parameters may be treated as

constants

3.2.2 Common-Base Transistor Connection

Fig 3-3 Common-base characteristics (pnp, Si device)

In the CB case, equations can be found specifically for small excursions about the Q point The results are:







eb ib e rb cb

c fb e ob cb

v h i h v

i h i h v

The definitions of the CB h-parameters are:

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Input resistance:   

ib

h

Reverse voltage ratio:   

rb

h

Forward current gain:    

fb

h

Output admittance:    

ob

h

The equivalent circuit is as follow:

Fig 3-4 CB small-signal equivalent circuit 3.2.3 Common-Collector Amplifier

The common-collector (CC) or emitter-follower (EF) amplifier, can be

modeled for small-signal ac analysis by replacing the CE-connected

transistor with its h-parameter model Assuming, for simplicity, that

  0

h h , we obtain the equivalent circuit:

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Fig 3-5 CC small-signal equivalent circuit

An even simler model can be obtained by finding a Thevenin equivalent

for the circuit to the right of a, a Application of KVL around the outer

loop gives:

v i h i R  i h  h  i R

The Thevenin impedance is the driving-point impedance:

b

v

i

The Thevenin voltage is zero (computed with terminals a, a open); thus,

the equivalent circuit consists only of R Th

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3.3 MEASURES OF AMPLIFIER CHARACTERISTIC

Fig 3-6 Amplifier circuit

1 Current amplification, measured by the current-gain ratio: i o

in

i A i



2 Voltage amplification, measured by the current-gain ratio: v o

in

v A v



3 Power amplification, measured by the ratio: p v i o o

in in

v i

A A A

v i

4 Phase shift of signals, measured by the phase angle of the

frequency-domain ratio A j v   or A j i 

5 Impedance input, measured by the input impedance Z (the in

driving-point impedance looking into the input port)

6 Power transfer ability, measured by the output impedance Z (the o

driving-point impedance looking into the output port with the load removed) If Z o Z L, the maximum power transfer occurs

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3.3.1 CE amplifier analysis

Fig 3-7 CE amplifier

In the CE amplifier, find expressions for :

(a) Current-gain ratio A i

(b) Voltage-gain ratio A v

(c) Input impedance Z in

(d) Output impedance Z o

Solution

(a) By the current division at node C,

1 /

oe

h



And :

1

fe L

i

h i

A

  



Note that A i  h fe, where the minus sign indicates a 180 phase 0

shift between input and output currents

(b) By KVL around B, E mesh,

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v v h i h v

Ohm’s law applied to the output network requires that

1

||

1

fe L b

h R i



fe L be

v

h R v

A

  

Observe that A v  h R fe L /h ie where the minus sign indicates a

0

180 phase shift between input and output voltages

(c)

1

re fe L s

h h R v



Note that for typical CE amplifier values, Z in h ie

(d) We deactivate (short) v and replace s R with a driving-point source L

so that v dpv ce Then, for the input mesh, Ohm’s law requires that

re

ie

h

However, at node C (with, now i c i dp), KCL yields

i i h i h v

/

dp o

v Z



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The output impedance is increased by feedback due to the presence

of the controlled source h v re ce

With typical CE amplifier values: h ie 1k , h re 104

 , h  fe 100, 12

oe

h   S, R L 2k

We have:

97.7

i

A   , A   v 199.2, Z  in 980.5 , Z o 500k

The characteristics of the CE amplifier can be summarized as follows:

1 Large current gain

2 Large voltage gain

3 Large power gain AA i v

4 Current and voltage phase shifts of 180 0

5 Moderate input impedance

6 Moderate output impedance

3.3.2 CB amplifier analysis

A simplified (bias network omitted) CB amplifier is shown, and the associated small-signal equivalent circuit:

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Fig 3-8 CB amplifier

In the CB amplifier, find expression for

Solution

(a)

1

fb i

ob L

h A

h R

 



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Note that A i  h fb  , and the input and output currents are in 1 phase because h  fb 0

(b)

fb L v

h R A

h R h h h h

 

Observe that A v  h R fb L /h ib, and the output and input voltages are

in phase because h  fb 0

(c)

1

rb fb L

in ib

ob L

h h R

Z h

h R



It is apparent that Z in h ib

/

o

Z

h h h h





Note that Z is decreased because of the feedback from the output o

mesh to the input mesh through h v rb cb

With typical CB amplifier values: h  ib 30 , h rb 4 106

  ,

0.99

fb

h   , h ob 8 107S

  , R L 2 0k

We have:

0.974

i

A  , A  v 647.9, Z  in 30.08 , Z o1.07M

The characteristic of the CB amplifier can be summarized as follows:

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1 Current gain of less than 1

2 High voltage gain

3 Power gain approximately equal to voltage gain

4 No phase shift for current or voltage

5 Small input impedance

6 Large output impedance

3.3.3 CC amplifier analysis

Fig 3-9 CC amplifier

In the CC amplifier, find expressions for

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Solution

(a)

1

fc i

oc L

h A

h R





Note that A i  h fc, and the input and output currents are in phase because h  fc 0

(b)

fc L v

h R A

h R h h h h

 

1

v

ic oc fc

A

h h h

 Since the gain is

approximately 1 and the output voltage is in phase with the input voltage,

this amplifier is commonly called a unity follower

(c)

1

rc fc L

in ic

oc L

h h R

Z h

h R



Note that in fc

oc

h Z

h

 

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/

o

Z

h h h h





Note that o ic

fc

h Z

h

 

With typical CC amplifier values: h ic 1k , h  , rc 1 h   fc 101, 12

oc

h   S, R L 2k

We have:

98.6

i

A  , A  v 0.995, Z in 8.41M  , Z  o 9.9

The characteristics of the CB amplifier can be summarized as follows:

1 High current gain

2 Voltage gain of approximately unity

3 Power gain approximately equal to current gain

4 No current or voltage phase shift

5 Large input impedance

6 Small output impedance

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