Single Stage Amplifier, Characterizing BJT
Amplifiers, CE, CC and CG Amplifiers, BJT Internal
Capacitances and High Frequency Model,
Frequency Response of CE, BJT logic Inverter
Inverter..
Lecture # 8
1
Single Stage Amplifier
3 Configurations, Common Emitter, Common Base and Common Collector. In the following circuit a constant current biasing is
selected, we would also like to select the base resistance to be large to have large input resistance and at the same time we would like
to limit the voltage drop across base resistance also more importantly the variability of this drop due to variations in the beta value for
different transistors of the same type. The dc voltage VB basically, determines the allowable signal swing at the collector.
Basic structure of the circuit used to realize single-stage, discrete-circuit BJT amplifier configurations.
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Exercise 5.41
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Characterizing BJT Amplifiers
Amplifier can be unilateral or non
non--unilateral
unilateral, basically a nonunilateral amplifier is the one in which Rin may depend on RL
and Rout may depend on Rsig, in contrast for unilateral amplifier
there is no such dependency, as Rin = Ri and Rout = Ro.
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Definitions
Rin ≡
Input resistance with no load:
vi
ii
Open circuit gain:
Avo ≡
vo
vi
Short circuit gain:
Ais ≡
io
ii
RL = 0
Short circuit trans-conductance:
Gm ≡
io
vi
RL = 0
Output resistance of amplifier proper:
Overall voltage gain:
Input resistance:
Rin ≡
vi
ii
Voltage gain:
Av ≡
vo
vi
Current gain:
Ai ≡
io
ii
Output resistance :
Rout ≡
RL = ∞
RL = ∞
Ro ≡
vx
ix
Gv ≡
vo
vsig
vo
Open circuit Overall voltage gain: Gvo ≡ v
sig
vi = 0
vi
Rin
=
vsig Rin + Rsig
Av = Avo
Avo = Gm Ro
Gv =
Gvo =
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Ri
Avo
Ri + Rsig
vx
ix
v sig = 0
RL = ∞
RL
RL + Ro
RL
Rin
Avo
RL + Ro
Rin + Rsig
Gv = Gvo
RL
RL + Rout
5
Example 5.17
Avo
Gvo
Ri
Av
Ro
Rout
Rin
Gm
Gv
Ai
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3
Exercise 5.42
7
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Common Emitter Amplifier
Unilateral or Non-Unilateral
Rin = Ri & Rout = Ro
Signal Ground, by pass capacitor (µF – 10 of µF)
(a) A common-emitter amplifier using the structure. (b) Equivalent circuit obtained by replacing the transistor with its hybrid-π model.
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Common Emitter Amplifier
Rin ≡
vi
= RB || Rib
ii
Rib is the input resistance looking into the base, since emitter is grounded
Rib = rπ normally RB >> rπ
Rin ≅ rπ (It is in the range of few kΩ, considered as low to moderate)
vsig
vi =
vi ≅
Rin + Rsig
vsig
rπ + Rsigg
Rin =
vsig
( RB || rπ ) + Rsig
( RB || rπ )
rπ
vπ = vi
vo = − g m vπ (ro || RC || RL )
Av = − g m (ro || RC || RL ) open circuit gain ( RL = ∞) Avo = − g m (ro || RC )
Avo ≅ − g m RC usually RC << ro (ro reduce the gain by 10%)
Rout = RC || ro , (ro reduce the output resistance slightly), Rout ≅ RC
Gv =
( RB || rπ )
g m (ro || RC || RL ) - - - -Gain from source to load
( RB || rπ ) + Rsig
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Exercise 5.43
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5
Exercise 5.43
Rin = ( RB || Rib )
( Rib = rπ )
Avo = − g m (ro || RC ), ro =
VA
I
, gm = C
IC
VT
Rout = RC || ro
Ais = − g m Rin = − g m ( RB || rπ )
Av = − g m (ro || RC || RL )
Gv =
( RB || rπ )
(r || R || RL )
g m (ro || RC || RL ) = β o C
( RB || rπ ) + Rsig
rπ + Rsig
vπ =
rπ
vsig ( RB || rπ → vi = vπ )
rπ + Rsig
Vˆo = − AvVˆi = g m (ro || RC || RL )vπ = g m ( RC || RL )vπ
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11
Common Emitter Amplifier with Emitter
Resistance
(a) A common-emitter amplifier with an emitter resistance Re. (b) Equivalent circuit obtained by replacing the transistor with its T model. The
advantage of using T model is that the re resistance is placed in series with the emitter resistance so it can just be added and it simplifies the
design.
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Common Emitter Amplifier with Emitter
Resistance
Rin = RB || Rib
Rib ≡
vi
ib
ib = (1 − α )ie =
ie =
ie
( β + 1)
vi
, Rib = ( β + 1)(re + Re ) This means that Rib is increased by a factor :
(re + Re )
Rib ( with − Re − included ) ( β + 1)(re + Re )
R
=
= 1 + e = 1 + g m Re
Rib ( without − Re )
( β + 1)re
re
vo = −iC ( RC || RL ) = −α ie ( RC || RL )
Av = −
Av =
α ( RC || RL )
(re + Re )
≅−
( RC || RL )
(re + Re )
(α ≅ 1)
g m RC
(1 + g m Re )
Rout = RC
Gv =
β ( RC || RL )
Rsig + ( β + 1)(re + Re )
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Characteristics Comparison
‰
The input resistance Rib is increased by a factor (1 + gmRe).
‰
The voltage
Th
lt
gain
i from
f
base
b
to
t collector
ll t is
i reduced
d
d by
b a
factor of (1 + gmRe).
‰
For the same non-linear distortion, the input signal vi can
be increased by the factor (1 + gmRe).
‰
The over all voltage gain is less dependent on the value of
beta.
‰
Th hi
The
high
h ffrequency response iis significantly
i ifi
tl improved.
i
d
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Exercise 5.44
15
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Common Base Amplifier
The gain of the CB amplifier is similar to CE, however, over all gain can be different, the low input resistance
of CB can severely affect/attenuate the input signal as:
v
vi =
sig
Rsig + Ri
Ri ,
vi
Ri
re
=
=
vsig Rsig + Ri Rsig + re
We can see if Rsig is of the order of re, otherwise signal transmission factor vi/vsig can be very small, one of the
application of CB is using to amplify high frequency signal that appears on coaxial cable, to stop the reflection
on the cable CB has to have an input resistance equal to the characteristics resistance of the cable, which is the
case for
f coaxial
i l cables
bl having
h i resistance
i
i the
in
h range 500 tp 75 ohms.
h
(a) A common-base amplifier using the basic structure shown earlier. (b) Equivalent circuit obtained by replacing the transistor with its T model.
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Common Base Amplifier
vi
re
=
vsig Rsig + re
Rin = re
vo ≅ −α ie ( RC || RL )
as ie = −
Av ≡
vi
re
vo α ( RC || RL )
=
= g m ( RC || RL )
vi
re
The over all gain is factor
Gv =
vi
multplying with Av
vsig
α ( RC || RL )
re
g m ( RC || RL ) =
Rsig + re
Rsig + re
since the over all gain is just the ratio of total resistance
in the collector to total resistance in emitter.
emitter If Rsig is of the same
order as RC and RL gain will be small.
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Common Base Amplifier Summary
‰
‰
‰
‰
‰
CB has a low input resistance.
The short circuit gain is near to unity.
The open circuit gain is positive and equal in magnitude to
CE amplifier (gmRC).
CB has high output resistance.
Because of the low input resistance CB is not attractive,
however, it is used in special applications.
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9
Exercise 5.45 & 5.46
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CC Amplifier (Emitter Follower)
(a) An emitter-follower circuit based on the basic structure. (b) Small-signal equivalent circuit of the emitter follower with the transistor replaced by its T
model augmented with ro. (c) The circuit in (b) redrawn to emphasize that ro is in parallel with RL. This simplifies the analysis considerably.
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10
CC Amplifier
The CC is unlike CE & CB as it is not a unilateral amplifier, the input resistance
depend upon RL and the output resistance depends upon Rsig.
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CC Amplifier
The emitter resistance has a series resistance equal to (ro || RL).
(a) An equivalent circuit of the emitter follower obtained from the previous slide (c) by reflecting all resistances in the emitter to the base side.
(b) The circuit in (a) after application of Thévenin theorem to the input circuit composed of vsig, Rsig, and RB.
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CC Amplifier
(a) An alternate equivalent circuit of the emitter follower obtained by reflecting all base-circuit resistances to the emitter side. (b) The circuit in (a)
after application of Thévenin theorem to the input circuit composed of vsig, Rsig / (β 1 1), and RB / (β 1 1).
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CC Amplifier Summary
As only a small fraction of the input signal
appears between base and emitter, so it exhibit
p
over a wide range,
g , however,, there
linear operation
is an upper limit imposed on the value of the
output signal amplitude by transistor cutoff.
IR
Vˆsig = L
Gv
Increasing vsig beyond this value will go into
cuttoff and the signal will be clipped off.
Thévenin equivalent circuit of the output of the emitter follower.
This circuit can be used to find vo and hence the overall voltage
gain vo/vsig for any desired RL.
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CC Amplifier Summary
‰
Emitter follower has high input resistance and a low output resistance.
‰
Voltage gain is small but close to unity.
‰
Current gain is relatively large.
‰
It is useful for applications where a high resistance source is to be connected with a
low resistance load (last stage or output stage of a multistage amplifier.
‰
This way its purpose is to provide a low output resistance and not the voltage gain.
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Exercise 5.47
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BJT Internal Capacitors
‰
Base Charging Capacitor or Diffusion Capacitance Cde.
‰
Base Emitter Junction Capacitance Cje.
‰
Collector Base junction Capacitance Cμ.
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Base Charging Capacitance
‰
As iC is dependent on vBE and iC is exponentially related to vBE,
therefore, charge storage mechanism represent a non linear
capacitive effect.
Qn =
W2
iC = τ F iC
2 Dn
Cde =
dQn
di
I
= τ F C = τ F gm = τ F C
dvBE
dvBE
VT
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Base Emitter Junction Capacitance
C je =
C jeo
⎛ VBE ⎞
⎜⎜1 +
⎟⎟
⎝ Voe ⎠
m
where C jeo is the value of C je at zero voltage,Voe is the EBJ built in voltage (typically 0.9 V),
m is the grading coefficient of the EBJ (typically 0.5V). It turns out that because EBJ is forward
biased in the active mode , the above equation does not provide accurate prediction of C je , so
it is approximated to;
C je ≅ 2C jeo
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Collector Base Junction Capacitance
Cμ =
Cμo
⎛ VCB ⎞
⎟⎟
⎜⎜1 +
⎝ Voc ⎠
m
where Cμo is the value of C μ at zero voltage, Voc is the CBJ built in voltage (typically 0.75 V),
m is the grading coefficient of the CBJ (typically 0.2 - 0.5 V).
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High Frequency Hybrid
Hybrid--π Model
C π = C de + C je
C π is in the range of few pF to few tens of pF, where as C μ is in the range of a fraction of a pF to a few pF.
rx is the resistance of the silicon material of the base region between th e base terminal and the fictitious
internal base terminal under the emitter region, it is typically of a few tens of ohms. Also, rx << rπ
The data sheet does not specify C π , rather the behaviour of β ( h fe ) vs frequency is specified (given).
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Frequency Response of CE
(a) Capacitively coupled common-emitter amplifier. (b) Sketch of the magnitude of the gain of the CE amplifier versus frequency. The graph
delineates the three frequency bands relevant to frequency-response determination.
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Expression for hfe(s) ≈ Ic/Ib.
h fe =
β0
1 + s ( C π + C μ ) rπ
β 0 is the low frequency value of β , thus h fe has a
single pole response with a 3 - dB frequency at w = w β .
wT =
gm
Cπ + C μ
fT =
gm
2π ( C π + C μ )
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BJT High Frequency Model
gm =
IC
VT
Cπ = Cde + C je
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ro =
VA
IC
rπ =
Cde = τ F g m
β0
gm
Cπ + C μ =
gm
2πfT
C je ≅ 2C je 0
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High Frequency Response
Determining the high-frequency response of the CE amplifier: (a) equivalent circuit; (b) the circuit of (a) simplified at both the input side and the
output side; (c) equivalent circuit with Cμ replaced at the input side with the equivalent capacitance Ceq; (d) sketch of the frequency-response plot,
which is that of a low-pass STC circuit.
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Low Frequency Response
Analysis of the low-frequency response of the CE amplifier: (a) amplifier circuit with dc sources removed; (b) the effect of CC1 is determined with
CE and CC2 assumed to be acting as perfect short circuits;
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Transfer Characteristics of BJT Inverter
Sketch of the voltage transfer characteristic of the inverter circuit for the case RB = 10 kΩ, RC = 1 kΩ, β = 50, and VCC = 5 V. For the
calculation of the coordinates of X and Y, refer to the text.
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