Announcements

• Assignment 2 due now

• Assignment 3 posted, due Thursday Oct 6th

• First mid-term Thursday October 27th

Lecture 9 Overview

• Transistors

Transistors

• Semiconductor device

• First Active circuit element - gain > 1

• Discuss the Bipolar Junction Transistor only

• See Simpson Chapter 5 for more detail.

Bipolar Junction Transistors

• NPN Bipolar Junction transistor shown (PNP also possible)

• 3 terminals: Emitter, Base, Collector

• Contains 2 p-n junctions: emitter-base junction, collector-base junction

• Can be thought of as two back-to-back diodes, but operating characteristics are very different

• Base region (P-type here) must be thin for transistor action to work

Base

Emitter

Collector

Modes of operation

• Use 2 voltage supplies to bias the two junctions (forward or reverse)• 3 basic modes: cutoff, active and saturation, correspond to three different bias conditions.

Base

Emitter

Collector

“OFF”

“ON”

Active Mode• Collector-Base junction is reverse biased• Emitter-Base junction is forward biased• iC=βiB (β=100 - 500) Active circuit element - gain > 1 !!• How does collector current flow when collector-base junction is reverse biased?

Emitter

CollectorBase

+

-

iC

iB

iE

VCE

VBE

Active Mode

• What's happening?• Emitter-base is forward biased; collector-base reverse biased.• Forward bias of emitter injects electrons into thin base region• Majority shoot through the base into the collector region where they encounter the voltage source on the collector and produce a current.• Electrons combine with holes in the base region and form negative ions which impede the flow• Drawing off negative charge via the base lead reduces this effect (“making the base smaller”) - so the base current controls the flow of electrons into the collector• Nobel Prize 1956; Shockley, Bardeen & Brattain

Direction of current flow

+-

Bill ShockleyBorn 1910London, EnglandDied 1989Stanford, California

Active Mode

• Can relate iB and iC

• β is defined mainly by the properties and geometry of the materials• Ideally constant for any particular type of transistor• Typically around 500• "Common-emitter current gain"• Actually varies with temperature and emitter current

• Collector current is controlled by the base current

BC ii

Emitter current

• Emitter current is the sum of iB and iC (KCL)

CE

C

CBE

ii

i

iii

1

where

1

• α is called the common-base current gain (~1.0)

BC ii

Circuit Symbols and Conventions

• BJTs are not symmetric devices• Doping and physical dimensions are different for collector and emitter

• Collector largest, connected to heat sink as most power dissipated there• Emitter region smaller, and more heavily doped to provide an abundance of charge carriers• Base region is very thin (~50nm) to enhance probability that electrons will cross it

• PNP devices also exist - diode senses are reversed, so bias voltage polarities must also be reversed

Emitter

CollectorBase

+

-

iC

iB

iE

VCE

VBE

i-v Characteristics

• Simplest model for low frequencies (DC condition) "Ebers-Moll". • Relates collector current IC to base-emitter voltage VBE:

• IS=Saturation Current• Similar to Diode Law• Recall IB=IC/β

VBE

IC

TBE

TBE

VVS

VVSC

eI

eII/

/ 1

• Collector current is controlled by the base-emitter voltage VBE

BJT Amplifier

• To act as an amplifier, first bias the transistor to get it into active mode• Then superimpose a small signal vbe on the base• Under DC conditions:

CCCCCE

CB

CE

VVSC

RIVV

II

II

eII TBE

100/

01.1 /

Added resistor RC

Note labelling scheme:iC=IC+ic

"Common emitter" configuration

BJT Amplifier• DC condition biases the BJT to the point Q on the plot• Adding a small voltage signal vbe translates into a current signal that we can write as:

• If vbe/VT is small:

So the small signal current is: bembeT

Cc vgv

V

Ii

gm is the "transconductance"; corresponds to the slope at point Q

DC component IC

Small signal component ic

i.e. a voltage-to-current amplifier; small signal collector current determined by base-to emitter voltage

T

beCcC V

vIiI 1

Tbe

TbeTBE

TbeBE

VvC

VvVVS

VvVScCC

eI

eeI

eIiIi

/

//

/) (

More on small-signals

• Base current also varies with vbe

beT

CCCB v

V

IIii

1

So, having small signal voltage at the base, and small signal current at the base, consider the small signal equivalent resistance into the base, rπ:

Alternatively, rearrange to give small signal resistance between base and emitter, re:

IB =DC component of base current iB

ib = small signal component of base current iB

Small signal models

Use these relations to represent the small signal model for the transistor by an equivalent circuit. Hybrid-π model:

e.g. as a voltage controlled current source:

or as a current controlled current source

m

T

Cm

gr

V

Ig

bemc vgi

Small signal models

Other small signal models may sometimes be more convenient. T model:

T

Cm V

Ig

Using small signal models

1) Determine the DC operating conditions (in particular, the collector current, IC)

2) Calculate small signal model parameters: gm, rπ, re

3) Eliminate DC sources: replace voltage sources with shorts and current sources with open circuits

4) Replace BJT with equivalent small-signal models. Choose most convenient depending on surrounding circuitry

5) Analyze

Voltage gain with small signal model

•To convert the voltage controlled current source into a circuit providing voltage gain, connect a resistor to the collector output and measure the voltage.• Find the gain using a small signal model:

vbe vbe

+

-

+

-

ic

re

RC

Cmbe

c

mme

e

C

ee

Ce

be

c

eebe

CeCe

Ccc

Rgv

v

ggr

r

R

ri

Ri

v

v

riv

RiRi

Riv

gain voltageso

1

gain Voltage

ic

vc

eliminate DC sources and apply T-model

Summary of useful equations

• Basic DC operating conditions:

CCCCC

VVSC

CE

BC

CBE

RIVV

eII

II

II

III

TBE

/

1

• Add a small signal: