# Bipolar Junction Transistor Amplifiers

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Bipolar Junction Transistor Amplifiers

2.1.0 Overview of the Diode

iD

i D  f (v D )
   vD     -

vD

reverse                                                                      Circuit symbol
breakdown
region            reverse bias region             forward bias region

(a)                                          (b)
Figure 2.1.0:
(a) Diode characteristic
(b) Circuit symbol

    A diode is a p-n junction
    The static VI characteristic is non linear
    The Shockley equation describes the diode VI characteristic
 vD       
          
i D  I s  e VT  1, v D  vbreakdown
          
          
Where
I s Is the saturation current  4  A
10
 is the emission coefficient 1    2
VT  kT q is the thermal voltage
K is Boltzmann’s constant
T is the temperature K
q is the electronic charge 1.6 10 19 C
At forward bias  0.3V  the diode current is expressed as:
 vD       
          
i D  I s  e VT    
          
          

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2.1.1   Amplifier Configurations

There are three basic configurations, considering the BJT amplifier configurations:
VCC

RC
C3
Z
C1
X
C2
Y

RB                  RE

 V EE
Figure 2.1.1 BJT amplifier basic configuration

The configurations will depend on where the input and output signals are taken from with
respect to the amplifier terminals.
Each student should be familiar with the terminal characteristics of each transistor
configuration i.e. input resistance Ri, output resistance Ro , voltage gain Avo and current
gain Ai for each configuration.

2.1.2 Common Emitter Amplifiers:

Consider the circuit below with point Y grounded. This makes point C2 common to both
input and output, thus the circuit is a common emitter amplifier.

VCC

RC
C3
Z
C1
X

Y

C2
RB                  RE

 V EE
Figure 2.1.2 Common Emitter BJT amplifier

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2.1.3 Common Base Amplifiers:

   If point X is grounded, the base terminal is common to both input and output circuits
and we have a common base amplifier circuit. The circuit looks like:

VCC

RC
C3
Z   Vout
C1
X

C2
Y
Vin

RB                       RE

 V EE
Figure 2.1.3 Common Base BJT amplifier

2.1.4 Common Collector Amplifiers:

   If point Z is grounded, the collector terminal is common to both input and output
circuits and we have a common collector amplifier configuration.

VCC

RC
C3
Z
C1
Vin          X

C2    Y      Vout

RB                  RE

 V EE

Figure 2.1.4 Common Collector BJT amplifier

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2.1.5 Summary:
Common Base                 Common                          Common Collector
Emitter
Voltage Gain
(Av)                            Large (noninverting)        Large (inverting)                1 (noninverting)
Current Gain
(Ai)                            1                          Large                           Large
Input Resistance
(Ri)                            Low                         Moderate                        High
Output      Resistance
(Ro)                             High                        Moderate                        Low

2.1.6 The CE Amplifier

The most widely used configuration.
In this instance we assume all coupling capacitors are shorts
VCC

RC
C3

Rs           C1

vs                                                              Y
RL
C2
RB              RE

Rout
 V EE
Rin
Figure 2.1.5 (a) CE transistor amplifier
The small signal equivalent circuit

ii                  ib
Rs                      B                                              io     C
Vs
g m v

v                                                                
RB                         r                                ro     RC    RL      Vout
                                                                 

Rib                  E
Rin                                                                                     Ro
Figure 2.1.5:(b) Small signal hybrid II equivalent circuit

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2.1.7 Input Impedance Ri:
vi
Rin  R B || Rib
ii
Where Rib is the input resistance looking into the base. Since the emitter is grounded
then
Rib  r but RB  r so that Rin  r ( normally equal to a few kΩ)

2.1.8 Voltage Gain:
The voltage at the input of the amplifier can be found as
Rin            RB || r 
vi  v s              vs
Rin  Rs        RB || r   Rs
If RB  r then
r
vi  v s             v  v i
r  Rs
The output of the amplifier then given by
vo   g m v ro || RC || RL    g m vi ro || RC || RL 
The voltage gain is thus
v
Av  o   g m ro || RC || R L 
vi
The open circuit voltage gain, i.e. when RL   is given by
Avo   g m ro || RC 
but the in most cases ro  Rc so that
Avo   g m RC
The overall voltage gain from source to load is
Gv  Av  vi v s
RB || r 
                      g m ro || RC || RL 
RB || r   Rs
For RB  r    and since r   g m the overall gain becomes
 ro || RC || R L 
Gv 
r  R s
Note: if Rs  r the overall gain will be unstable i.e. highly dependent on  .
But if R s  r the overall gain will be independent of 
Gv  g m ro || RC || RL 
For discrete circuits: when RC  ro ; and the gain equals Av   g m RC
For IC’s RC   and gain equals Av   g m ro and since g m  I C VT and ro  V A I C
Then the maximum gain of the IC is Av   V A VT and independent of current IC.

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2.1.9 Current gain:

io
Ai 
ib
 ro 
io  g mV 
r R        currentdivision 
 o  C 

V
ib   ;
r
 ro         
g mV  
r R        

 o            gm   ro   r
Ai                                
r R  
C

V r                    o  C 


sin ce r 
gm
 ro 
r R 
Ai          
 o  C 

For RC  ro ;   Ai    ;
For RC  ro ;   Ai  0;

2.2.0 Output Resistance:
The output resistance looks back into the output terminal while short circuiting the
terminal source, figure 2.1.5. This means v  0 so that
Rout  RC || ro
Typically ro  RC so that Rout  RC

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2.2.1 CE Amplifier with bypass capacitor CE

Including the resistor Re in the emitter means that the amplifier characteristics can be
modified. The circuit in figure 2.1.6(a) can be analysed using the small signal hybrid 
model and the T model.
VCC

RC
C3

Rsig         C1

vs
Re                                      RL

Vi R B
CE

Re1                              Rout
Rin
 V EE

Figure 2.1.6 (a) CE transistor amplier with Re

ic            io          Vo
C

ie                                            
RC          RL
Vout

RS ii
Vs                      B ib                   ie       ro

                 re        vbe
Rout
Vi R                        
B
                 E
vi
ie 
Re           re  Re
Rin                       Rib

Figure 2.1.6:(b) Small signal T model equivalent circuit

It is most convenient to use the T-model because it leads to easier analysis. In figure
2.1.6(b) ro is left out because
 it has little effect on the solution
 but complicates the analysis because it connects output to input.
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Figure 2.1.7 results
C       ic            io         Vo

ie                                           
RC            RL
Vout

RS ii
Vs                  B ib                  ie

re       vbe                Rout
RB                     
E
vi
ie 
Re           re  Re
Rin                    Rib

Figure 2.1.7:(b) Small signal T model equivalent circuit

2.2.2 Input Resistance (Rin):

vi
Rin  R B || Rib Here the input resistance at the base is given by Rib 
ib
Where
ie                   
ib  ie  ie  1   ie 
1
and since         1 
 1                   1          1
i
ib  e
 1
vi
and                               ie 
re  Re
Therefore
Rib    1re  Re  resistance reflection rule

This is the resistance reflection rule. This result shows that the inclusion of R e
substantially increases Rib the input resistance at the base by the ratio
Rib with Re included    1re  Re  1  Re
                         1  g m Re
Rib without Re           1re        re
The value of R e can be used to control Rib and hence Rin this is valid when Rib
dominates the input resistance.

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2.2.3 Voltage Gain:
Referring to figure 2.1.7
vo  ic RC || RL   ie RC || RL 
Substituting for ie
vo     RC || RL 
Av        
vi       re  Re
RC || RL 
And since          1            then        Av  
re  Re
i.e the voltage gain from base to collector is equal to the ratio of the total resistance in the
collector to the total resistance in the emitter.
The open circuit voltage gain is when R L   and is given by

  RC 
Avo            also equal to
re  Re
      RC           g m RC        g R
Avo                                m C
re 1  Re re     1  Re re    1  g m Re

The voltage gain has been reduced by a factor equal to 1  g m Re  i.e the same factor by
which input resistance at the base Rib is increased.
The overall voltage gain is given by

vi vo    Rin       RC || RL 
Gv                   
vs vi  Rs  Rin      re  Re
 RC || RL 

Rs    1re  R e

The overall result for including Re is therefore
1. The gain is lower than in a CE amplifier by but less sensitive to .
2. The amplifier can handle large input signals without incurring nonlinear distortion.
This is because only a fraction of the input signal at the base v i appears between the base
and emitter so that
v       re        1
         
vi    re  Re 1  g m Re

2.2.4 Output Resistance:
The output resistance can be obtained by inspection of figure 2.1.7
Rout  RC

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2.2.5 Current Gain
ios  ie
ii  vi Rin
Therefore the short circuit current gain is
R i
Ais  in e
vi
Substituting ie gives
 RB || Rib 
Ais  
re  Re
If RB>>Rib then
   1re  Re 
Ais                                same as the CE amplifier.
re  Re

2.2.6 Summary
 input resistance Rib increased by 1  g m Re .
 The voltage gain from base to collector is reduced by the same amount 1  g m Re .
 For the same nonlinear distortion the input signal v i can be increased by 1  g m Re .
 The voltage gain is less dependent on 
 The high frequency response is improved

2.2.7 Frequency response

Thus far we looked at CE amplifier gain at midband frequencies.
In determining an amps gain we look for at three regions:
 Low frequency
 Midband
 High-frequency

2.2.8 Effect of Coupling capacitors on gain at low frequencies

C1                Coupling capacitors                        C2
Rs                                                           Ro
Vs

   Av v               
v     Rin                                    RL          Vo
                       


E

where        v  v x       and       v y  Av v
Figure 2.1.8: Amplifier with coupling capacitors

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   At low frequencies the coupling and bypass capacitors cause the gain of RC
coupled amplifiers to decline.
   Coupling capacitors block DC currents from flowing while providing a low
impedance path for ac signals to pass through.
   In descrete amplifiers the coupling amplifiers set between stages allows the bias
points in each stage to be set independently.
   Bypass capacitors are used to provide a low impedance path in parallel with bias
resistors for ac signal currents.
   In IC amplifiers are directly coupled that is coupling and bypass capacitors are
not used. Sometimes descrete components external to the chip are used for
coupling.

The overall voltage gain for the amplifier in figure 2.8 is given by
V     V Vy V
Avo  o  x   o
Vs Vs V x V y
where          V  V x     and   Vy  AvoV

The student is advised to revisit Laplace transforms and see if you can come to the
result in the following sections. The transfer functions are each calculated below
For the first stage
Vx        Rin        j  f f1 
            
Vs Rs  Rin 1  j  f f1 
Where the break frequency f1 is given by
1
f1 
2 Rs  Rin C1
Secondly
Vo       RL         j f f 2 
           
V y Ro  RL 1  j  f f 2 
where
1
f2 
2 Ro  RL C 2
Finally
Vy
 Av         the open circuit voltage gain
Vx

Thus the total amplifier gain is
Rin        j  f f1           RL       j f f 2 
Avo                           Av         
Rs  Rin 1  j  f f1          Ro  RL 1  j  f f 2 
j  f f1      j f f 2 
Avo                                   Avomid
1  j  f f1  1  j  f f 2 

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Where
Rin            RL
Avomid      Av 
Rs  Rin        Ro  R L
Is the mid band gain the taken when the coupling capacitors are shorts.

Avo dB                                                           j  f f1 
This term contributes to
roll off of frequencies

j f f 2                           1  j  f f1 
below the break frequency
f1

20 log Avomid dB                 1  j f f 2 

This term contributes for
roll off below the frequency

f2                    f1

Figure 2.1.9: Magnitude Bode Plot fo the amplifier of the figure in 2.8

2.2.9 Bypass Capacitors

VCC

R1                      RC
C2

Rs         C1

RL             
vs
vo
CE                 
R2                     RE

Figure 2.2.0 (a) CE transistor amplifier

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   Assuming coupling capacitors C1 and C2 are shorts.
   Above a certain frequency f1 capacitor CE acts as a short and the emitter is
grounded giving a high gain.
   Below f2 CE has high impedance and the impedance of RE||CE is  RE. Then
the gain.

CE acts as a short circuit

20 log Avo dB 

CE acts as a open circuit

f2                  f1
Figure 2.2.1: Magnitude Bode Plot showing effects of CE

Bypass capacitors cause the gains of CE to decline at low frequencies. At very
low frequencies, the gain again levels off. The break frequency at which the gain
begins to fall is
1
f1 

2R E C E

Where RE is resistance seen by the bypass capacitor
 r  R1 || R2 || Rs 

RE  RE ||  
                    

       1          
This is the resistance “seen” by CE looking back into the circuit. The emitter
bypass capacitor needs to be about  times the value of the input coupling
capacitor for both to have about the same influence on the lower half-power
frequency.

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2.3.0 CE Amplifiers at High Frequency

VCC

R1               RC
C2

Rs            C1

RL     
vs
vo
CE          
R2               RE

Figure 2.2.2 (a) CE transistor amplifier

r


RL
Rs                  b    rx                 b'
Vs
g m v               c
                                       C

vin            RB v r                                         ro        RC        RL      Vout

                                  C

E
R B  R1 || R2                                                                 
RL  ro || RC || RL

Figure 2.2.2:(b) high frequency small signal hybrid II equivalent circuit

The high frequency operation of the CE amplifier can be analysed to see the
effects of C and C  on the voltage gain. You will need to revise miller’s
theorems(Hambley Chapter 8). The circuit above is simplified
 At high frequencies C  dominates the parallel combination of r and C 
therefore we can neglect r .
                                                
The output resistance is replaced by RL  ro || RC || RL
       The circuit to the left of C by its thevenin equivalent
Rs  r || rx  RB || RS 


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
Rs
C                       c
Vs                          b
g m v
                                                           
v                    C                             RL      Vout


Rs  r || rx  RB || RS 
E


Figure 2.2.2(c) : equivalent circuit of figure 2.2.2(b) after removing rμ , replacing
output resistance with R  and replacing the circuit to the left of b by its thevenin
L

equivalent circuit

To find the high frequency voltage gain we neglect the current through C 

Vo  g mV RL .
From the above circuit in figure 2.2.2 (c)The voltage gain is Avb
V

Avb  o   g m R L
V
We can use the miller effect to redraw the circuit with C  replaced by an
equivalent capacitance C   C  1  Avb  across the input terminals, neglecting
the effect of C  on the output.


Rs
b                                           c
Vs
g m v
                       
C                                   
C                                     
RL
v                                                           Vout


E
C   C  1  g m RL 
                 

Figure 2.2.2(d) : simplified high frequency equivalent circuit of CE amplifier

The total capacitance between terminal b and ground will be
CT  C  C  1  g m R L 

A simple RC low pass filter with a break frequency given below results
1
fH 

2RS CT
The high frequency behaviour is shown in figure 2.2.3.

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20 log Avo dB 

 20 log dB / decade
3dB

fH

figure 2.2.3 : High frequency behaviour of the CE amplifier

Ref:
Hambley A. R. - Chapters 4 and 8 2nd edition
Sedra and Smith- Chapter 5    5th edition

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