# SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT. Content BJT – Small Signal Amplifier BJT complete...

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SMALL-SIGNAL HYBRID- EQUIVALENT CIRCUIT

Content BJT Small Signal AmplifierBJT complete Hybrid equivalent circuitBJT approximate Hybrid model

ObjectivesDevelop the small-signal models of transistor that are used in analysis of linear amplifier.

Basic knowledge..Ohms LawKirchoffs LawThevenin and Nortons Theorem

All electronic circuit analysis require these for mathematical manipulation.

Small signal hybrid- equivalent circuit of bipolar transistorNeed 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.

2-port systemAC analysis require simplification of transistors as 2-port system.

Simplification leads to new parameters / definitions.

2-port system cont..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.

Single-ended 2-port network

Differential 2-port networkThe differential 2-port network will be the basis for forthcoming analysis of all types of transistors (BJT and FET).

Port variables2-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.

2-port variablesBelow are the equations for BJTs derived from 2-port network simplification.

Small signal hybrid- equivalent circuitBased 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- network.

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, r

Cont..We can relate small-signal input base current to small-signal input voltage by:

Finding r from Q-point slope lead to:

r also known as diffusion resistance and is a function of Q-point parameters.

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,

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.

Cont..Using these new parameters develop a simplified small-signal hybrid- equivalent cct for npn BJT.Phasor components given in parentheses.This circuit can be inserted into ac equivalent circuit shown previously.

Small-signal hybrid- equivalent circuit using transconductanceTransconductance parametergm=ICQ/VTr=VT/ICQ

Cont..We can relate small-signal collector current to small-signal base current for o/p of equivalent cct.

Where

is called ac common-emitter current gain.Thus:

Small-signal hybrid- equivalent circuit using common-emitter current gainCurrent gain parameter

Small-signal circuit parameters

Small-signal voltage gainCombine BJT equivalent cct to ac equivalent cct.

Small-signal voltage gainVoltage gain, Av = ratio of o/p voltage to i/p voltage.

Small-signal B-E voltage is called control voltage, Vbe or V.

The dependent current source is gmV flows through RC produce ve C-E voltage at the output.

Cont..From the input portion of the circuit:

The small-signal voltage gain is:

Example 1Given : = 100, VCC = 12VVBE = 0.7V, RC = 6k, VT=0.026V, RB = 50k and VBB = 1.2VCalculate the small-signal voltage gain.

Solutions1.

2.

3.

4.

5.

6.

Example 2Given VCC=5V, VBB=2V, RB=650k, RC=15k, =100 and VBE(on)=0.7V. Determine a) Q-points, b) gm and r c) voltage gain.

Early effect Early Voltage (VA)

Early voltageFigure 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.

Hybrid- equivalent circuit with Early EffectEarly Effect => collector current, iC is dependent to collector-emitter voltage, vCE (refer Chapter 5-Neaman):

The output resistance, rO:

Substitute and rearrange both equation,

Cont..Hence, small-signal transistor output resistance, rO become:

rO is equivalent to Norton resistance rO is parallel with dependent current sources.

Modified bipolar equivalent circuits including rO due to Early Effect.Transconductance parameterCurrent gain parameterro=VA/ICQ

Self study for pnp transistorFrom Neaman textbook,Ac equivalent circuit pg 386Transconductance and current gain pg 386 & 387Small-signal hybrid- equivalent circuit pg 387Do example 6.3

- Expanded hybrid- equivalent circuitInclude 2 additional resistance, rb and r.rb series resistance of semiconductor material.Since rb
Other small-signal parameters -h parameterh-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 inputr for reversef for forwardo for outpute for common-emitter

h-parameterThese equations represent KVL at input and KCL at output applied to h-parameter model for common-emitter BJT.

h-parameter in relation to hybrid-