Chapter 3 small signal midfrequency BJT

CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.40 CHAPTER 3: SMALL-SIGNAL MIDFREQUENCY BJT Table of Contents 3.1. INTRODUCTION 42 3.2. HYBRID-PARAMETER MODELS 43 3.2.1. Common-Emitter Transistor Connection 43 3.2.2. Common-Base Transistor Connection 45 3.2.3. Common-Collector Amplifier 46 3.3. MEASURES OF AMPLIFIER CHARACTERISTIC 48 3.3.1. CE amplifier analysis 49 3.3.2. CB amplifier analysis 51 3.3.3. CC amplifier analysis 54 Table of Figures Fig. 3-1 Common-emitter characteristics (npn, Si device) 43 Fig. 3-2 CE small-signal equivalent circuit 44 Fig. 3-4 CB small-signal equivalent circuit 46 Fig. 3-5 CC small-signal equivalent circuit 47 Fig. 3-6 Amplifier circuit 48 Fig. 3-7 CE amplifier 49 CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.41 Fig. 3-8 CB amplifier 52 Fig. 3-9 CC amplifier 54 CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.42 CHAPTER 3: SMALL-SIGNAL MIDFREQUENCY BJT 3.1. INTRODUCTION For sufficiently small emitter-collector voltage and current excursions about the quiescent point (small signals), the BJT is considered linear; it may then be replaced with small-signal equivalent- circuit models. There is a range of signal frequencies which are large enough so that coupling or bypass capacitors can be considered short circuits, yet low enough so that inherent capacitive reactances associated with BJTs can be considered open circuits. In this chapter, all BJT voltage and current signals are assumed to be in this midfrequency range. In practice, the design of small-signal amplifiers is divided into two parts: (1) setting the dc bias or Q point. (2) determining voltage- or current-gain ratios and impedance values at signal frequencies. CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.43 3.2. HYBRID-PARAMETER MODELS 3.2.1. Common-Emitter Transistor Connection Fig. 3-1 Common-emitter characteristics (npn, Si device)            1 2 , , BE B CE C B CE v f i v i f i v If the total emitter-to-base voltage BE v goes through only small excursions (ac signals) about the Q point, then     , BE be C c v v i i , and so on. Therefore, CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.44          BE BE be BE BE b ce B CE Q Q v v v v dv i v i v          C C c C C b ce B CE Q Q i i i i di i v i v The four partial derivatives, evaluated at the Q point, are called CE hybrid parameters and are denoted as follows: Input resistance:       BE BE ie B B Q Q v v h i i Reverse voltage ratio:       BE BE re CE CE Q Q v v h v v Forward current gain:       C C fe B B Q Q i i h i i Output admittance:       C C oe CE B Q Q i i h v i Therefore:          be ie b re ce c fe b oe ce v h i h v i h i h v The equivalent circuit is shown : Fig. 3-2 CE small-signal equivalent circuit CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.45 The circuit is valid for use with signals whose excursion about the Q point is sufficiently small so that the h parameters may be treated as constants. 3.2.2. Common-Base Transistor Connection Fig. 3-3 Common-base characteristics (pnp, Si device) In the CB case, equations can be found specifically for small excursions about the Q point. The results are:          eb ib e rb cb c fb e ob cb v h i h v i h i h v The definitions of the CB h-parameters are: CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.46 Input resistance:       EB EB ib E E Q Q v v h i i Reverse voltage ratio:       EB EB rb CB CB Q Q v v h v v Forward current gain:       C C fb E E Q Q i i h i i Output admittance:       C C ob CB CB Q Q i i h v v The equivalent circuit is as follow: Fig. 3-4 CB small-signal equivalent circuit 3.2.3. Common-Collector Amplifier The common-collector (CC) or emitter-follower (EF) amplifier, can be modeled for small-signal ac analysis by replacing the CE-connected transistor with its h-parameter model. Assuming, for simplicity, that   0 re oe h h , we obtain the equivalent circuit: CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.47 Fig. 3-5 CC small-signal equivalent circuit An even simler model can be obtained by finding a Thevenin equivalent for the circuit to the right of a, a. Application of KVL around the outer loop gives:   1 b ie e E b ie fe b E v i h i R i h h i R      The Thevenin impedance is the driving-point impedance:       1 Th ie fe E b v R h h R i The Thevenin voltage is zero (computed with terminals a, a open); thus, the equivalent circuit consists only of Th R . CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.48 3.3. MEASURES OF AMPLIFIER CHARACTERISTIC Fig. 3-6 Amplifier circuit 1. Current amplification, measured by the current-gain ratio: o i in i A i  2. Voltage amplification, measured by the current-gain ratio: o v in v A v  3. Power amplification, measured by the ratio: o o p v i in in v i A A A v i   4. Phase shift of signals, measured by the phase angle of the frequency-domain ratio   v A j  or   i A j  . 5. Impedance input, measured by the input impedance in Z (the driving-point impedance looking into the input port). 6. Power transfer ability, measured by the output impedance o Z (the driving-point impedance looking into the output port with the load removed). If o L Z Z  , the maximum power transfer occurs. CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.49 3.3.1. CE amplifier analysis Fig. 3-7 CE amplifier In the CE amplifier, find expressions for : (a) Current-gain ratio i A (b) Voltage-gain ratio v A (c) Input impedance in Z (d) Output impedance o Z Solution (a) By the current division at node C,   1/ 1/ oe L fe b oe L h i h i h R    And : 1 fe L i b oe L h i A i h R     Note that i fe A h   , where the minus sign indicates a 0 180 phase shift between input and output currents. (b) By KVL around B, E mesh, [...]... current gain 2 Large voltage gain  3 Large power gain AAv i  4 Current and voltage phase shifts of 1800 5 Moderate input impedance 6 Moderate output impedance 3. 3.2 CB amplifier analysis A simplified (bias network omitted) CB amplifier is shown, and the associated small- signal equivalent circuit: Val de Loire Program p.51 CHAPTER 3: Small- Signal Midfrequency BJT Fig 3- 8 CB amplifier In the CB amplifier,... voltage gain 3 Power gain approximately equal to voltage gain 4 No phase shift for current or voltage 5 Small input impedance 6 Large output impedance 3. 3 .3 CC amplifier analysis Fig 3- 9 CC amplifier In the CC amplifier, find expressions for Val de Loire Program p.54 CHAPTER 3: Small- Signal Midfrequency BJT (a) Current-gain ratio Ai (b) Voltage-gain ratio Av (c) Input impedance Zin (d) Output impedance... With typical CB amplifier values: hib  30  , hrb  4  10 6 , h fb   0.99 , hob  8  107 S , RL  2 0k  We have: Ai  0.974 , Av  647.9 , Z in  30 .08  , Zo  1.07 M  The characteristic of the CB amplifier can be summarized as follows: Val de Loire Program p. 53 CHAPTER 3: Small- Signal Midfrequency BJT 1 Current gain of less than 1 2 High voltage gain 3 Power gain approximately equal to voltage... hoc p.55 CHAPTER 3: Small- Signal Midfrequency BJT (d) Zo  1 hoc  h fchrc / hic Note that Zo   hic h fc With typical CC amplifier values: hic  1 k  , hrc  1 , h fc   101 , hoc  12 S , RL  2 k  We have: Ai  98.6 , Av  0.995 , Z in  8.41 M  , Zo  9.9  The characteristics of the CB amplifier can be summarized as follows: 1 High current gain 2 Voltage gain of approximately unity 3 Power... requires that ib   hre v hie dp However, at node C (with, now ic  idp ), KCL yields ic  idp  h feib  hoevdp Then Zo  vdp idp  1 hoe  h fehre / hie Val de Loire Program p.50 CHAPTER 3: Small- Signal Midfrequency BJT The output impedance is increased by feedback due to the presence of the controlled source hrevce With typical CE amplifier values: hie  1 k  , hre  104 , h fe  100 , hoe .. .CHAPTER 3: Small- Signal Midfrequency BJT vs  vbe  hieib  hrevce Ohm’s law applied to the output network requires that  1  h R i vce   h feib  || RL   fe L b h  1h R  oe  oe L Av  h feRL vbe  vs hie ... amplifier, find expression for (a) Current-gain ratio Ai (b) Voltage-gain ratio Av (c) Input impedance Zin (d) Output impedance Zo Solution (a) Ai   h fb 1  hobRL Val de Loire Program p.52 CHAPTER 3: Small- Signal Midfrequency BJT Note that Ai   h fb  1 , and the input and output currents are in phase because h fb  0 (b) Av   h fbRL  hib  RL hibhob  h fbhrb  Observe that Av   h fbRL / hib , and... amplifier can be summarized as follows: 1 High current gain 2 Voltage gain of approximately unity 3 Power gain approximately equal to current gain 4 No current or voltage phase shift 5 Large input impedance 6 Small output impedance Val de Loire Program p.56 . CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.40 CHAPTER 3: SMALL-SIGNAL MIDFREQUENCY BJT Table of Contents 3. 1. INTRODUCTION 42 3. 2. HYBRID-PARAMETER MODELS 43 3. 2.1 amplifier 52 Fig. 3- 9 CC amplifier 54 CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.42 CHAPTER 3: SMALL-SIGNAL MIDFREQUENCY BJT 3. 1. INTRODUCTION. Fig. 3- 5 CC small-signal equivalent circuit 47 Fig. 3- 6 Amplifier circuit 48 Fig. 3- 7 CE amplifier 49 CHAPTER 3: Small-Signal Midfrequency BJT Val de Loire Program p.41 Fig. 3- 8 CB