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LECTURE 1: SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT OF BIPOLAR TRANSISTOR (BJT) By: Syahrul Ashikin Azmi PPKSE 1 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 circuits2 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 -- 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 **2-port system** • AC analysis require simplification of transistors as 2-port system. • Simplification leads to new parameters / definitions. 5 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. 6 Small signal hybrid- equivalent circuit of bipolar transistor **2-port system** 7 Small signal hybrid- equivalent circuit of bipolar transistor **2-port system** • The ‘differential 2-port’ network are the basis for forthcoming analysis of all types of transistors (BJT and FET). 8 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. 9 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. 10 Small signal hybrid-π equivalent circuit of bipolar transistor cont.. • Figure shows iB vs. vBE with small-time varying signal superimposed at Qpt. • Since sinusoidal signals are small, the slope at Qpt treated as a constant, has units of conductance. • The inverse of this conductance is smallsignal resistance, rπ 11 Small signal hybrid-π equivalent circuit of bipolar transistor cont.. • We can relate small-signal input base current to smallsignal input voltage by: v be i b r • Finding rπ from Q-point slope lead to: v be VT VT r ib I BQ I CQ • rπ also known as diffusion resistance and is a function of Q-point parameters. VT is known as thermal voltage. 12 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 collectoremitter voltage collector-current is a function of baseemitter voltage, so the equation: i C i C v BE .v BE Q pt • From eq 5.2 in Chapter 5 Neaman, v BE i C I S exp VT 13 Small signal hybrid-π equivalent circuit of bipolar transistor cont.. • After substitution and rearrange the above, we obtain: I CQ v BE iC 1 . I S exp v BE Q pt VT VT Q pt VT • 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: gm I CQ VT • Transconductance also a function of Q-pt parameters and directly proportional to dc bias current. 14 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. 15 Small-signal hybrid- equivalent circuit using transconductance gm=ICQ/VT r=VT/ICQ Transconductance parameter 16 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. i C ic .i b i B Q pt • Where i C i B Q pt • β is called ac common-emitter current gain. • Thus: i c i b 17 Small-signal hybrid- equivalent circuit using common-emitter current gain ib (Ib ) Current gain parameter 18 Small-signal voltage gain cont.. • Combine BJT equivalent cct to ac equivalent cct. Small-signal hybrid-π model 19 Small-signal voltage gain cont.. • Voltage gain, Av = ratio of o/p voltage to i/p voltage. • Small-signal B-E voltage is called the control voltage, Vbe or V. • The dependent current source is gmV flows through RC produce –ve C-E voltage at the output. Vo Vce g mVbe RC 20 Small-signal voltage gain cont.. • From the input portion of the circuit, using voltage divider: r Vs Vbe r RB • The small-signal voltage gain is: r Vo Av g m RC Vs r RB 21 Example 1 Given : = 100, VCC = 12V VBE = 0.7V, RC = 6k, VT=0.026V, RB = 50k and VBB = 1.2V Calculate the small-signal voltage gain. 22 Solutions 1. I BQ VBB VBE ( on) RB 1.2 0.7 10 A 50 2. I CQ I BQ 100(10A) 1 mA 3. VCEQ VCC I CQ RC 12 (1)(6) 6V 4. 5. 6. VT (100)(0.026) r 2.6 k I CQ 1 I CQ 1 gm 38.5 mA / V VT 0.026 r Vo 11.4 Av g m RC Vs r RB 23 Example 2 • Given VCC=5V, VBB=2V, RB=650kΩ, RC=15kΩ, β=100 and VBE(on)=0.7V. • Determine: a) Q-points, b) gm and r c) voltage gain. 24 Hybrid-π equivalent circuit including Early effect Early Voltage (VA) 25 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 with typical value in range of 50 < VA < 300V. 26 Hybrid-π equivalent circuit including Early Effect • Early Effect => collector current, iC is dependent to collector-emitter voltage, vCE (refer Chapter 5-Neaman): v BE v CE i C I S exp . 1 VA VT • The output resistance, rO: v CE rO i C Q pt • Substitute and rearrange both equation, v BE 1 I S exp rO VT 1 . V A Q pt I CQ VA 27 Hybrid-π equivalent circuit including Early effect cont.. • Hence, small-signal transistor output resistance, rO become: VA rO I CQ • rO is equivalent to Norton resistance rO is parallel with dependent current sources. 28 Modified bipolar equivalent circuits including rO due to Early Effect. Transconductance parameter ro=VA/ICQ Current gain parameter 29 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 30 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. 31 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: • Vbe hie I b hreVce Equation 1 • Where: I c h fe I b hoeVce Equation 2 – i for input – – – – r for reverse f for forward o for output e for common-emitter • Equation 1: KVL at input, hie in series with dependent voltage source, hreVce • Equation 2: KCL at output, hoe is in parallel with dependent current source, hfeIb. 32 h-parameter Common-emitter transistor h-parameter model of C-E BJT 33 h-parameter h-parameter in relation with hybrid-π are shown below: 34