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Voltage Gain without the bypass Capacitor
Without C2, emitter is no longer at ac ground, instead RE is now seen by the
signal between emitter and ground and adds to internal re’ .
Av = RC/(re’+RE).
Example : Calculate base-to-collector voltage gain of the amplifier both
without and with an emitter bypass capacitor if there is no load resistor.
Without C2 gain is, Av = RC/(r’e+RE) = 1.0 kΩ/6.58Ω =1.76
With C2 gain is, Av = RC/r’e = 1.0kΩ/6.58Ω = 152
The effect of RE is to decrease the ac voltage gain
Effect of a Load on the Voltage Gain
When load RL is added at the output capacitor end C3, effective resistance
seen by the signal is RC in parallel with RL.
Rc = RC//RL
Replace RC with Rc, Av = Rc/re’
When Rc < RC, Av reduced, if RL >> RC, then Rc = RC and RL have little
effect on Av.
Example : Calculate the base-to-collector voltage gain of the amplifier when
load resistance of 5 kΩ in connected to output and RC is 1 k Ω. emitter is
effectively bypassed and r’e = 6.58Ω.
ac collector resistance, Rc = RC||RL =RCRL/(RC+RL) = ((1.0 kΩ)(5 kΩ))/6 kΩ
= 833 Ω
Therefore, Av = Rc/r’e = 833 Ω/6.58 Ω = 127
unloaded gain was found to be 152
Stability of the Voltage Gain
Stability is a measure of how well an amplifier maintains its design values
over changes in temperature or for a transistor with a different β.
Bypassing RE with capacitor causes the gain to be more dependent on re’
since (Av = RC/r’e) ; r’e depends on IE and on temperature; reduced
Without bypass capacitor, the gain is Av=RC/(re’+RE) and if RE is big
enough. Av = RC/RE…. Which is less dependent on re’ or IE.
Swamping r’e to stabilize the voltage gain
• Swamping is a method used to minimize the effect of r’e without
reducing the voltage gain to it minimum value.
• In a swamp amplifier, RE is partially bypassed so that a reasonable
gain can be achieved and the effect of r’e on the gain is greaty
reduced or eliminated.
• The total external emitter resistance, RE is formed with two separate
emitter resistors, RE1 and RE2 (RE2 is bypassed and the other is not).
Av= RC/(r’e + RE1)
= RC/RE1 (if RE1 is at least ten times larger than r’e then
the effect of r’e is minimized)
Both resistors (RE1 and RE2) affects the dc bias while only RE1 affects the ac
voltage gain.
Examples :
RE2 bypassed by C2. Assume r’e = 20 Ω and since RE1 is more
than 10 times r’e, the approximate voltage gain is
So, Av = RC/RE1 = 3.3kΩ/330Ω = 10
The Effect of Swamping on the Amplifier’s Input
ac input resistance, with RE completely bypassed, is
Rin = βacr’e
When emitter resistance, partially bypassed,
Rin = βac(re’+ RE1)
Vout at collector is 1800 out of phase with Vin at base, shown by – Av.
Current Gain
Overall current gain of the common-emitter, Ai = Ic/Is
Is is total signal current produced by the source, part of which is base current
(Ib) and part of which (Ibias) goes through the bias circuit (R1||R2).
Total current signal produce by source is, Is = Vs/(Rin(tot) + Rs)
Power gain is, Ap = A’vAi, where A’v = Vc/Vs
3.4 Common-Collector Amplifier
Common-collector amplifier is usually referred to as the emitter follower
because there is no phase inversion or voltage gain. The output is taken
from the emitter. The common-collector amplifier’s main advantages are it’s
high current gain and high input resistance.
Voltage Gain
Input signal is capacitive coupled to base, output signal is capacitive
coupled to emitter, and collector is at ac ground.
No phase inversion and Vout approx same as Vin.
Av = Vout/Vin, Xc are negligible at freq
Re = RE ||RL
Vout = IeRe and Vin = Ie(r’e + Re)
Av = Re/(re’ +Re)
if no load, Re = RE
Gain is always less than 1.
If Re >> r ’e than Av = 1
And since no inversion
So called emitter-follower
Emitter-follower model for voltage gain derivation
Input Resistance
Because of the high input resistance it used as a buffer to reduce the
loading effect when a circuit is driving a low impedance loads.
Emitter resistor is never bypassed because Vout is taken across Re.
Rin(base) = Vin/Iin = Vb/Ib = Ie(re’+Re)/Ib
Since Ie = Ic = βIb
Rin(base) = βIb(re’+Re)/Ib = β(re’+Re)
If Re >> re’ so Rin(base) = βRe
Rin(tot) = R1 || R2 || Rin(base)
Output resistance
With the load removed, Rout looking at emitter of emitter follower:
Rout = (Rs/ β) || RE
(Rs - resistance of input source)
Output resistance is very low and this makes it useful for driving low
impedance loads.
Current Gain
Current gain for emitter follower , Ai = Ie/Iin
where Iin = Vin/Rin(tot)
Power Gain
Power gain, Ap = AvAi
Since Av = 1, so Ap = Ai
Darlington Pair
Darlington pair is used to boost the input resistance to reduce loading of high
output impedance circuits. Collectors are joined together and emitter of the
input transistor is connected to the base of the output transistor.
Ie1 = βac1Ib1
Ie1 = Ib2, so Ie2 = βac2Ie1
= βac1βac2Ib1
βac = βac1βac2
Neglecting r’e by assuming it is much
smaller than RE (r’e<<RE)
So Rin = βac1βac2RE
Emitter-follower or buffer often used as interface between a circuit with high Rout
and low RL.
Example : common-emitter amp with RC = 1.0kΩ and RL = 8Ω
If re’ = 5Ω, so Av = RC/re’ = 200 (with no load)
With load;
Rc = RC||RL = 1.0k Ω || 8 Ω = 7.94Ω,
Av = Rc/re’
= 7.49/5 = 1.59Ω (so not
acceptable because Av is lost)
So it can be used to interface the
amplifier and speaker.
3.5 Common-Base Amplifier
Common-base amplifier has high voltage gain with a current gain no
higher than 1. It has a low input resistance making it ideal for low
impedance input sources. ac signal is applied to emitter and output is
taken from the collector.
Base is the common terminal and is at ac ground because of C2. Input
signal is capacitive coupled to emitter and output is capacitive coupled
from collector to RL.
Voltage gain:
Av = Vout/Vin = Vc/Ve = IcRc/(Ie(r’e||RE)) = IeRc/(Ie(r’e||RE))
If RE >> r’e, then Av = Rc/r’e
where Rc = RC||RL
No phase inversion from emitter to collector
Input resistance (looking in emitter):
Rin(emitter) = Vin/Iin = Ve/Ie = (Ie(r’e||RE))/Ie
If RE >> r’e then Rin(emitter) = r’e
Output resistance (looking in collector):
Rout = r’c||RC
Typical value rc >> RC, so Rout = RC
Current gain, Ai = 1
Power gain, Ap = Av
this is typical
3.6 Multistage Amplifiers
Two or more amplifiers can be connected to increase the gain of an ac
signal. Basic objective is to increase overall voltage gain, Av.
Overall gain can be calculated by simply multiplying each gain.
A’v = Av1Av2Av3 ……
Voltage gain often expressed in decibels dB, Av (dB) = 20logAv
So, A’v(dB) = A’v1(dB) + A’v2(dB) + A’v3(dB) +…
Capacitively-Coupled Multistage Amplifier
Use two stage capacitive coupled amplifier where capacitive coupling keeps dc
bias voltages separate but allows the ac to pass through to the next stage
because Xc = 0 at frequency operation.
Av1 have loading effect on stage 2. Rin(tot)2 presents an ac load to first stage
because coupling capacitor C3 appear short at signal freq.
From collector Q1, R5 and R6 appear parallel with Rin(base2). In other word, signal
at collector Q1 see R3, R5, R6 and Rin(base2) of stage 2 all parallel to ac ground.
Thus, effective ac collector resistance, Rc(Q1) is total of all this resistor in parallel.
A two-stage commonemitter amplifier
Av stage1 decrease by loading of stage 2 because effective collector
resistance of stage1 is less than actual value of collector R3. Remember,
Av = Rc/re’.
The ac collector resistance of the first stage, Rc1 = R3||R5||R6||Rinbase2
The voltage gain of the first stage, Av1 = Rc1/re’
The voltage gain of the second stage, Av2 = R7/re’
Overall voltage gain, Av’ = Av1 x Av2
Dc voltages in the capacitively coupled multistage
Since Q1 and Q2 identical, the dc voltage is same.
βdcR4 >> R2 and βdcR8 >> R6, so ;
VB = R2/(R1 + R2) x VCC
VE = VB – 0.7
IE = VE/R4
Direct coupled Multistage Amplifiers
For direct-coupled multi stage amplifiers, there are no coupling and no
bypass capacitor in the circuit. dc collector voltage of stage 1, provide basebias voltage for stage 2.
It’s has better low-frequency response than capacitive coupled type in which
reactance of coupling and by-pass capacitor are increase. The increased
reactance of capacitors at lower frequencies produces gain reduction in
capacitively coupled amplifiers.
So the amplifiers are used to amplify
low frequency without gain loss
because no capacitive reactance in
The disadvantage is that small changes
in dc bias from temperature changes or
supply variations are amplifier by
succeeding stage, which result in drift in
dc level in circuit.