SMALLSIGNAL HYBRID EQUIVALENT CIRCUIT Content BJT Small Signal

SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT

Content BJT – Small Signal Amplifier BJT complete Hybrid equivalent circuit BJT approximate Hybrid model Objectives Develop the small-signal models of transistor that are used in analysis of linear amplifier.

Basic knowledge. . Ohm’s Law Kirchoff’s Law Thevenin and Norton’s Theorem All electronic circuit analysis require these for mathematical manipulation.

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.

2 -port system AC 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 which only three connection leads, i. e transistor falls into this category.

Single-ended 2 -port network

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

Port variables 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.

2 -port variables Below are the equations for BJT’s derived from 2 -port network simplification.

Small signal hybrid-π equivalent circuit 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.

Cont. . Figure shows i. B vs. v. BE 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

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.

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-π 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 transconductance gm=ICQ/VT r = VT/ICQ Transconductance parameter

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:

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

Small-signal circuit parameters

Small-signal voltage gain Combine BJT equivalent cct to ac equivalent cct.

Small-signal voltage gain Voltage 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 gm. V 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 1 Given : = 100, VCC = 12 V VBE = 0. 7 V, RC = 6 k , VT=0. 026 V, RB = 50 k and VBB = 1. 2 V Calculate the small-signal voltage gain.

Solutions 1. 2. 3. 4. 5. 6.

Example 2 Given VCC=5 V, VBB=2 V, RB=650 kΩ, RC=15 kΩ, β=100 and VBE(on)=0. 7 V. Determine a) Q-points, b) gm and r c) voltage gain.

Early effect Early Voltage (VA)

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 < 300 V.

Hybrid-π equivalent circuit with Early Effect => collector current, i. C is dependent to collector-emitter voltage, v. CE (refer Chapter 5 Neaman): The output resistance, r. O: Substitute and rearrange both equation,

Cont. . Hence, small-signal transistor output resistance, r. O become: r. O is equivalent to Norton resistance r. O is parallel with dependent current sources.

Modified bipolar equivalent circuits including r. O due to Early Effect. Transconductance parameter ro=VA/ICQ Current gain parameter

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

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.

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 forward o for output e for common-emitter

h-parameter These equations represent KVL at input and KCL at output applied to h-parameter model for commonemitter BJT.

h-parameter in relation to hybrid-π