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# USA ECE 334 - Chapter 6 Small-Signal Modeling and Linear Amplificati

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1Chapter 6Small-Signal Modeling and Linear Amplificationpp.218TYU 4.3pp.2224.25D2D4.65Introduction to Amplifiers• BJT is an excellent amplifier when biased in forward-active region• In these regions, transistors can provide high voltage, current and power gains.• Bias is provided to stabilize the operating point in desired operation region.• Q-point also determines– Small-signal parameters of transistor– Voltage gain, input resistance, output resistance– Maximum input and output signal amplitudes–Power consumptionLinear Amplifier● To create a linear amplifier♦ Bias the transistor in the forward-active mode♦ Establish Q-point near the center of the load line♦ Connect the AC-signal to the transistor base♦ AC-signal should be small enough to ensure linearity and to avoid cut-off and saturation modes● The output signal is proportional to the input signal3Linear Amplifier Operation Analysis● Two types of analysis♦ DC analysis – large signal analysis (Chapter 5), AC source is set to zero♦ AC analysis – small signal analysis, DC sources are set to zero● Total response of the amplifier is the sum of the AC and the DC responses (superposition theorem) AC Equivalent Circuit for Common EmitterSet DC to zeroNotice: lower case letters for AC voltages and currentsTransistor Inverter Voltage Transfer CharacteristicsBase Current verses Base-emitter Voltage C/Cs● The AC input voltage produce AC base current around the Q-point● The AC base current produces AC base-emitter voltage● If the AC base current is small in amplitude, the base-emitter voltage will be sinusoidal● If AC base current has a big amplitude, the base-emitter voltage will be distorted (non-sinusoidal4Graphic Analysis of Amplifier CircuitsBJT is biased in active region by dc voltage source VBE. Q-point is set at (IC, VCE)=(1.5 mA, 5 V) with IB = 15 µA.Total base-emitter voltage is: bevBEVBEv+=Collector-emitter voltage is: This gives the load lineCRCiCEv−=10BJT Amplifier (contd.)8 mV peak change in vBEgives 5 µAchange in iBand 0.5 mA change in iC0.5 mA change in iCgives 1.65 Vchange in vCE(output voltage in common emitter circuit)If changes in operating currents and voltages are small enough, then ICand VCEwaveforms are undistorted replicas of input signal.Small voltage change at base causes large voltage change at collector. Voltage gain is given by:Minus sign indicates 1800phase shift between input and output signals.20618020600080180651−=∠=∠∠==..vAbevcevCoupling and Bypass Capacitors• AC coupling through capacitors is used to inject ac input signal and extract output signal without disturbing Q-point• Capacitors provide negligible impedance at frequencies of interest and provide open circuits for dc current.C1and C3are large coupling capacitors or dc blocking capacitors, their reactance at signal frequency is negligible.C2is bypass capacitor, provides low impedance path for ac current from emitter to ground, removing RE(required for good Q-point stability) from circuit when ac signals are considered. R1RCR2RE1.5 k1.5 kC3R3VO+-100 kC2C14.3 k30 kVCC= 12 VRIVI1 kDC Equivalent for BJT AmplifierAll capacitors in original amplifier circuits are replaced by open circuits, disconnecting vI, RI, and R3from circuit.5AC Equivalent for BJT AmplifierTo find the ac equivalent circuit, replace all capacitors by a short circuitΩΩΩΩk//k.R//RRk//kR//RRCB100343010321====Hybrid-π Model of AmplifierHybrid parameter: diffusion resistance/input impedanceThe diffusion resistance rπis define as the reciprocalof theiB-vBEcurve, which can be find as:The resistance rπis called the diffusion resistance or base-emitter input resistance. Note that rπis a function of the Q-point parametersCQTFBQTbbeTBQptQTBEFSTptQTBEFSBEptQBEBIVIVrivThenVIVvexpIVrorVvexpIvvirβββπππ====+=+∂∂=∂∂=−−−11111Output terminal characteristics of the bipolar transistor: transconductance• If we assume constant collector-emitter voltage then:mTCQptQTBESTptQBECTBEScbeptQBECcgVIVvexpIVviThenVvexpIiv.vii===∂∂=∂∂=−==αα1 and The term ICQ/VTis a conductance. Since this conductance relates the collector current to the voltage in the B-E circuit, this parameter is called a transconducatance6• By using the two hybrid parameters (rπ, gm), we can develop a simplified small signal hybrid-π- equivalent circuit for the npn transistor.•Voltage -controlled current source gmvbecan be transformed into current-controlled current source,Small-Signal Equivalent Circuit Using Common-Emitter Current Gainββππ===rgIVrVIgmCQTTCQmSmall-Signal Equivalent Circuit for npn Common Emitter circuitCmceoR)Vg(VVπ−==)Rrr)(Rg(VVABCmsov+−==ππsBV.RrrV+=πππVoltage gain Av:DC and AC Analysis• DC analysis: (Refer to Table 6.2)– Find dc equivalent circuit by replacing all capacitors by open circuits and inductors by short circuits.– Find Q-point from dc equivalent circuit by using appropriate large-signal transistor model.• AC analysis: (Refer to Table 6.2)– Find ac equivalent circuit by replacing all capacitors by short circuits, inductors by open circuits, dc voltage sources by ground connections and dc current sources by open circuits.– Replace transistor by small-signal model to analyze ac characteristics of amplifier– Combine end results of dc and ac analysis to yield total voltages and currents in the network.7Hybrid π Model for npn with Early Effect8If we include the early effect then collector current in terms of early voltage as:+=ACETBESCVvVvexpIi 1αHybrid π Model for npn with Early EffectThe output resistance is defined aswhere VAis the Early voltageCQAOACQptQATBESptQCECOIVrorVIV.VvexpIvir=≅=∂∂=−−11αwhere rOis the small signal transistor output resistanceHybrid π Model for npn with Early EffectCQAoIVr =Summary of hybrid-π-model parametersDiffusion resistancetransconductanceCurrent gainOutput resistance• The hybrid-π-equivalent circuit model can be completed by adding two additional resistance, rband rµ.9ExampleFor the circuit in Fig. let β= 150, VCC= 7.5 V, VA= 200 V, VBE(on) = 0.7 V, RB= 100 kΩ, and RC= 15 kΩ, VBB= 0.92 V. Determine (a) the small signal hybrid π parameter rπ,

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