1
Emitter degeneration
Consider a typical common emitter amplifier with an un-bypassed emitter resistor RE (
FIGURE 1). Also consider the simplified AC equivalent circuit shown in FIGURE 2.
VCC
RC
OUT
CIN
COUT
RL
Rsig
RB
RE
FIGURE 1
_____________________________________________________________
Signal Processing Group Inc., technical memorandum. May 2013.
Website: http://www.signalpro.biz
2
ic io
C
Out
RC
αie
ii
RL
A
ib
ie
B
Rsig
re
RB
Vsig
vi
vx
E
RE
FIGURE 2
_____________________________________________________________
Signal Processing Group Inc., technical memorandum. May 2013.
Website: http://www.signalpro.biz
3
Effect on input resistance.:
Writing the nodal equations:
Input resistance =
vi
ib
(1)
vi  ie (re  RE )
(2)
ie
 1
(3)
Rib =
also
ib 
Thus
Rib = (β+1)(re + RE)
(4)
This result is also referred to as the resistance reflection rule. i.e. when an un-bypassed
resistor is inserted in the emitter, the total input resistance in the emitter circuit is
multiplied by (β+1).
Obviously the total input resistance of the above CE amplifier, RIN, is the parallel
combination of RB and the total input resistance seen at the base terminal..
This is very useful since the bipolar is inherently a low input impedance device.
Effect on linearity
Additionally,
The emitter degenerated amplifier above can handle larger input signals without
distortion. This is demonstrated below:
vi =
RIN
vsig
RIN  Rsig
(5)
vx =
re
vi
re  RE
(6)
Substituting (5) into (6) we get,
_____________________________________________________________
Signal Processing Group Inc., technical memorandum. May 2013.
Website: http://www.signalpro.biz
4
vsig =
RIN  Rsig re  RE
.
vx
RIN
re
(7)
Assume that vx has to be limited to some minimum voltage ( e.g. 10mV because of the
exponential nature of the voltage - current characteristic of the bipolar. Then using
emitter degeneration the maximum input signal can be increased to that indicated by (7).
In many applications this is desirable as it prevents non-linear distortion from occurring.
Effect on bandwidth.
Emitter degeneration also results in an increase in the bandwidth of the amplifier. This
effect is difficult to analyze in detail so a method called the OCT ( Open Circuit Time
Constant) is used to gain an intuitive understanding of the effect, and also to arrive at a
close approximation of the bandwidth. The OCT method is first introduced below, and
then used to estimate the bandwidth of the emitter degenerated common emitter
amplifier.
OCT method:
OCT analysis identifies which elements are responsible for bandwidth limitations. This
is, of course, a great help in amplifier design ( among other circuits). In order to
understand this method let us consider the transfer function shown below:
Vo ( s)
ao

Vi ( s) ( 1 s  1)( 2 s  1)....( n s  1)
(8)
Here the various time constants may or may not be real. If the terms in the denominator
are multiplied and the denominator is expanded, we get a denominator polynomial.
bn s n  bn 1 s n 1  ...  b1 s  1
(9)
It can be stated without proof, that near the – 3 dB frequency, the first order term
dominates over all other higher order terms. Thus,
Vo ( s )
ao
a

 n o
Vi ( s ) b1 s  1 

  i  s  1
 i 1 
(10)
The estimated bandwidth is then simply the reciprocal of the b1 term. Or ,
1
H 
( estimated)
(11)
b1
_____________________________________________________________
Signal Processing Group Inc., technical memorandum. May 2013.
Website: http://www.signalpro.biz
5
Please note that the bandwidth estimate arrived at using this technique is conservative, in
the sense that the actual bandwidth will almost always be at least as high as that
estimated by this method.
To follow through. It is possible to relate the desired time constant, b1 to computed
network quantities. For example, assume a network consisting of only resistors, sources
and ‘m’ capacitors. Then we can do the following, to compute the required time constant
b1
(1)
(2)
(3)
Calculate the effective resistance Rjo facing each jth capacitor with all other
capacitors removed from the circuit. ( open circuited).
Generate the product τjo = RjoCj
Generate the sum of all ‘m’ such time constants which is b1
This technique will now be used to estimate the bandwidth of a emitter degenerated CE
amplifier.
The small signal equivalent circuit of the degenerated common emitter circuit is shown
below.
RS
+
+
Vi
V1
rπ
Cπ
gmV1
A
ro
RL
Vo
-
+
VE
RE
Cμ
Figure 3.0
_____________________________________________________________
Signal Processing Group Inc., technical memorandum. May 2013.
Website: http://www.signalpro.biz
6
The OCT technique is used to derive an estimate of the bandwidth of this amplifier as
shown below.
R
1 E
Rs RsC
τ = RS (1 | Av 0 |)  Rc C  
ω-3dB ~ 1/τ
(12)

1  g m RE
where the network constants are defined above in Figure 3.0.
In contrast to this, the non-degenerated time constant is given by:
τ = RS (1 | Av 0 |)  Rc C   RsC 
(13)
Using RE improves the bandwidth as long as gm > 1/RS. gm has to be increased ( by
increasing the current) to maintain the same value of Avo.
Additionally, in the special case of gmRE >>1, and if the time constant due to Cμ is
negligible, then
τ=

R C
1  S   and ω-3dB = T
 RE  g m
 R 
/1  S  almost at T for small RS
 RE 
(14)
These expressions provide a easier way to estimate the bandwidth. Simulations can then
be a way of confirming these results.
_______________________________________________________________________
Please address any questions to the SPG TechTeam using the email address of
spg@signalpro.biz.
Note: A number of papers and articles are freely available on the web on the subject of
OCT.
_____________________________________________________________
Signal Processing Group Inc., technical memorandum. May 2013.
Website: http://www.signalpro.biz