1 lecture 1: small-signal hybrid-Π equivalent circuit of bipolar transistor (bjt) by: syahrul...
TRANSCRIPT
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LECTURE 1:SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT OF
BIPOLAR TRANSISTOR (BJT)
By:Syahrul Ashikin Azmi
PPKSE
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Lecture’s content
• Objectives– Develop the small-signal models of transistor that are
used in analysis of linear amplifier.
• BJT – Small Signal AmplifierSmall-signal hybrid-π equivalent circuit of BJTSmall-signal hybrid-π equivalent circuit using
transconductanceSmall-signal hybrid-π equivalent circuit using common
current gainSmall-signal voltage gainHybrid- π equivalent circuit including Early EffectExpanded hybrid- π equivalent circuitOther small-signal parameters and equivalent circuits
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Basic knowledge..
• Ohm’s Law
• Kirchoff’s Law
• Thevenin and Norton’s Theorem
• All electronic circuit analysis require these for mathematical manipulation.
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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.
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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.
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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.
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Small signal hybrid- equivalent circuit of bipolar transistor
**2-port system**
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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).
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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.
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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.
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Small signal hybrid-π equivalent circuit of bipolar transistor cont..
• Figure shows iB vs. vBE with small-time varying signal superimposed at Q-pt.
• Since sinusoidal signals are small, the slope at Q-pt treated as a constant, has units of conductance.
• The inverse of this conductance is small-signal 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 small-signal input voltage by:
• Finding rπ from Q-point slope lead to:
• rπ also known as diffusion resistance and is a function of Q-point parameters. VT is known as thermal voltage.
riv bbe
CQ
T
BQ
T
b
be
I
V
I
Vr
i
v
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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 collector-
emitter voltage collector-current is a function of base-emitter voltage, so the equation:
• From eq 5.2 in Chapter 5 Neaman,
BE
ptQBE
CC v
v
ii
.
T
BESC V
vIi exp
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Small signal hybrid-π equivalent circuit of bipolar transistor cont..
• After substitution and rearrange the above, we obtain:
• 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:
• Transconductance also a function of Q-pt parameters and directly proportional to dc bias current.
T
CQ
ptQT
BES
TptQBE
C
V
I
V
vI
Vv
i
exp.1
T
CQm V
Ig
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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.
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Small-signal hybrid- equivalent circuit using transconductance
Transconductance parameter
gm=ICQ/VT
r=VT/ICQ
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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.
• Where
• β is called ac common-emitter current gain.• Thus:
b
ptQB
Cc i
i
ii .
ptQB
C
i
i
bc ii
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ib(Ib )
Current gain parameter
Small-signal hybrid- equivalent circuit using common-emitter current gain
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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.
Cbemceo RVgVV
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Small-signal voltage gain cont..
• From the input portion of the circuit, using voltage divider:
• The small-signal voltage gain is:
s
B
be VRr
rV
B
Cms
ov Rr
rRg
V
VA
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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
AR
VVI
B
onBEBBBQ 10
50
7.02.1)(
mAAII BQCQ 1)10(100
VRIVV CCQCCCEQ 6)6)(1(12
kI
Vr
CQ
T 6.21
)026.0)(100(
VmAV
Ig
T
CQm /5.38
026.0
1
4.11
B
Cms
ov Rr
rRg
V
VA
1.
2.
3.
4.
5.
6.
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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):
• The output resistance, rO:
• Substitute and rearrange both equation,
A
CE
T
BESC V
v
V
vIi 1.exp
ptQC
CEO i
vr
A
CQ
ptQAT
BES
O V
I
VV
vI
r
1.exp
1
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Hybrid-π equivalent circuit including Early effect cont..
• Hence, small-signal transistor output resistance, rO become:
• rO is equivalent to Norton resistance rO is parallel with dependent current sources.
CQ
AO I
Vr
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Modified bipolar equivalent circuits including rO due to Early Effect.
Transconductance parameter
Current gain parameter
ro=VA/ICQ
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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:
•
• Where:– 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.
ceoebfec
cerebiebe
VhIhI
VhIhV
Equation 1
Equation 2
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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: