Transcript BJT Model
Chapter 8: BJT Small-Signal Analysis Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 1 BJT Small Signal Analysis The re and hybrid models will be used to analyze AC small-signal transistor circuits. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 2 Common-Emitter (CE) Fixed-Bias Configuration The input (Vi) is applied to the base and the output (Vo) is from the collector. The Common-Emitter is characterized as having high input impedance and low output impedance with a high voltage and current gain. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 3 Robert Boylestad Digital Electronics Removing DC effects of VCC and Capacitors Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 4 re Model Determine , re, and ro: and ro: look in the specification sheet for the transistor or test the transistor using a curve tracer. re: calculate re using dc analysis: re 25mV IE Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 5 Input Impedance: Impedance Calculations Zi RB || re Zi re Output Impedance: Zo R C || rO Zo Rc Robert Boylestad Digital Electronics RE 10re ro 10Rc [Formula 8.1] [Formula 8.2] [Formula 8.3] [Formula 8.4] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 6 Voltage Gain (Av): Gain Calculations Av Vo (R C ||ro) Vi re Av Current Gain (Ai): Ai RC re ro 10R C Io RBro Ii (ro RC)(RB re) Ai ro 10RC, RB 10re [Formula 8.5] [Formula 8.6] [Formula 8.7] [Formula 8.8] Current Gain from Voltage Gain: Ai Av Robert Boylestad Digital Electronics Zi RC [Formula 8.9] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 7 Phase Relationship The phase relationship between input and output is 180 degrees. The negative sign used in the voltage gain formulas indicates the inversion. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 8 Robert Boylestad Digital Electronics CE – Voltage-Divider Bias Configuration Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 9 re Model You still need to determine , re, and ro. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 10 Input Impedance: Impedance Calculations R R1 ||R2 R1R2 R1 R2 Zi R || re Output Impedance: Zo RC || ro Zo RC Robert Boylestad Digital Electronics [Formula 8.10] [Formula 8.11] ro 10RC [Formula 8.12] [Formula 8.13] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 11 Gain Calculations Voltage Gain (Av): Current Gain (Ai): Av Vo RC ||ro Vi re [Formula 8.14] Av Vo RC Vi re ro 10R C [Formula 8.15] Ai Io R ro Ii (ro RC)(R re) Ai Ai Io R Ii R re ro 10R C Io ro 10RC, R 10 re Ii [Formula 8.16] [Formula 8.17] [Formula 8.18] Current Gain from Voltage Gain: Ai Av Robert Boylestad Digital Electronics Zi RC [Formula 8.19] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 12 Phase Relationship A CE amplifier configuration will always have a phase relationship between input and output is 180 degrees. This is independent of the DC bias. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 13 CE Emitter-Bias Configuration Unbypassed RE Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 14 re Model Again you need to determine , re. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 15 Input Impedance: Impedance Calculations Zb re ( 1)RE Zb (re RE) Zb RE RE re Zi RB || Zb Output Impedance: Robert Boylestad Digital Electronics Zo RC [Formula 8.20] [Formula 8.21] [Formula 8.22] [Formula 8.23] [Formula 8.33] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Gain Calculations Slide 16 Voltage Gain (Av): or Av Vo RC Vi Zb [Formula 8.25] Av Vo RC Vi re RE Av Vo RC Vi RE Zb RE Current Gain (Ai): Ai Zb (r e RE) Io RB Ii RB Zb [Formula 8.26] [Formula 8.27] [Formula 8.28] Current Gain from Voltage Gain: Ai Av Robert Boylestad Digital Electronics Zi RC [Formula 8.29] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 17 Phase Relationship A CE amplifier configuration will always have a phase relationship between input and output is 180 degrees. This is independent of the DC bias. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 18 Bypassed RE CE Emitter-Bias Configuration This is the same circuit as the CE fixed-bias configuration and therefore can be solved using the same re model. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 19 Emitter-Follower Configuration You may recognize this as the Common-Collector configuration. Indeed they are the same circuit. Note the input is on the base and the output is from the emitter. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 20 re Model You still need to determine , re, and ro. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 21 Input Impedance: Impedance Calculations Zi RB || Zb Zb re ( 1)RE Zb (re RE) Zb RE Robert Boylestad Digital Electronics [Formula 8.37] [Formula 8.38] [Formula 8.39] [Formula 8.40] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 22 Impedance Calculations (cont’d) Output Impedance: Zo RE || re Zo re Robert Boylestad Digital Electronics RE re [Formula 8.42] [Formula 8.43] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Gain Calculations Slide 23 Voltage Gain (Av): Av Av Current Gain (Ai): Vo RE Vi RE re Vo 1 Vi Ai RB RB Zb [Formula 8.44] RE re, RE re RE [Formula 8.45] [Formula 8.46] Current Gain from Voltage Gain: Ai Av Robert Boylestad Digital Electronics Zi RE [Formula 8.47] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 24 Phase Relationship A CC amplifier or Emitter Follower configuration has no phase shift between input and output. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 25 Common-Base (CB) Configuration The input (Vi) is applied to the emitter and the output (Vo) is from the collector. The Common-Base is characterized as having low input impedance and high output impedance with a current gain less than 1 and a very high voltage gain. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 26 re Model You will need to determine and re. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 27 Input Impedance: Output Impedance: Robert Boylestad Digital Electronics Impedance Calculations Zi RE || re [Formula 8.54] Zo RC [Formula 8.55] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Gain Calculations Slide 28 Voltage Gain (Av): Av Vo RC RC Vi re re [Formula 8.56] Current Gain (Ai): Ai Robert Boylestad Digital Electronics Io 1 Ii [Formula 8.57] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 29 Phase Relationship A CB amplifier configuration has no phase shift between input and output. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 30 CE Collector Feedback Configuration This is a variation of the CE Fixed-Bias configuration. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 31 re Model You will need to determine and re. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 32 Input Impedance: Output Impedance: Robert Boylestad Digital Electronics Impedance Calculations Zi re 1 RC RF Zo RC || RF [Formula 8.58] [Formula 8.59] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 33 Gain Calculations Voltage Gain (Av): Av Vo RC Vi re [Formula 8.60] Ai Io RF Ii RF RC [Formula 8.61] Current Gain (Ai): Ai Robert Boylestad Digital Electronics Io RF Ii RC [Formula 8.62] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 34 Phase Relationship This is a CE amplifier configuration; therefore there is a 180-degree phase shift between input and output. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 35 Approximate Hybrid Equivalent Circuit The h-parameters can be derived from the re model: hie = re hfe = hoe = 1/ro hib = re hfb = - The h-parameters are also found in the specification sheet for the transistor. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 36 Robert Boylestad Digital Electronics CE Fixed-Bias Configuration Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 37 Hybrid Equivalent Circuit Zi RB || hie Impedances: Gain: Robert Boylestad Digital Electronics Zo RC || 1 hoe hfe(RC || 1 ) Vo hoe Av Vi hie Io Ai hfe Ii [Formula 8.83] [Formula 8.84] [Formula 8.85] [Formula 8.86] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 38 Robert Boylestad Digital Electronics CE Voltage-Divider Configuration Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 39 Impedances: Gain: Hybrid Equivalent Circuit Zi R || hie [Formula 8.87] Zo RC [Formula 8.88] Av hfe(R C || 1 Ai Robert Boylestad Digital Electronics hoe ) hie hfeR R hie [Formula 8.89] [Formula 8.90] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 40 Robert Boylestad Digital Electronics CE Unbypassed Emitter-Bias Configuration Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 41 Impedances: Hybrid Equivalent Circuit Zb hfeRE Zi RB || Zb Zo RC Gain: Av Ai RC RE hfeRB RB Zb [Formula 8.91] [Formula 8.92] [Formula 8.93] [Formula 8.94] [Formula 8.95] [Formula 8.96] Ai Av Robert Boylestad Digital Electronics Zi RC Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 42 Robert Boylestad Digital Electronics CC or Emitter-Follower Configuration Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 43 Impedances: Gain: Hybrid Equivalent Circuit Zb hfeRE [Formula 8.97] Zi RB || Zb [Formula 8.98] hie Zo RE || hfe [Formula 8.99] Av Vo RE Vi RE hie Ai hfe hfeRB RB Zb [Formula 8.101] Zi RE [Formula 8.102] Ai Av Robert Boylestad Digital Electronics [Formula 8.100] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 44 Robert Boylestad Digital Electronics CB Configuration Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 45 Impedances: Gain: Robert Boylestad Digital Electronics Hybrid Equivalent Circuit Zi RE || hib Zo RC Av Vo hfbRC Vi hib Ai Io hfb 1 Ii [Formula 8.103] [Formula 8.104] [Formula 8.105] [Formula 8.106] Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 46a Robert Boylestad Digital Electronics Summary Table Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 46b Robert Boylestad Digital Electronics Summary Table Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 47 Troubleshooting 1. Check the DC bias voltages – if not correct check power supply, resistors, transistor. Also check to ensure that the coupling capacitor between amplifier stages is OK. 2. Check the AC voltages – if not correct check transistor, capacitors and the loading effect of the next stage. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Practical Applications Slide 48 • Audio Mixer • Preamplifier • Random-Noise Generator • Sound Modulated Light Source Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.