Small Signal ModelPNP Transistor

Section 4.1-4.4,4.6

Schedule

9 2/11 Tuesday Physics of a BJT 4.1-4.3

L 2/11 Tuesday Measure Beta of a transistor  

10 2/13 Thursday

PNP 4.5

11 2/18 Tuesday BJT in saturation mode 4.5

L 2/18 Tuesday BJT in saturation/BJT implementation of an NAND gate

 

12 2/20 Thursday

Small Signal model [homework: small eq. circuit, (PNP)]

4.4,4.6

Overview

Review

Small Signal Model

Section 4.4

Schematic of an Audio Amplifier

Microphone produces a small signal.

How does the amplifier circuit respond to a small change in the input signal?How is the analysis performed? Small signal model

Small Signal Analysis (For a Circuit You have not Seen Before)

1. Replace each ideal DC voltage source with a small signal ground.

2. Replace each ideal DC current source with an open circuit.

3. Replace each transistor by its small signal model4. Analyze the small signal equivalent circuit.

Small Signal Analysis (For a Circuit You have not Seen Before)

1. Analyze the Circuit by Inspection

Voltage Source

DC Voltage Source in Small Signal Analysis

RS should be 0 for a good battery!

Current SourceRS should be infinity for a good battery!

Small Signal Model

(NPN) (PNP)

Statements that are always true for both NPN and PNP.1.rπ is between B and E. 2.the direction of the dependent current source always pointsfrom the collector to emitter.3. ro is always between B and C.

Question

Replace Q1 and Q2 by their small equivalent circuit.

Answer

Question

Answer

Derivation of the Small Signal Model

Change in the Collector Current Due to a Small Change in Base-Emitter

Voltage

If a signal changes the base-emitter voltage by a small amount, how much change is produced in the collector current?

Derivation of Transconductance

If a signal changes the base-emitter voltage by a small amount, how much change is produced in the collector current?

Small signal modelof Q1

But there is something else….

A change in VBE creates a change in base current!

Small signal model

Example 4.10

Signal Generated By a microphone

Small Signal Equivalent CircuitVBE=800 mVβ=100IS,Q1=3 x 10-16 A Question: If a microphone generates a 1 mV signal,

how much change is observed in the collector and base current?

A Simple Amplifier

Determine the output signal level if the microphone produces a 1 mV signal.

AC Ground

• The voltage produced by a voltage source is constant.

• The small signal model is concerned only with changes in quantities.

• Therefore, a DC voltage source must be replaced with a ground in small signal analysis.

Example

Small Signal Model

Summary

Output Resistance Due to Early Effect

A larger reverse bias voltage leads to a larger BC depletion region.

The effective base width (WB) is reduced.The slope of the electron profile increases.IC increases as VCE is increased.

Early Effect

James M. Early

Modeling of Early Effect

What Doesn’t Change with Early Effect?

Modification of the Small Signal Model

Slides to Cover During the Lab

A Simple Cadence Example

Assumption

Assume that1.The DC at Vout is 0.9 V2.gm=1 mS

Gain is approximately equal to –gmRC.Bias current is IC=gmVt

R=(1.8V-0.9V)/26uA=34.6 KohmsGain is -34.6.

DC Bias of the Amplifier

Sweep the Base Voltage to Get the IC=26 uA

Display the Transconductance

Display Transconductance

Verify Transconductance (1)

Verify Transconductance (2)

Transconductance

VB IC

562.5 mV 25.64 uA

563.5 mV 26.64 uA

∆VBE 1 mV

∆IC 1 uA

gm=∆VBE/∆IC 1 mS

Introduce a Small Signal

Calculate Peak to Peak Voltage

Peak to Peak Voltage=67.78 mV

67.78 mV/2=33.9