ETI2205 AnalogueElectronics II
BJT Review
Textbook –Microelectronics, Circuit Analysis & Design, 4th edition, Donald A. Neamen
Chapter5 & 6
"Small signals, applied to the transistor base, determine strong variations of the
current flowing through the device (at the collector and emitter). This property
makes the transistor an essential element in electronics. Some of its uses are in
electronic switching circuits, control circuits of current or voltage, amplifiers,
oscillators, digital logic, and memory circuits."
S. Kiambi
BJT Review, Page- 1
npn Output Family of Curves
Output characteristic (
versus
)
;
;
DC load line equation:
S. Kiambi
BJT Review, Page- 2
npn BJT dc Equivalent
Reverse biased
Forward biased
iB 
1

I S evBE VT
Forward biased
Diode relationship
VBE ~ 0.6 – 0.7 V for Si transistors at room temperature
S. Kiambi
BJT Review, Page- 3
Calculating Bias Currents & Voltages
Q-point is specified by
(and ) and
 Apply KVL on BE loop to get , (and
 Apply KVL on CE loop to get
).
What is IC, IE, VCE, etc., for the circuit below?
DC model for npn BJT
Key to solving circuits such this is that if the transistor is in the forward active mode,
VBE ~ 0.7 (for Si)
S. Kiambi
BJT Review, Page- 4
Calculating Bias Currents
Q-point is specified by
(and ) and
 Apply KVL on BE loop to get , (and
 Apply KVL on CE loop to get
S. Kiambi
).
BJT Review, Page- 5
Voltage Transfer Characteristic for npn Circuit
Junc. BE
Junc. CB
Operation .
Properties
Forw. Bias Rev. Bias
Active Region IC ~ IB
VCE =0.2 to 0.4 V
Forw. Bias Forw. Bias Saturation
IE = 0 A
Rev. Bias Rev. Bias
Cutoff
Transistor parameters of
S. Kiambi
(
)
(
)
BJT Review, Page- 6
Voltage Transfer Characteristic for pnp Circuit
Notations for junction voltages:
Transistor parameters of
(
)
, and
(
)
Recall: Allows for use of +ve voltage sources!
S. Kiambi
BJT Review, Page- 7
Digital Logic
Inverter
S. Kiambi
NOR gate
BJT Review, Page- 8
Bipolar Inverter as Amplifier
Determines the Q-point
(and ) and
Q-point is specified by
.
If Q-point is given apply KVL on BE and CE loops
to solve for biasing network resistors.
S. Kiambi
BJT Review, Page- 9
BJT Biasing:
Improper Biasing
Output voltage is clipped
Input voltage
S. Kiambi
BJT Review, Page- 10
BJT biasing:Single, BaseResistor Biasing


(
)⁄
and
CE
.
Generally a bad idea
Reason 1: varies significantly from device to device; also increases with temperature.
Reason 2: Thermal runaway
VBE decreases by about 2 mV/oC. This increases IC, which heats up the
transistor, which further decreases VBE . Increase of with rise in temperature also leads to thermal runaway
S. Kiambi
BJT Review, Page- 11
BJT biasing: Voltage Divider Biasing and
Emitter Resistor
Find IB, IC, etc.
VBE ~0.7 V
IB not zero, so
VB  [ R2 /( R1  R2 )]VCC
Replace base network with Thevenin equivalent
VTH  [ R2 /( R1  R2 )]VCC RTH  R1 || R2
IB  0
 VTH  I B RTH  0.7  (1   ) I B RE  0
VB  VTH  I B RTH
S. Kiambi
BJT Review, Page- 12
Voltage Divider Biasing and Emitter Resistor
VBE ~0.7 V
ib  0
VTH  [ R2 /( R1  R2 )]VCC
This biasing scheme is one of several methods referred WRas “self-bias” schemes
(and
) and allow the BJT to adjust
(through negative feedback
which fix
provided by ) to achieve a stable bias.
S. Kiambi
here
BJT Review, Page- 13
Example
Find Q-point voltages and currents. For the Si transistor,  = 50
VBE ~0.7 V
Determine Q-point:
BE-KVL:
𝑉𝑇𝐻 = 𝑅𝑇𝐻 𝐼𝐵𝑄 + 𝑉𝐵𝐸 + 𝐼𝐸𝑄 𝑅𝐸
=> 𝑰𝑩𝑸 =
CE-KVL:
𝑉𝑇𝐻 − 𝑉𝐵𝐸
; 𝑰𝑪𝑸 = 𝛽𝐼𝐵𝑄 ; 𝑰𝑬𝑸 = 1 + 𝛽 𝑅𝐸
𝑅𝑇𝐻 + 1 + 𝛽 𝑅𝐸
𝑉𝐶𝐶 = 𝑅𝐶 𝐼𝐶𝑄 + 𝑉𝐶𝐸𝑄 + 𝐼𝐸𝑄 𝑅𝐸
=> 𝑽𝑪𝑬𝑸 = 𝑉𝐶𝐶 − 𝐼𝐶𝑄 𝑅𝐶 − 𝐼𝐸𝑄 𝑅𝐸
To ensure a stable bias point (i.e. 𝐼𝐶𝑄 𝑎𝑛𝑑 𝑉𝐶𝐸𝑄 independent of 𝛽) we choose 𝑅𝑇𝐻 s.t.
𝑹𝑻𝑯 ≪ 𝜷𝑹𝑬:
=> 𝑰𝑩𝑸 ≈
S. Kiambi
𝑉𝑇𝐻 −𝑉𝐵𝐸
1+𝛽 𝑅𝐸
; 𝑰𝑪𝑸 ≈
𝑉𝑇𝐻 −𝑉𝐵𝐸
𝑅𝐸
; 𝑽𝑪𝑬𝑸 ≈ 𝑉𝐶𝐶 −
𝑅𝐶 +𝑅𝐸
𝑅𝐸
(𝑉𝑇𝐻 − 𝑉𝐵𝐸 )
BJT Review, Page- 14
Example
Find Q-point voltages and currents. For the Si transistor,  = 75
VBE ~0.7 V
S. Kiambi
BJT Review, Page- 15
BJT biasing with two voltage sources
 Is a self-bias method similar to the voltage-divider biasing and provides a
stable bias point as long as 𝑅𝐵 ≪ 𝛽𝑅𝐸 .
 A voltage of −𝑉𝐸𝐸 is assigned to the ground (reference voltage).
 BE-KVL:
𝐼𝐶𝑄 ≈
𝑉𝐸𝐸 −𝑉𝐵𝐸
𝑅𝐸
= constant.
 CE-KVL: 𝑉𝐶𝐸𝑄 ≈ 𝑉𝐶𝐶 + 𝑉𝐸𝐸 − 𝐼𝐶𝑄 (𝑅𝐶 + 𝑅𝐸 )=constant
 Both 𝐼𝐶𝑄 and 𝑉𝐶𝐸𝑄 are independent of 𝛽.
 Uses two bias resistors 𝑅𝐵 and 𝑅𝐸 (as opposed to three in the voltage
divider biasing.
 In most applications 𝑅𝐵 can be removed and directly couple the input
signal (without a capacitor) to the BJT: as such this configuration can also
amplify DC signals.
S. Kiambi
BJT Review, Page- 15
Integrated Circuit
Biasing: current mirror
Constant Current Source
IC  IQ 
I1
1
2

Question: what is I1?
I1 
4.3
R1
Current mirror
 This circuit is called a “current mirror" as the two transistors work
in tandem to ensure that current remains the same as reference
current no matter what circuit is attached to the collector of .
 As such, the circuit behaves as a current source and can be used to
bias BJT circuits, i.e.,
collector is attached to the emitter circuit
of the BJT amplifier to be biased.
S. Kiambi
BJT Review, Page- 16
Multistage Circuits: cascade, cascode,
Darlington pairs, etc.




S. Kiambi
Transistor amplifier circuits can be connected in series, or cascaded, as shown
below. This may be done either to increase the overall small-signal voltage
gain or to provide an overall voltage gain greater than 1, with a very low
output resistance.
The overall voltage or current gain, in general, is not simply the product of
the individual amplification factors.
The input and output resistances (or impedances) come into play by reducing
the overall gain.
If the amplifiers were ideal (
and
), and each had a gain of ,
the overall gain would simply be
See illustration below.
BJT Review, Page- 17
Cascade Circuit
 “Staged” amplifiers are often used to achieve higher power
gains than what would be possible using a single transistor.
 Examples are on the right:
o 1st with DC blocking between stages, and all NPN
transistors
Voutput
Vinput
First stage
Second stage
Third stage
o 2nd with two common-emitter circuits: NPN and PNP; both
biased in the forward-active mode.
npn transistor
S. Kiambi
pnp transistor
BJT Review, Page- 17
Cascode Circuit



Cascode amplifier is a CE amplifier driving a CB stage.Is quite a faster
amplifier.
Idea: Combine the advantages of common emitter (high input resistance)
with common base (no Miller effect, t.b.d. later) to get greatly improved
performance. The output resistance looking into the collector of
is much
larger than the output resistance of a simple common-emitter circuit. Another
important advantage of this circuit is its large bandwidth.
, , and
set the bias points, and
is used to adjust the current through
both transistors. In fact, if the ß values are relatively large, the collector
currents are equal:
;
CB
 CB configuration is known for wider bandwidth than the CE
configuration, but the low input impedance (10s of Ω) of CB is a
limitation for many applications.
 Solution is to precede the CB stage by a low gain CE stage which
has moderately high input impedance (kΩs). The stages are said to
be in a cascode configuration, i.e. stacked in series, as opposed to
cascaded for a standard amplifier chain.
 The cascode configuration has both wide bandwidth and
moderately high input impedance.
Voltages are in blue
CE
Currents are in green
S. Kiambi
BJT Review, Page- 18
CE with Time-Varying Input
iC  I S e
Collector current:
CE voltage:
Slope = -1/RC
vBE VT
Q-point (and without the sinusoidal input):
With the addition of the sinusoidal input we have
Input:
Base current:
BE voltage:
Load line:
(dc quantities)
are time-varying or ac signals
vs changes vBE, which moves the Q-point along the load line
A. Kruger
BJT Review, Page- 20
IB Versus VBE Characteristic
iC  I S evBE VT
What is the incremental
resistance?
iC  I S evBE VT
1
i
 B
r vBE
S. Kiambi
iB 
IS

e vBE VT
vbe or vπ

  I S vBE
e
vBE  

1  I S vBE VT 
e

VT  
 Q  pt

1
I BQ
VT
Q  pt
VT
r 


 Q  pt
VT
V
 T
I BQ
I CQ
is the BE small-signal input resistance with
BJT Review, Page- 21
IC Versus VBE Characteristic
iC  I S evBE VT
iC  I S evBE VT
What is the incremental increase
in IC as a function of an
incremental change in VBE?
I CQ
iC  I S evBE VT
gm 
S. Kiambi
iC
vBE

Q  pt


I S e vBE VT
v BE


1
I S evBE
VT

1
I CQ
VT
VT

vbe or vπ

Q  pt
Q  pt
gm 
I CQ
VT
is the small-signal transconductance with
BJT Review, Page- 22
AC Equivalent Circuit for CE
r 
Above two
and
VT
V
 T
I BQ I CQ
are sufficient for specifying small signal model when
gm 
I CQ
VT
is large.
The small-signal resistance when looking into the BE junction from the emitter side is given
by
.
Other important relations:
S. Kiambi
BJT Review, Page- 23
Small Signal Equivalent Circuits
Original
Small Signal Model I
Small Signal Model II
AC Equivalent
S. Kiambi
BJT Review, Page- 24
Small-Signal Hybrid- Model for npn BJT
gm 
vπ
r 
I CQ
VT
 40 I CQ
VT
I CQ
g m r  
VT = ?
S. Kiambi
VT ~ 26 mV at room temp., => gm ~ 40 ICQ at room temp.
BJT Review, Page- 25
Small Signal Equivalent Circuits
Small Signal Model I
Small Signal Model II
AC Equivalent
S. Kiambi
BJT Review, Page- 26
Hybrid- Model for npn with Early Effect
VA
ro 
I CQ
How do we account for the slope?
The linear dependence of
versus
in the forward-active mode can be described by:
⁄
The output resistance
(
)
looking into the collector.
is the Q-point collector current. The Early voltage
is in the range
;
is thus
quite large and can sometimes be ignored.
S. Kiambi
BJT Review, Page- 27
Hybrid- Model for pnp with Early Effect
In AC analysis, we are interested in determining the following
quantities:
i) Voltage gain,
ii) Input resistance and
iii) Output resistance
S. Kiambi
BJT Review, Page- 28
Small-Signal Equivalent Circuit for npn CE
VO
 r 

Av  ? Av 
Vo   RC ( g mV ) V  VS 
VS
 r  RB 
 r 

Vo   RC g m VS 
 r  RB 
S. Kiambi
 r

Av  ( gm RC )  
 r  RB 
BJT Review, Page- 29
CE with RE
B
B
C
C
E
E
C
B
E
S. Kiambi
BJT Review, Page- 30
CE with RE
Rib 
KVL:
Vin
Ib
 Vin  I b r  I b  I b RE  0
Vin  I b r  I b  I b RE
Rib 
I b r  I b  I b RE
Ib
Rib  r  (1   ) RE
Ri  R1 R 2 Rib
Av 
S. Kiambi
VO
VS
 I b RC

VS
 Vin  1
 RC  
 Rib  VS
BJT Review, Page- 31
CE with RE
S. Kiambi
Av  
RC
if Ri  RS
RE
Av  
RC
2

 5
RE
0.4
BJT Review, Page- 32
CE with RE
Av  ?
Av  
S. Kiambi
RC
1

 10
RE
0.1
BJT Review, Page- 33
CC or Emitter-Follower Amplifier
Homework: verify that
,
is high, and
is low.
Av < 1
Ri is high (for BJT)
S. Kiambi
RO is low
BJT Review, Page- 34
Common-Base Amplifier
E
C
B
B
C
E
Note sign of Vπ and direction of Io
S. Kiambi
BJT Review, Page- 35
CB Small Signal Model
E
Vo   gmV RC || RL 

V V
 V  Vs
  gmV  
0
RE r
RS
r  
1
gm
V  
VS
RS
S. Kiambi
 r 

R
||
R



 E S
1





KCL for node E: sum of current flowing away from node is 0

 R || R   r 
Av   gm  C L     RE || RS  Av  gm RC || RL  as RS  0
 RS   1   

BJT Review, Page- 36
Input Resistance: CB
Assuming
,
I i  I b  g mV

V
 g mV
r
V
r
Rie 

Ii 1  
1  

 V 
 r 
S. Kiambi
BJT Review, Page- 37
Output Resistance: CB
Ro  ?
Turn off independent sources
and add text source Vx
Ro 
Vx
Ix
 Ix 
KCL at collector (C):
Ix 
Vx
 g mV
RC
g mV  constant
Why?
Vx
 g mV  0
RC
g mV  ?
Vx cannot change the current flowing through the current source so gmVπ is fixed
and we can remove it from the circuit just like any normal current source.
Thus
S. Kiambi
Ix 
Vx
RC
RO 
Vx
 RC
Ix
BJT Review, Page- 38
Output Resistance: CB Take 2
Ro  ?
Turn off independent sources
and add text source Vx
Ro 
Vx
Ix
 Ix 
KCL at collector (C):
Ix 
Vx
 g mV
RC
g mV  constant
Why?
Vx
 g mV  0
RC
g mV  ?
Vx cannot change the current flowing through the current source so gmVπ is fixed
and we can remove it from the circuit just like any normal current source.
Thus
S. Kiambi
Ix 
Vx
RC
RO 
Vx
 RC
Ix
In other words, looking into the current source
from C, once sees and infinite resistance.
BJT Review, Page- 39
Output Resistance: CB Take 2
If the previous result seems counterintuitive, below is an alternative approach. Start with a
BJT model that includes the output resistance ro. Then turn off independed sources, add a
test source, etc., to determine the output resistance:
KCL equations at the collector and emitter
nodes, using the convention that currents
flowing into a node are positive are:
(carefully note the sign of Vπ) give
𝐼𝑥 − 𝑔𝑚 𝑉𝜋 −
𝑔𝑚 𝑉𝜋 +
Combining give
Letting
S. Kiambi
𝑟𝑜 → ∞
𝑉𝑥
= 𝑅𝑂𝐶 = 𝑟𝑜 1 + 𝑔𝑚 𝑅𝑆 𝑅𝐸 𝑟𝜋
𝐼𝑋
results in
𝑅𝑂𝐶 → ∞
𝑉𝑥 − −𝑉𝜋
𝑟𝑜
𝑉𝜋
𝑅𝑆 𝑅𝐸 𝑟𝜋
−
=0
−𝑉𝜋 − 𝑉𝑥
=0
𝑟𝑜
+ 𝑅𝑆 𝑅𝐸 𝑟𝜋
Same result as before: looking into the current
source, once sees an infinite resistance
BJT Review, Page- 40
DC and AC Load Lines





The load lines are found by writing a KVL equation around the collector–
emitter loop.
A dc load line helps to visualize the relationship between the Q-point and the
transistor characteristics.
When capacitors are included in a transistor circuit, a new effective load line,
called an ac load line, may exist. The ac load line helps to visualize the
relationship between the small-signal response and the transistor
characteristics. The ac operating region is on the ac load line.
When the ac quantities
, we are at the Q-point. When ac signals
are present, we deviate about the Q-point on the ac load line.
The ac load line can be used to determine the maximum output symmetrical
swing. If the output exceeds this limit, a portion of the output signal will be
clipped and signal distortion will occur.
V + = +5 V
RC
RS = 0.5 kΩ
vs
+
–
vO
CC
RB =
100 kΩ
RE1
RE2
CE
V – = –5 V
S. Kiambi
BJT Review, Page- 42
BTJ Impedance Scaling or
Resistance Reflection Rules
S. Kiambi
BJT Review, Page- 43
Emitter Follower Analysis
Ro = ?
Ri = ?
S. Kiambi
Notice that ro is in parallel with RE
Rib = ?
BJT Review, Page- 44
Emitter Follower Analysis
Rib = ?
Ro = ?
Vo  I o ro RE 
I o  1   I b Vo  I b 1   ro RE 
Vin  I b r  Vo
Vin  I b r  (1   ) I b (ro || RE )
Rib 
Vin
 r  (1   )( ro RE )
Ib
r  R1 || R2 || RS
Ro  
RE ro
1 
S. Kiambi
}
Somewhat
involved to
derive each
time
Ro = ?
Rib = ?
Notice that Rib is rπ plus resistance
at emitter scaled up with (1+β)
Notice that Ro is base resistance
scaled down with (1+β), in parallel
with other resistance at emitter
BJT Review, Page- 45
Emitter Follower Small Signal Model
ro
rπ
ro
Rib = ?
Rib  r  (1   )(ro RE )
S. Kiambi
Example of BJT resistance scaling: looking
from the base, the emitter impeadance is
scaled up by (1+
BJT Review, Page- 46
BJT Resistance Scaling
r  RS || R1 || R2
Ro 
RE ro
1 
Resistance in base circuit divided by β+1
Rib = ?
Rib  r  (1   )(ro RE )
S. Kiambi
BJT Review, Page- 47
Resistance Scaling Example
The transistor in the circuit below has β =150. Neglect ro , and estimate the input
and output resistances shown. The collector current is IC = 0.8 mA, VA = ∞
g m  40I C  32 mA/V
r 
rπ
Ro
Rib
Ro 
S. Kiambi
r  RS || R1 || R2
RE
1 

gm
 4.7K
Rib  r  (1   ) RE
 4.7K  302K
 306K
4.7K  0.49K

2K  33.8 
151
BJT Review, Page- 48
BJT Resistance Scaling
The following sub-circuit often appears in small signal circuits
Ro  R  ro (1  g m R)
Question: can you derive this?
ADD A TEST VOLTAGE SOURCE
AT THE OUTPUT TERMINALS
Ro  (r || RE )  ro 1  g m r || RE 
 ro 1  g m r || RE 
S. Kiambi
BJT Review, Page- 49
Darlington Pair
In some applications, it is desirable to have a BJT stage with a much larger current
gain than can normally be obtained. A multitransistor configuration, called
Darlington pair provides such increased current gain.
Ai  1 2
S. Kiambi
Ri  ?
Av  ?
BJT Review, Page- 41
Composite Transistors
iCp   p iBP  iBn
i 2  (1  n )iBn
i 2  (1  n ) piBp   p niBp
S. Kiambi
i 2   p niBp
Ai  1 2
Current gain
BJT Review, Page- 51
Example
Darlington
END
S. Kiambi
BJT Review, Page- 52