BJT Small-Signal Analysis

ContentsCommon-Emitter fixed-bias configurationVoltage divider biasCE Emitter biasEmitter-follower configurationCommon-base configurationCollector-feedback configurationHybrid equivalent circuit and model

re transistor model employs a diode and controlled current source to duplicate the behavior of a transistor in the region of interest.The re and hybrid models will be used to analyze small-signal AC analysis of standard transistor network configurations.Ex: Common-base, common-emitter and common-collector configurations.The network analyzed represent the majority of those appearing in practice today.BJT Small Signal Analysis

AC equivalent of a network is obtained by:Setting all DC sources to zero Replacing all capacitors by s/c equiv.Redraw the network in more convenient and logical form

Common-Emitter (CE) Fixed-Bias ConfigurationThe 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.

Removing DC effects of VCC and CapacitorsCommon-Emitter (CE) Fixed-Bias Configuration

re ModelDetermine , 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: Common-Emitter (CE) Fixed-Bias Configuration

Impedance CalculationsInput Impedance:Output Impedance:

Common-Emitter (CE) Fixed-Bias Configuration

Gain CalculationsVoltage Gain (Av):

Current Gain (Ai):

Current Gain from Voltage Gain:

Common-Emitter (CE) Fixed-Bias Configuration

Voltage GainCommon-Emitter (CE) Fixed-Bias Configuration

Current gainCommon-Emitter (CE) Fixed-Bias Configuration

Phase RelationshipThe phase relationship between input and output is 180 degrees. The negative sign used in the voltage gain formulas indicates the inversion.Common-Emitter (CE) Fixed-Bias Configuration

CE Voltage-Divider Bias Configuration

re ModelYou still need to determine , re, and ro.CE Voltage-Divider Bias Configuration

Impedance CalculationsInput Impedance:Output Impedance:

CE Voltage-Divider Bias Configuration

Gain CalculationsVoltage Gain (Av):

Current Gain (Ai):

Current Gain from Voltage Gain:

CE Voltage-Divider Bias Configuration

Voltage GainCE Voltage-Divider Bias Configuration

Current gainCE Voltage-Divider Bias Configuration

CE Voltage-Divider Bias Configuration

Phase RelationshipA CE amplifier configuration will always have a phase relationship between input and output is 180 degrees. This is independent of the DC bias.CE Voltage-Divider Bias Configuration

CE Emitter-Bias ConfigurationUnbypassed RE

re ModelAgain you need to determine , re.CE Emitter-Bias Configuration

Impedance CalculationsInput Impedance:Output Impedance:CE Emitter-Bias Configuration

Defining the input impedance of a transistor with an unbypassed emitter resistorCE Emitter-Bias Configuration

Voltage Gain (Av):

Current Gain (Ai):

Current Gain from Voltage Gain:

Gain CalculationsorCE Emitter-Bias Configuration

Voltage GainCE Emitter-Bias Configuration

Current GainCE Emitter-Bias Configuration

Phase RelationshipA CE amplifier configuration will always have a phase relationship between input and output is 180 degrees. This is independent of the DC bias.CE Emitter-Bias Configuration

Bypassed RE

This is the same circuit as the CE fixed-bias configuration and therefore can be solved using the same re model.CE Emitter-Bias Configuration

Emitter-Follower ConfigurationYou 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.

re ModelYou still need to determine and re.Emitter-Follower Configuration

Impedance CalculationsInput Impedance:Emitter-Follower Configuration

Calculation for the current IeEmitter-Follower Configuration

Impedance Calculations (contd)Output Impedance:

Emitter-Follower Configuration

Gain CalculationsVoltage Gain (Av):

Current Gain (Ai):

Current Gain from Voltage Gain:

Emitter-Follower Configuration

Voltage gainEmitter-Follower Configuration

Current GainEmitter-Follower Configuration

Phase RelationshipA CC amplifier or Emitter Follower configuration has no phase shift between input and output.Emitter-Follower Configuration

Common-Base (CB) ConfigurationThe 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.

re ModelYou will need to determine and re.Common-Base (CB) Configuration

Impedance CalculationsInput Impedance:Output Impedance:Common-Base (CB) Configuration

Gain CalculationsVoltage Gain (Av):

Current Gain (Ai):

Common-Base (CB) Configuration

Voltage & Current gainCommon-Base (CB) Configuration

Phase RelationshipA CB amplifier configuration has no phase shift between input and output.Common-Base (CB) Configuration

Collector DC Feedback ConfigurationThe network has a dc feedback resistor for increased stability, yet the capacitor C3 willshift portions of the feedback resistance to the input and output sections of the networkin the ac domain. The portion of RF shifted to the input or output side will be determinedby the desired ac input and output resistance levels.

Substituting the re equivalent circuit into the ac equivalent networkCollector DC Feedback ConfigurationImpedance CalculationsInput Impedance:Output Impedance:

Voltage GainCollector DC Feedback Configuration

Current GainCollector DC Feedback Configuration

Approximate Hybrid Equivalent CircuitThe h-parameters can be derived from the re model:

hie = re hib = rehfe = hfb = -hoe = 1/ro

The h-parameters are also found in the specification sheet for the transistor.

Hybrid equivalent model re equivalent modelApproximate Common-Emitter Equivalent Circuit

Hybrid equivalent model re equivalent modelApproximate Common-Base Equivalent Circuit

Troubleshooting1. 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.

Practical Applications Audio MixerPreamplifier Random-Noise Generator Sound Modulated Light Source

Assignment #1Derive the formulas for Zi, Zo, AV and Ai in a CE Emitter-Bias Configuration with unbypassed RE and Emitter Follower Configulation with the effect of ro. Show your equivalent circuit and complete derivations. You can use approximations to simply your answers. Derive and solve for the value of Zi, Zo, AV and Ai.

3. Determine Zi, Zo, AV and Ai.

Vo = -(Bib)(Rc||ro)Vi = IbBre*Vcc=12 ; Rc = 3k Rb = 470k; B = 100Ro=50k

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