Download small-signal hybrid-π equivalent circuit of bipolar

LECTURE 1:
SMALL-SIGNAL HYBRID-Π
EQUIVALENT CIRCUIT OF
BIPOLAR TRANSISTOR (BJT)
By:
Syahrul Ashikin Azmi
PPKSE
1
Lecture’s content
• Objectives
– Develop the small-signal models of transistor that are
used in analysis of linear amplifier.
• BJT – Small Signal Amplifier
 Small-signal hybrid-π equivalent circuit of BJT
 Small-signal hybrid-π equivalent circuit using
transconductance
 Small-signal hybrid-π equivalent circuit using common
current gain
 Small-signal voltage gain
 Hybrid- π equivalent circuit including Early Effect
 Expanded hybrid- π equivalent circuit
 Other small-signal parameters and equivalent circuits2
Basic knowledge..
• Ohm’s Law
• Kirchoff’s Law
• Thevenin and Norton’s Theorem
• All electronic circuit analysis require
these for mathematical manipulation.
3
Small signal hybrid- equivalent
circuit of bipolar transistor
• Need to develop a small-signal equivalent
cct -- use hybrid- model because is
closely related to the physic of transistor.
• Treat transistor as two-port network.
4
Small signal hybrid- equivalent
circuit of bipolar transistor
**2-port system**
• AC analysis require simplification of
transistors as 2-port system.
• Simplification leads to new parameters /
definitions.
5
Small signal hybrid- equivalent circuit
of bipolar transistor
**2-port system**
• ‘Single ended’ 2-port system has 1 input
port shorted to 1 output port.
• Alternative view =>system has a
common input/output port.
• Three terminal device  device which
only three connection leads, i.e transistor
falls into this category.
6
Small signal hybrid- equivalent
circuit of bipolar transistor
**2-port system**
7
Small signal hybrid- equivalent
circuit of bipolar transistor
**2-port system**
• The ‘differential 2-port’ network are the
basis for forthcoming analysis of all types
of transistors (BJT and FET).
8
Small signal hybrid- equivalent
circuit of bipolar transistor
**2-port system**
• 2-port network analysis is all about current and voltage by
breaking down voltage direction (-ve to +ve or +ve to –ve)
and current direction (to or from).
• Each current and voltage has 2 possible directions.
9
Small signal hybrid-π equivalent
circuit of bipolar transistor
cont..
• Based on 2-port network, 1 input port and 1 output port
shorted together to form a common port of both input
and output.
• Transistor has input and output ports shorted (emitter)
resulting a small-signal 2-port hybrid- π network.
10
Small signal hybrid-π equivalent
circuit of bipolar transistor
cont..
• Figure shows iB vs. vBE
with small-time varying
signal superimposed at Qpt.
• Since sinusoidal signals
are small, the slope at Qpt treated as a constant,
has units of conductance.
• The inverse of this
conductance is smallsignal resistance, rπ
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Small signal hybrid-π equivalent
circuit of bipolar transistor
cont..
• We can relate small-signal input base current to smallsignal input voltage by:
v be  i b r
• Finding rπ from Q-point slope lead to:
v be
VT
 VT
 r 

ib
I BQ
I CQ
• rπ also known as diffusion resistance and is a function of
Q-point parameters. VT is known as thermal voltage.
12
Small signal hybrid-π equivalent
circuit of bipolar transistor
cont..
• Now, we consider the output terminal characteristic of BJT.
• Assume o/p collector current is independent of collectoremitter voltage collector-current is a function of baseemitter voltage, so the equation:
i C
i C 
v BE
.v BE
Q  pt
• From eq 5.2 in Chapter 5 Neaman,
 v BE 

i C  I S exp
 VT 
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Small signal hybrid-π equivalent
circuit of bipolar transistor
cont..
• After substitution and rearrange the above, we obtain:
I CQ
 v BE 
iC
1


. I S exp

v BE Q  pt VT
 VT  Q  pt VT
• The term ICQ / VT is a conductance. Since this term relates
current in collector to a voltage in B-E circuit, it is called
transconductance and is written:
gm 
I CQ
VT
• Transconductance also a function of Q-pt parameters and
directly proportional to dc bias current.
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Small signal hybrid-π equivalent
circuit of bipolar transistor
cont..
• Using these new parameters  develop a
simplified small-signal hybrid-π equivalent
cct for npn BJT.
• Phasor components given in parentheses.
• This circuit can be inserted into ac
equivalent circuit shown previously.
15
Small-signal hybrid- equivalent
circuit using transconductance
gm=ICQ/VT
r=VT/ICQ
Transconductance parameter
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Small-signal hybrid- equivalent
circuit using transconductance
cont..
• We can relate small-signal collector current to small-signal
base current for o/p of equivalent cct.
i C
ic 
.i b
i B Q  pt
• Where
i C
i B

Q  pt
• β is called ac common-emitter current gain.
• Thus:
i c  i b
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Small-signal hybrid- equivalent
circuit using common-emitter
current gain
ib
(Ib )

Current gain parameter
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Small-signal voltage gain cont..
• Combine BJT equivalent cct to ac
equivalent cct.
Small-signal hybrid-π model
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Small-signal voltage gain cont..
• Voltage gain, Av = ratio of o/p voltage to i/p voltage.
• Small-signal B-E voltage is called the control voltage, Vbe or
V.
• The dependent current source is gmV flows through RC
produce –ve C-E voltage at the output.
Vo  Vce  g mVbe RC
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Small-signal voltage gain cont..
• From the input portion of the circuit, using voltage
divider:
 r 
Vs
Vbe  
 r  RB 
• The small-signal voltage gain is:
 r 
Vo

Av 
 g m RC 
Vs
 r  RB 
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Example 1
Given :  = 100, VCC = 12V
VBE = 0.7V, RC = 6k, VT=0.026V,
RB = 50k and
VBB = 1.2V
Calculate the small-signal
voltage gain.
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Solutions
1.
I BQ 
VBB  VBE ( on)
RB
1.2  0.7

 10 A
50
2.
I CQ  I BQ  100(10A)  1 mA
3.
VCEQ  VCC  I CQ RC  12  (1)(6)  6V
4.
5.
6.
VT
(100)(0.026)
r 

 2.6 k
I CQ
1
I CQ
1
gm 

 38.5 mA / V
VT
0.026
 r

Vo
  11.4
Av 
 g m RC 
Vs
 r  RB 
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Example 2
• Given VCC=5V, VBB=2V, RB=650kΩ, RC=15kΩ,
β=100 and VBE(on)=0.7V.
• Determine:
a) Q-points,
b) gm and r
c) voltage gain.
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Hybrid-π equivalent circuit
including Early effect
Early Voltage
(VA)
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Hybrid-π equivalent circuit
including Early effect
**Early voltage**
• Figure above show current-voltage characteristic for
constant values of B-E voltage.
• The curves are linear with respect to C-E voltage in
forward-active mode.
• The slope is due to base-width modulation effect  Early
Effect.
• When the curves extrapolated at zero current, they meet
a point on –ve voltage axis, vce = -VA. VA --- Early voltage
with typical value in range of 50 < VA < 300V.
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Hybrid-π equivalent circuit
including Early Effect
• Early Effect => collector current, iC is dependent to
collector-emitter voltage, vCE (refer Chapter 5-Neaman):

 v BE  
v CE 




i C  I S exp
 . 1 

VA 
 VT   

• The output resistance, rO:
v CE
rO 
i C Q  pt
• Substitute and rearrange both equation,

 v BE
1
 I S exp
rO
 VT

 1
.
 V A

Q  pt
I CQ
VA
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Hybrid-π equivalent circuit
including Early effect cont..
• Hence, small-signal transistor output resistance, rO
become:
VA
rO 
I CQ
• rO is equivalent to Norton resistance  rO is parallel with
dependent current sources.
28
Modified bipolar equivalent circuits including
rO due to Early Effect.
Transconductance
parameter
ro=VA/ICQ
Current gain
parameter
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Self study for pnp
transistor
• From Neaman textbook,
– Ac equivalent circuit – pg 386
– Transconductance and current gain – pg 386
& 387
– Small-signal hybrid-π equivalent circuit – pg
387
– Do example 6.3
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Expanded hybrid-π
equivalent circuit
• Include 2 additional resistance,
rb and rμ.
• rb  series resistance of
semiconductor material.
• Since rb << rμ., rb is neglected
(short cct) at low freq.
• rμ  reverse-biased diffusion
resistance of B-C junction.
Typically in megaohms and
neglected (open cct).
• Normally, in hybrid-π model,
we neglect both rb and rμ.
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Other small-signal parameters
-h parameter
• h-parameter -> relate small-signal terminal currents and voltages
of 2-port network.
• The linear r/ship between terminal currents and voltages are:
•
Vbe  hie I b  hreVce
Equation 1
• Where:
I c  h fe I b  hoeVce
Equation 2
– i for input
–
–
–
–
r for reverse
f for forward
o for output
e for common-emitter
• Equation 1: KVL at input, hie in series with dependent voltage
source, hreVce
• Equation 2: KCL at output, hoe is in parallel with dependent current
source, hfeIb.
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h-parameter
Common-emitter transistor
h-parameter model of C-E BJT
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h-parameter
h-parameter in relation with hybrid-π are shown below:
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