1 LECTURE 1: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT OF BIPOLAR TRANSISTOR (BJT) By: Syahrul Ashikin Azmi PPKSE

2 Lecture’s content Objectives –Develop the small-signal models of transistor that are used in analysis of linear amplifier. BJT – Small Signal Amplifier  Small-signal hybrid-π equivalent circuit of BJT  Small-signal hybrid-π equivalent circuit using transconductance  Small-signal hybrid-π equivalent circuit using common current gain  Small-signal voltage gain  Hybrid- π equivalent circuit including Early Effect  Expanded hybrid- π equivalent circuit  Other small-signal parameters and equivalent circuits

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

4 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.

5 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.

6 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.

7 Small signal hybrid-  equivalent circuit of bipolar transistor ** 2-port system**

8 The ‘differential 2-port’ network are the basis for forthcoming analysis of all types of transistors (BJT and FET).

9 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.

10 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.

11 Small signal hybrid-π equivalent circuit of bipolar transistor 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, r π

12 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 r π from Q-point slope lead to: r π also known as diffusion resistance and is a function of Q-point parameters. V T is known as thermal voltage.

13 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,

14 Small signal hybrid-π equivalent circuit of bipolar transistor cont.. After substitution and rearrange the above, we obtain: The term I CQ / V T 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.

15 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.

16 Small-signal hybrid-  equivalent circuit using transconductance Transconductance parameter g m =I CQ /V T r  =V T /I CQ

17 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:

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

19 Small-signal voltage gain cont.. Combine BJT equivalent cct to ac equivalent cct. Small-signal hybrid-π model

20 Small-signal voltage gain cont.. Voltage gain, A v = ratio of o/p voltage to i/p voltage. Small-signal B-E voltage is called the control voltage, V be or V . The dependent current source is g m V  flows through R C  produce –ve C-E voltage at the output.

21 Small-signal voltage gain cont.. From the input portion of the circuit, using voltage divider: The small-signal voltage gain is:

22 Example 1 Given :  = 100, V CC = 12V V BE = 0.7V, R C = 6k, V T =0.026V, R B = 50k and V BB = 1.2V Calculate the small-signal voltage gain.

23 Solutions

24 Example 2 Given V CC =5V, V BB =2V, R B =650kΩ, R C =15kΩ, β=100 and V BE(on) =0.7V. Determine: a) Q-points, b) g m and r  c) voltage gain.

25 Hybrid-π equivalent circuit including Early effect Early Voltage (V A )

26 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, v ce = -V A. V A --- Early voltage with typical value in range of 50 < V A < 300V.

27 Hybrid-π equivalent circuit including Early Effect 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,

28 Hybrid-π equivalent circuit including Early effect 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.

29 Modified bipolar equivalent circuits including r O due to Early Effect. Transconductance parameter Current gain parameter r o =V A /I CQ

30 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

31 Expanded hybrid-π equivalent circuit Include 2 additional resistance, r b and r μ. r b  series resistance of semiconductor material. Since r b << r μ., r b is neglected (short cct) at low freq. r μ  reverse-biased diffusion resistance of B-C junction. Typically in megaohms and neglected (open cct). Normally, in hybrid-π model, we neglect both r b and r μ.

32 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, h ie in series with dependent voltage source, h re V ce Equation 2: KCL at output, h oe is in parallel with dependent current source, h fe I b. Equation 1 Equation 2

33 h-parameter Common-emitter transistor h-parameter model of C-E BJT

34 h-parameter h-parameter in relation with hybrid-π are shown below: