Chapter 7: BJT Transistor Modeling

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Chapter 7 BJT Transistor Modeling
Faculty of Electrical and Electronic Eng.
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Topic objectives

• At the end of the course you will be able to
• Understand about the small signal analysis of
  circuit network using re model and hybrid
  equivalent model
• Understand the relationship between those two
  available model for small signal analysis

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• INTRODUCTIONTRANSISTOR MODELING
• To begin analyze of small-signal AC response of
  BJT amplifier the knowledge of modeling the
  transistor is important.
• The input signal will determine whether its a
  small signal (AC) or large signal (DC) analysis.
• The goal when modeling small-signal behavior is
  to make of a transistor that work for
  small-signal enough to keep things linear
  (i.e. not distort too much) 3
• There are two models commonly used in the small
  signal analysis
• a) re model
• b) hybrid equivalent model

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How does the amplification be done?

• Conservation output power of a system cannot be
  large than its input and the efficiency cannot be
  greater than 1
• The input dc plays the important role for the
  amplification to contribute its level to the ac
  domain where the conversion will become as
  ?Po(ac)/Pi(dc)
• Simply speaking

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Disadvantages

• Re model
• Fails to account the output impedance level of
  device and feedback effect from output to input
• Hybrid equivalent model
• Limited to specified operating condition in order
  to obtain accurate result

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DC supply ? 0 potential

• O/p coupling capacitor ? s/c
• Large values
• Block DC and pass AC signal

• I/p coupling capacitor ? s/c
• Large values
• Block DC and pass AC signal

• Bypass
• capacitor ? s/c
• Large values

Voltage-divider configuration under AC analysis
Redraw the voltage-divider configuration after
removing dc supply and insert s/c for the
capacitors
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Modeling of BJT begin HERE!
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AC bias analysis 1) Kill all DC sources 2)
Coupling and Bypass capacitors are short cct. The
effect of there capacitors is to set a lower
cut-off frequency for the cct. 3) Inspect the
cct (replace BJTs with its small signal modelre
or hybrid). 4) Solve for voltage and current
transfer function, i/o and o/p impedances.
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• IMPORTANT PARAMETERS
• Input impedance, Zi
• Output impedance, Zo
• Voltage gain, Av
• Current gain, Ai
• Input Impedance, Zi(few ohms ? M?)
• The input impedance of an amplifier is the value
  as a load when connecting a single source to the
  I/p of terminal of the amplifier.

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Two port system-determining input impedance Zi

• The input impedance of transistor can be
  approximately determined using dc biasing because
  it doesnt simply change when the magnitude of
  applied ac signal is change.

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Demonstrating the impact of Zi
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Example 6.1 For the system of Fig. Below,
determine the level of input impedance
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Output Impedance, Zo (few ohms ? 2M?) The output
impedance of an amplifier is determined at the
output terminals looking back into the system
with the applied signal set to zero.
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Example 6.2 For the system of Fig. below,
determine the level of output impedance
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Example 6.3 For the system of Fig. below,
determine Zo if V600mV, Rsense10k? and Io10?A
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Example 6.4 Using the Zo obtained in example
6.3, determine IL for the configuration of Fig
below if RL2.2 k? and Iamplifier6 mA.
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• Voltage Gain, AV
• DC biasing operate the transistor as an
  amplifier. Amplifier is a system that having the
  gain behavior.
• The amplifier can amplify current, voltage and
  power.
• Its the ratio of circuits output to circuits
  input.
• The small-signal AC voltage gain can be
  determined by

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By referring the network below the analysis are
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Example 6.5 For the BJT amplifier of fig. below,
determine a)Vi b) Ii c) Zi d) Avs
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• Current Gain, Ai
• This characteristic can be determined by

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• re TRANSISTOR MODEL
• employs a diode and controlled current source to
  duplicate the behavior of a transistor.
• BJT amplifiers are referred to as
  current-controlled devices.
• Common-Base Configuration
• ?Common-base BJT transistor
• ?re model
• ?re equivalent cct.

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Therefore, the input impedance, Zi re that less
than 50O. For the output impedance, it will be as
follows
isolation part, Zire
Zo ? ??
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The common-base characteristics
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• Example 6.6 For a common-base configuration in
  figure
• below with IE4mA, ?0.98 and AC signal of 2mV is
• applied between the base and emitter terminal
• Determine the Zi b) Calculate Av if RL0.56k?
• c) Find Zo and Ai

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Solution
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• Example 6.7 For a common-base configuration in
  previous
• example with Ie0.5mA, ?0.98 and AC signal of
  10mV is
• applied, determine
• Zi b) Vo if RL1.2k? c) Av d)Ai e) Ib

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• Common-Emitter Configuration
• ?Common-emitter BJT transistor
• ?re model
• ?re equivalent cct.
• Still remain controlled-current source (conducted
  between collector and base terminal)
• Diode conducted between base and emitter terminal

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The output graph
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Output impedance Zo
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• Example 6.8 Given ?120 and IE(dc)3.2mA for a
  common-
• emitter configuration with ro ? ?, determine
• Zi b)Av if a load of 2 k? is applied c) Ai with
  the 2 k? load

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• Example 6.9 Using the npn common-emitter
  configuration,
• determine the following if ?80, IE(dc)2 mA and
  ro40 k?
• Zi b) Ai if RL 1.2k ? c) Av if RL1.2k ?

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Hybrid Equivalent Model

• re model is sensitive to the dc level of
  operation that result input resistance vary with
  the dc operating point
• Hybrid model parameter are defined at an
  operating point that may or may not reflect the
  actual operating point of the amplifier

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Hybrid Equivalent Model
The hybrid parameters hie, hre, hfe, hoe are
developed and used to model the transistor. These
parameters can be found in a specification sheet
for a transistor.
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Determination of parameter
H22 is a conductance!
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General h-Parameters for any Transistor
Configuration
hi input resistance hr reverse transfer
voltage ratio (Vi/Vo) hf forward transfer
current ratio (Io/Ii) ho output conductance
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Common emitter hybrid equivalent circuit
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Common base hybrid equivalent circuit
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Simplified General h-Parameter Model
The model can be simplified based on these
approximations hr ? 0 therefore hrVo 0 and
ho ? ? (high resistance on the output)
Simplified
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Common-Emitter re vs. h-Parameter Model
hie ?re hfe ? hoe 1/ro
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Common-Emitter h-Parameters
Formula 7.28 Formula 7.29
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Common-Base re vs. h-Parameter Model
hib re hfb -?
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Common-Base h-Parameters
Formula 7.30 Formula 7.31