LECTURE 2 SMALLSIGNAL HYBRIDEQUIVALENT CIRCUIT OF BIPOLAR TRANSISTOR

LECTURE 2: SMALL-SIGNAL HYBRIDEQUIVALENT CIRCUIT OF BIPOLAR TRANSISTOR (BJT) π 1

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

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

Small signal hybrid- equivalent circuit of bipolar transistor • Need to develop a small-signal equivalent cct. for transistor -- use hybrid- model because is closely related to the physic of transistor. Treat transistor as two-port network. 4

Small signal hybrid- equivalent circuit of bipolar transistor…cont. • We can treat the BJT as a two port network • The input port is between the base and emitter and the output port is between the collector to emitter. 5

Small signal hybrid- 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 can be treated as a constant, which has units of conductance. • The inverse of this conductance is smallsignal resistance, rπ 6

Small signal hybrid- equivalent circuit of bipolar transistor…cont. Input Base-Emitter Port • We can relate small-signal input base current to smallsignal input voltage by: • Finding rπ from Q-point slope lead to: • rπ is called diffusion resistance or base-emitter input resistance and is a function of Q-point parameters. • VT is known as thermal voltage. 7

Small signal hybrid- equivalent circuit of bipolar transistor…cont. Output Collector-Emitter Port • Now, we consider the output terminal characteristic of BJT. • Assume o/p collector current is independent of collectoremitter voltage collector-current is a function of baseemitter voltage, so the equation: • From eq 3. 78 in Chapter 3 Sedra, 8

Small signal hybrid- equivalent circuit of bipolar transistor…cont. • After substitution and rearrange the above, we obtain: • The term Is exp (vbe/VT) is quiescent collector current, ICQ • 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 is also a function of Q-pt parameters and directly proportional to dc bias current. 9

Small signal hybrid- 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. 10

Small-signal hybrid- equivalent circuit using transconductance gm=ICQ/VT r = VT/ICQ Transconductance parameter 11

Small-signal hybrid- equivalent circuit using transconductance cont. . • We can relate small-signal collector current to smallsignal base current for o/p of equivalent cct. • Where • β is called ac common-emitter current gain. • Thus: 12

Small-signal hybrid- equivalent circuit using common-emitter current gain Current gain parameter 13

Small-signal voltage gain cont. . • Combine BJT equivalent cct to ac equivalent cct. Small-signal hybrid-π model a) BJT simplified cct b) AC equivalent cct 14

Small-signal voltage gain cont. . • Voltage gain, Av = ratio of o/p signal voltage to i/p signal voltage. • Small-signal B-E voltage is called the control voltage, Vbe or V . • The dependent current source is gm. V flows through RC produce –ve C-E voltage at the output. 15

Small-signal voltage gain cont. . • From the input portion of the circuit, using voltage divider: • The small-signal voltage gain is: 16

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 Q-point values & small-signal voltage gain. 17

Solutions 1. 2. 3. 4. 5. 6. 18

Example 2 • Given VCC=3. 3 V, VBB=0. 850 V, RB=180 kΩ, RC=15 kΩ, β=120 and VBE(on)=0. 7 V. • Determine: a) Q-points values, ICQ and VCEQ b) gm and r c) voltage gain. 19

Hybrid-π equivalent circuit including Early effect Early Voltage (VA) 20

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, vce = -VA. VA --- Early voltage • Typical values of VA are in the range of 50 < VA < 300 V. 21

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, 22

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. 23

Modified bipolar equivalent circuits including r. O due to Early Effect. Transconductance parameter ro=VA/ICQ Current gain parameter 24

Example 3 Determine the small signal voltage gain, including the effect of the transistor output resistance. Given : = 100, VCC = 12 V, VA=50 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. 25

Solutions 1. 2. 3. 26

Solutions 4. 5. 6. 7. 8. 27

Expanded hybrid-π equivalent circuit • Include 2 additional resistance, rb and rμ. • rb series resistance of semiconductor material between the external base B and an idealized internal base region B’. • 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. 28

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: • Equation 1 • Where: Equation 2 – i for input – – r for reverse f forward o for output e for common-emitter • Equation 1: KVL at input, hie in series with dependent voltage source, hre. Vce • Equation 2: KCL at output, hoe is in parallel with dependent current source, hfe. Ib. 29

h-parameter Common-emitter transistor h-parameter model of C-E BJT 30

h-parameter in relation with hybrid-π are shown below: 31