Electronic Devices and Circuit Theory Boylestad BJT AC Analysis Chapter 5 Ch.5 Summary BJT Transistor Modeling A model is an equivalent circuit that represents the AC characteristics of the transistor. A model uses circuit elements that approximate the behavior of the transistor. There are two models commonly used in small signal AC analysis of a transistor: re model Hybrid equivalent model Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary The re Transistor Model BJTs are basically current-controlled devices; therefore the re model uses a diode and a current source to duplicate the behavior of the transistor. One disadvantage to this model is its sensitivity to the DC level. This model is designed for specific circuit conditions. Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Common-Base Configuration Input impedance: re 26 mV Ie Zi re Output impedance: Zo Voltage gain: AV RL RL re re Current gain: Ai 1 Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Common-Emitter Configuration The diode re model can be replaced by the resistor re. Ie 1 Ib Ib re 26 mV Ie Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Common-Emitter Configuration Input impedance: Zi re Output impedance: Zo ro Voltage gain: AV RL re Current gain: Ai ro Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Common-Collector Configuration Input impedance: Zi ( 1)re Output impedance: Zo re || RE Voltage gain: AV RE RE re Current gain: Ai β 1 Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary The Hybrid Equivalent Model Hybrid parameters are developed and used for modeling the transistor. These parameters can be found on a transistor’s specification sheet: hi = input resistance hr = reverse transfer voltage ratio (Vi/Vo) 0 hf = forward transfer current ratio (Io/Ii) ho = output conductance Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Simplified General h-Parameter Model hi = input resistance hf = forward transfer current ratio (Io/Ii) Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary re vs. h-Parameter Model Common-Emitter hie βre hfe βac Common-Base hib re hfb α 1 Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary The Hybrid Model The hybrid pi model is most useful for analysis of high-frequency transistor applications. At lower frequencies the hybrid pi model closely approximate the re parameters, and can be replaced by them. Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Common-Emitter Fixed-Bias Configuration The input is applied to the base The output is taken from the collector High input impedance Low output impedance High voltage and current gain Phase shift between input and output is 180 Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Common-Emitter Fixed-Bias Configuration AC equivalent re,model Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Common-Emitter Fixed-Bias Calculations Input impedance: Output impedance: Zi RB||β|e Zi βre Zo RC||rO Zo RC Av Voltage gain: Av RC re Current gain: Ai ro 10 RC Io βRB ro Ii (ro RC )(RB βre ) Ai β ro 10RC Vo (R ||r ) C o Vi re Electronic Devices and Circuit Theory Boylestad RE 10 βre Current gain from voltage gain: ro 10 RC , R B 10 βre Ai AV Zi RC © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Common-Emitter Voltage-Divider Bias re model requires you to determine , re, and ro. Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Current gain Common-Emitter Voltage-Divider Bias Calculations Input impedance Io R ro Ii (ro RC )(R re ) I R Ai o r 10R Ii R re o C Ai Output impedance R R1 || R2 Zi R || βre Zo RC || ro Zo RC ro 10RC Ai Io ro 10R C , R10 re Ii Current gain from Av Ai Av Zi RC Voltage gain Av Vo RC || ro Vi re Av Vo R C Vi re ro 10R C Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Common-Emitter Emitter-Bias Configuration Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Impedance Calculations Input impedance: Zi RB || Zb Zb re ( 1)RE Zb (re RE ) Zb RE Output impedance: Zo RC Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Gain Calculations Voltage gain: Av Vo R C Vi Zb Av Vo RC Vi re RE Av Vo R C Vi RE Z b (re RE ) Z b RE Current gain: Ai Io RB Ii RB Zb Electronic Devices and Circuit Theory Boylestad Current gain from Av: Ai Av Zi RC © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Emitter-Follower Configuration This is also known as the common-collector configuration. The input is applied to the base and the output is taken from the emitter. There is no phase shift between input and output. Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Impedance Calculations Input impedance: Zi RB ||Zb Zb βre (β 1)RE Zb β(re RE ) Zb βRE Output impedance: Electronic Devices and Circuit Theory Boylestad Zo RE||re Zo re RE re © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Gain Calculations Voltage gain: Av Vo RE Vi RE re Av Vo 1 Vi RE re , R E re RE Current gain: Ai βRB RB Zb Current gain from voltage gain: Electronic Devices and Circuit Theory Boylestad Ai Av Zi RE © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Common-Base Configuration The input is applied to the emitter The output is taken from the collector Low input impedance. High output impedance Current gain less than unity Very high voltage gain No phase shift between input and output Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Calculations Input impedance: Zi RE || re Output impedance: Zo RC Voltage gain: Av Vo RC RC Vi re re Current gain: Ai Io 1 Ii Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Common-Emitter Collector Feedback Configuration • • • • A variation of the common-emitter fixed-bias configuration Input is applied to the base Output is taken from the collector There is a 180 phase shift between the input and output Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Calculations Input impedance: Output impedance: Voltage gain: Av Zi re 1 RC β RF Zo RC || RF Vo R C Vi re Current gain: Ai Io βRF Ii RF βRC Ai Io R F Ii RC Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Collector DC Feedback Configuration This is a variation of the commonemitter, fixed-bias configuration • The input is applied to the base • The output is taken from the collector • There is a 180 phase shift between input and output Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Calculations Input impedance: Zi re 1 RC β RF Output impedance: Zo RC||RF Voltage gain: Av Vo R C Vi re Electronic Devices and Circuit Theory Boylestad Current gain: Ai Io RF Ii RF RC Ai Io R F Ii RC © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Two-Port Systems Approach With Vi set to 0 V: ZTh Zo Ro The voltage across the open terminals is: ETh AvNLVi where AvNL is the noload voltage gain Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Effect of Load Impedance on Gain This model can be applied to any current- or voltagecontrolled amplifier. Adding a load reduces the gain of the amplifier: V RL Av o AvNL Vi RL Ro Electronic Devices and Circuit Theory Boylestad Zi Ai Av RL © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Effect of Source Impedance on Gain The amplitude of the applied signal that reaches the input of the amplifier is: Vi RiVs Ri Rs The internal resistance of the signal source reduces the overall gain: Avs Electronic Devices and Circuit Theory Boylestad Vo Ri AvNL Vs Ri Rs © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Combined Effects of RS and RL on Voltage Gain Effects of RL: Av Vo RL AvNL Vi RL Ro Ai Av Ri RL Avs Effects of RL and RS: Electronic Devices and Circuit Theory Boylestad Vo Ri RL AvNL Vs Ri Rs RL Ro Ais Avs Rs Ri RL © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Cascaded Systems • The output of one amplifier is the input to the next amplifier • The overall voltage gain is determined by the product of gains of the individual stages • The DC bias circuits are isolated from each other by the coupling capacitors • The DC calculations are independent of the cascading • The AC calculations for gain and impedance are interdependent Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary R-C Coupled BJT Amplifiers Voltage gain: Av 1 RC || R1 || R2 || Re re Av 2 RC re Av Av 1Av 2 Input impedance, first stage: Zi R1 || R2 || Re Electronic Devices and Circuit Theory Boylestad Output impedance, second stage: Zo RC © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Cascode Connection This example is a CE–CB combination. This arrangement provides high input impedance but a low voltage gain. The low voltage gain of the input stage reduces the Miller input capacitance, making this combination suitable for highfrequency applications. Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Darlington Connection The Darlington circuit provides very high current gain, equal to the product of the individual current gains: D = 1 2 The practical significance is that the circuit provides a very high input impedance. Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary DC Bias of Darlington Circuits Base current: IB VCC VBE RB DRE Emitter current: IE (D 1)IB DIB Emitter voltage: VE IE RE Base voltage: VB VE VBE Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Feedback Pair This is a two-transistor circuit that operates like a Darlington pair, but it is not a Darlington pair. It has similar characteristics: • High current gain • Voltage gain near unity • Low output impedance • High input impedance The difference is that a Darlington uses a pair of like transistors, whereas the feedback-pair configuration uses complementary transistors. Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Current Mirror Circuits Current mirror circuits provide constant current in integrated circuits. Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Current Source Circuits Constant-current sources can be built using FETs, BJTs, and combinations of these devices. I IE VZ VBE RE Electronic Devices and Circuit Theory Boylestad IE IC © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Current Source Circuits VGS = 0V ID = IDSS = 10 mA Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Fixed-Bias Input impedance: Zi RB || hie Output impedance: Zo RC || 1/ hoe Voltage gain: Av Vo h R || 1/ ho e fe C Vi hie Electronic Devices and Circuit Theory Boylestad Current gain: Ai Io hfe Ii © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Voltage-Divider Configuration Input impedance: Zi R || hie Output impedance: Zo RC Voltage gain: Av Current gain: Ai Electronic Devices and Circuit Theory Boylestad hfe RC || 1/hoe hie hfe R R hie © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Emitter-Follower Configuration Input impedance: Zb hfe RE Zi Ro || Zb Z b h fe R E Z i R o || Z b Output impedance: Zo RE || hie hfe Voltage gain: Av Vo RE Vi RE hie / hfe Electronic Devices and Circuit Theory Boylestad Ai Current gain: hfe RB RB Zb Ai Av Zi RE © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Common-Base Configuration Input impedance: Zi RE || hib Output impedance: Zo RC Voltage gain: Av Vo h R fb C Vi hib Current gain: Ai Io hfb 1 Ii Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved Ch.5 Summary Troubleshooting Check the DC bias voltages If not correct, check power supply, resistors, transistor. Also check the coupling capacitor between amplifier stages. Check the AC voltages If not correct check transistor, capacitors and the loading effect of the next stage. Electronic Devices and Circuit Theory Boylestad © 2013 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved