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

• 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-