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Unit II BJT Amplifiers Outline • • • • • • • Small signal analysis of common Emitter Small signal analysis of common Base Small signal analysis of common Collector Differential Amplifiers-CMRR Darlington Amplifier Bootstrap Technique cascaded Stages,Cascode stage Linear analog amplifier Notation Basic characteristics of an amplifier Basic BJT amplifier Analysis of BJT amplifiers Dc analysis and equivalent circuit Ac analysis and equivalent circuit BJT Small-Signal Models • h-parameter model – More complex – Better for ac operation – Common Emitter model • hie = input impedance (Ω) • hre = reverse voltage transfer ratio (unitless) • hfe = forward current transfer ratio (unitless) • hoe = output admittance (S) ib iC B hie hfeib hreVce ie E 1/hoe Calculating Av, zin, zout, and Ai of a Transistor Amplifier • Voltage Gain, Av – Output voltage divided by input voltage • Input Impedance, zin – Input voltage divided by input current vout Av vin vin zin iin Calculating Av, zin, zout, and Ai of a Transistor Amplifier vout(OC) • Output Impedance, zout z out • Current Gain, Ai iout Ai iin • Power Gain, Ap iout(SC) Pout Ap Pin 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 Simplified General h-Parameter Model hi = input resistance hf = forward transfer current ratio (Io/Ii) Common-Emitter • General BJT circuit analysis – Find operating point – Determine ac parameters (T- or h- models) – Remove dc Voltage sources & replace with short circuits – Replace coupling & bypass capacitors with short circuits – Replace BJT with circuit model – Solve resulting circuit Common-Emitter Amplifier • ac equivalent of fixed-bias CE amplifier using hparameter model Common-Emitter Amplifier-contd… • Equations for h-parameter model for fixed-bias CE amplifier – Circuit voltage gain a function of • Model forward current transfer ratio, hfe • Model input impedance, hie • Circuit collector resistance, RC • Circuit load resistance, RL Av hfe RC RL hie Common-Emitter Amplifier-contd… • Circuit current gain a function of – Same parameters, plus Fixed bias resistance, RB hfe RB RC Ai RC RL RB hie Common-Emitter Amplifier-contd… • Equations for h-parameter model for fixed-bias CE amplifier – Circuit input impedance a function of • Model forward current transfer ratio, hfe • Model input impedance, hie zin RB hie Common-Emitter Amplifier-contd… • Circuit output impedance a function of – Collector resistance (model output admittance), hoe very low zout RC 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 Fixed-Bias-contd… Input impedance: Zi RB || hie Output impedance: Zo RC || 1/ hoe Voltage gain: Av Vo h R || 1/ ho e fe C Vi hie Current gain: Ai Io hfe Ii Emitter-Follower Configuration Input impedance: Zb hfeRE 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 Ai Current gain: h fe RB RB Z b Ai Av Zi RE Common Base Configuration 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 Hybrid pi 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. Small-signal hybrid-π equivalent circuit Small-signal hybrid-π equivalent circuit (Cont’d) Small-signal voltage gain Input and output resistances Common-emitter amplifiers (with voltagedivider biasing & coupling capacitor) Common-emitter amplifiers (with voltagedivider biasing & coupling capacitor)Cont’d Common-emitter amplifiers (with voltagedivider biasing & coupling capacitor & emitter resistor) Dc & Ac load lines • Dc load line is used to find Q-point • Ac load line is used to determine graphically the operation of a BJT amplifier • Dc and ac load lines are essentially different since capacitors appear as an open circuit for a de operation but a short circuit for an ac operation Ac load line 35 Maximum output symmetrical swing 36 Common-Collector Amplifier • Circuit gains and impedances – Av ≈ 1 – zin = RB||zin(Q) – A z close to hfe Ai V in RL RS || RB zout (Q ) re h fe 1 – very small 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 The re Transistor Model BJTs are basically current-controlled devices. 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. Common-Emitter Configuration-re model The diode re model can be replaced by the resistor re. Ie 1 Ib Ib re 26 mV Ie Input and Output Impedances An equivalent small signal circuit of a differential amplifier can be drawn as Input Impedance During the small signal analysis, it was shown that: vB1 vB 2 But, 2iC1 2iC 2 1 iC1 iC 2 gm gm gm iCx iBx vB1 vB 2 2 iB1 gm vB1 vB 2 2 rin iB1 gm Output Impedance Set vIN 0 iC 0 Applying Kirchoff’s current law: iC iRC iOUT 0 iOUT iRC By Ohm’s law: vC vOUT VC 15 I RC RC RC iRC iRC rOUT vOUT vOUT RC RC iOUT iRC Coupling and Biasing • Input and output coupling capacitors may be required to remove d.c. bias voltages • If input coupling capacitors are used, a d.c. bias current path to the transistors’ bases must be established • Extra base resistors accomplish this • These will appear in parallel with the input impedance Non-Ideal D.C. Effects • If operation down to d.c is required, the coupling components are omitted • This leads to some effects that are peculiar to d.c. operation: – Offset Voltage – Bias Current Offset Voltage • With zero differential input, the collector currents and, therefore, the collector voltages should be identical • This assumes that: – The transistors are identical – The loads are also identical • In practice, loads will vary and the quiescent conditions will not be perfectly symmetrical • There will be an offset voltage between the actual output and the ideal assumption Bias Current • In order to bring the transistors into the active region, a small d.c. base bias current is required I Bx I Cx / • This d.c. current must be supplied by the signal source • This is a separate issue to the current drawn by the input impedance • Note that bias current and offset voltage effects are identical to those observed with op-amps Differential Amplifier-Common mode Differential Amplifier-Differential mode Differential Amplifier-Transfer Characteristics Differential Amplifier-Emitter Resistor Differential Amplifier-one half Equivalent Circuit Differential Amplifier –active loaded Differential Amplifier –active loaded small signal equivalent Applications • Differential inputs and outputs – Useful when negative feedback is required in a multi-stage amplifier – Also useful for balanced signals Noisy Channel Transmitter Noisy received signals Difference Amp Output Bootsrap Technique • The field of electronic a bootstrap circuit is one where part of the output of an amplifier stage is applied to the input, so as to alter the input impedance of the amplifier. • When applied deliberately, the intention is usually to increase rather than decrease the impedance. Bootsrap Technique • The effect of a high input impedance is to reduce the input current to the amplifier. • If the input current for a given input voltage is reduced by whatever method, the effect is to increase the input impedance. • The emitter follower has a high input impedance, but this may be reduced to an unacceptable level by the presence of the base bias resistor. Boosted Output Impedances Rout1 1 g m RE || r rO RE || r Rout 2 1 g m RS rO RS Darlington Amplifier • One emitter follower (Tr1) to drive another (Tr2) the overall current gain becomes the product of the individual gains, hfe1 x hfe2 and can be typically 1000 or more. • This greatly reduces the signal current required by the base of Tr1 and thereby dramatically increases the input impedance. Darlington Amplifier(cont) 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. DC Bias of Darlington Circuits Base current: IB VCC VBE RB D RE Emitter current: IE (D 1)IB DIB Emitter voltage: VE IE RE Base voltage: VB VE VBE 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. 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 Cascaded Systems CE-CC • The cascade of a Common Emitter amplifier stage followed by a Common Collector amplifier stage can provide a good overall voltage amplifier Cascaded Systems CE-CC • The Common Emitter input resistance is relatively high and Common Collector output resistance is relatively low. • The voltage follower second stage, Q2, contributes no increase in voltage gain but provides a near voltage-source (low resistance) output so that the gain is nearly independent of load resistance. Cascaded Systems CE-CC • The high input resistance of the Common Emitter stage, Q1, makes the input voltage nearly independent of input-source resistance. • Multiple Common Emitter stages can be cascaded with emitter follower stages inserted between them to reduce the attenuation due to inter-stage loading. Cascaded Systems CE-CE •Each stage is separately biased and coupled to adjacent stages via DC blocking capacitors. •Inserting coupling capacitors between stages blocks the DC operating bias level of one stage from affecting the DC operating point of the next. Cascaded Systems 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 Output impedance, second stage: Zo RC Bipolar Cascode Stage Rout [1 g m (rO 2 || r 1 )]rO1 rO 2 || r 1 Rout g m1rO1 rO 2 || r 1 Maximum Bipolar Cascode Output Impedance Rout , max g m1rO1r 1 Rout , max 1rO1 • The maximum output impedance of a bipolar cascode is bounded by the ever-present r between emitter and ground of Q1. Example: Output Impedance RoutA 2rO 2 r 1 r 1 rO 2 • Typically r is smaller than rO, so in general it is impossible to double the output impedance by degenerating Q2 with a resistor. PNP Cascode Stage Rout [1 g m (rO 2 || r 1 )]rO1 rO 2 || r 1 Rout g m1rO1 rO 2 || r 1 Improved Cascode Stage Rout g m3 rO3 (rO 4 || r 3 ) || g m2 rO 2 (rO1 || r 2 ) • In order to preserve the high output impedance, a cascode PNP current source is used. 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. MOS Cascode Stage Rout 1 g m1rO 2 rO1 rO 2 Rout g m1rO1rO 2 Improved MOS Cascode Amplifier Ron g m 2 rO 2 rO1 Rop g m3 rO 3 rO 4 Rout Ron || Rop • Similar to its bipolar counterpart, the output impedance of a MOS cascode amplifier can be improved by using a PMOS cascode current source.