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School of Electronic Engineering

Bangor University IES2012 Analogue Electronics: Lecture 7 & 8

IES 2012 Analogue Electronics

Introduction to AC Amplifiers

Winter 2012

Dr. Julian Burt

School of Electronics

Bangor University

United Kingdom

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Bangor University IES2012 Analogue Electronics:

Lecture Aims and Outcomes

• Review AC amplifiers

• To discuss sources of signal distortion in bipolar transistors

• To discuss simple AC equivalent circuits for bipolar transistors

• To introduce frequency limitations of bipolar transistors

• To discuss Common Emitter voltage amplifiers

• To introduce multistage amplifiers

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Emitter Biased AC Amplifier

Coupling Capacitors: Block DC Voltages, transmit AC voltages

Good coupling: XC

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Amplifier Distortion

-

Input

EQ p pe I i 1.0)(

Amplifier distortion occurs when the

input signal is large enough to be

influenced by the non-linear

characteristics of the transistor

junctions.

Distortion can be reduced by using onlysmall input signals. This allows us to

assume the transistor characteristics to

be linear over the signal variation

Small Signal Definition:

IEQ = Q point emitter current

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Amplifier Distortion

-

Output

The non-linear properties of the

transistor’s gain, b, can cause distortion

in the output side of the circuit.

b varies with the magnitude of the

collector current as well as temperature.

This variation will be different in

individual transistors, even those of the

same type.

Ensuring that the emitter and collector

current vary by less than 10% of the Q

point (DC Bias) current reduces the

influence of transistor non-linearities.

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Amplifier Gain

Common Emitter DC current gain

Previously, the DC current gain has been defined as

Common Emitter AC current gain

For the AC case a similar definition applies

bDC for a circuit is a point on the IC vs IB graph AT the

Q point. So, as the instantaneous operating point

moves so does bDC. b is the gradient of the graph

ABOUT the Q point

bDC b. If only a value of bDC is available this can be

used for preliminary analysis

β =Δ

Δ=

β =

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AC Transistor Models

bce iii b

T model

model

The T model is also known as the Ebers-Moll model

The p model is a variation of the Ebers-Moll Model and is used commonly for analysis since it is easy toidentify the input resistance of the transistor. br’ e is a simplification, from an analysis of the T model

the value should be (1+b)r’ e.. Since b>>1 the error is less than 1% - an acceptable error.

b

be

i

v

basein Z )( bee

i

r i

basein Z '

)( ebasein r Z ')( b Since

b

eb

i

r i

basein Z '

)(

b

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AC Resistance of the Emitter Diode

The ac resistance of the base-emitter diode can be

calculated from the gradient about the Q point of the

VBE vs IE graph

However, this graph is defined by the diode equation,

so the resistance is the differential of the diode

equation

E I mV

er 25'

We find that, at room temperature kT/q is a

constant (25mV) and 1

r’ e (prime denotes internal) varies with DC emitter current, the greater the current the smaller the

resistance. if IE=100mA, r e=250W. if IE=500µA, r e=50W

E kT

qq

kT V

skT

q

edV

dI

e I e I g g

BE

BE

E

E qI

kT

eee r g r

'' 1

)1( qkT

V

s E

BE

e I I

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Bangor UniversityIES2012 Analogue Electronics:

Transconductance Model

bevv p

So far, we have used a current amplifier approach to analyse and model the small signal performanceof transistors. In a current amplifier a small input current is amplified to a larger output current

gm v r

E

B C

v

+

-

A tranconductance amplifier uses an input voltage

and an output current and is often an easier

approach for analysing and modelling transistors

'

er r b p '1

e

mr

g

p p r i g v g i bmmc

b

e

ebebmc i

r

r ir i g i b

b b

'

''

It is easy to convert between the current amplifier

and tranconductance amplifier representations

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Frequency Effects in AC Models

Capacitances occur at the pn junctions in the transistor,

Cm is the base-collector junction capacitance

Cp is the base-emitter diffusion and junction capacitance

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Frequency Limits of a Transistor

If the collector and emitter of the transistor are short circuited (similar to transistor

saturation) then Cm can be considered as appearing between the base and emitter.

The combination of the two capacitances will limit the current flowing through the

emitter resistance at high frequencies so reducing the collector current.

eT r C hfe f

'21 b p

f hfe is the frequency where the gain (b or hfe) is 3dB (a

factor of 1/ 2) below its low-frequency value and CT is

the parallel combination of Cp and Cm

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Analysing Transistor Amplifiers

1) DC Equivalent Circuit Analysis

• Open circuit all capacitors, (Xc= when f=0)

• Calculate transistor DC currents and voltages

• Most important, calculate emitter current IE – you need this to find r’ e

2) AC Equivalent Circuit Analysis

• Short circuit all capacitors (depending on capacitance, Xc≈ 0 when f is high)

• Short Circuit all DC voltage sources (superposition, examining the AC input only)

• Replace transistor with either the p, T or Transconductance model

• Draw the equivalent circuit and simplify if possible

• Calculate currents and voltages as required

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Base Biased Amplifier Analysis

In an AC equivalent circuit of a base

bias transistor amplifier, the input

voltage appears across the base

resistor with the transistor input

resistance in parallel.

The collector resistor appears in

parallel with the load resistor

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Two Supply Emitter Bias Analysis

The two supply emitter bias

amplifier ac equivalent is

identical to the base bias

equivalent circuit.

RC appears in parallel with the

load resistor

RE is short circuited by the

emitter bypass capacitor

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Voltage Divider Bias Amplifier Analysis

The input voltage appears

across R1, R2 and the

transistor input resistance

in parallel.

Again RC is in parallel with

the load, RL

RE does not appear in the

AC equivalent circuit as it is

short circuited by the

emitter bypass capacitor

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Voltage Amplifier – T Model

What is the gain of this amplifier?

in

out

V

V A

eein r iV '

ee

cc

r i

r i A

'

cccout r i RiV )R ||( LC

As i ei c we can simplify the gain to be

e

c

r

r A

'

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Infinite Gain?

12 CBCB

V V

From our derivation, it seems that the gain can be

increased by increasing RC. The formula does not

seem to limit the magnitude of the gain so allowing

infinite gain!

Could there be something in the transistor that will

limit the available gain?

The base-collector PN junction is typically reverse

biased. The depletion region occurring at the junction

will change its size according to the amount of

reverse bias (VCB). This effectively reduces the size of

the base within the transistor and is referred to as

Base Width Modulation or the Early Effect after its

discoverer (James M Early 1922-2004).

P

N

N

+ + + + +

+ + + + +

- - - - -

- - - - -

VCB1

Collector

Base

Emitter

P

N

N

+ + + + +

+ + + + +

- - - - -

- - - - -

VCB2

Collector

Base

Emitter

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Infinite Gain? – The Early Effect

C

Ao

I

V r

The Early Effect influences the collector current and reveals that the collector does NOT operate

as an ideal current source but has a parallel resistance, ro, often known as the ‘output resistance’

of the transistor.

b r’e b iB roWhere VA is the Early Voltage which, for

a typical transistor, has a value of

15 - 150V.

ro typically has a resistance of 10’s kW.

Both r’e and ro are inversely proportional to the collector/emitter current. As IC increases with

increasing gain, so ro decreases which, in turn, reduces the effective AC collector resistance and hence

reduces the transistor gain since some of the collector current will flow through ro rather than RC

ACE V V

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Amplifier Input Impedance

From the p-model equivalent circuit, the

input impedance of the stage can be

calculated as

Therefore, the actual input voltage tothe amplifier stage is

)||||( 21)( e stagein r' R R Z b

s Z R

Z

in V V stageinS stagein

)(

)(

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Common Emitter Voltage Amplifier

Example: What is the voltage gain of this amplifier? If the input voltage is 2mV, what is

the voltage across the load resistor?

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WWW 4.48k 100k ||k 7.4)R ||( LC Rr c

mA1.1k 17.08.1

k 17.0 W

W

V V V V E

B I

V V V B 8.1102.2k 10k k 2.2

WW

W

W 7.22'mA1.1mV25

er

Therefore,

1977.22

48.4'

W

Wk r

r

e

c A

Also,

mV mV V AV inout 394)2(197

Example: What is the voltage gain of this amplifier? If the input voltage is 2mV, what is

the voltage across the load resistor?

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Example: What is the output voltage of the following circuit if the input is 2mV?

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We know from the previous example that r’ e = 22.7W and that the voltage gain, A = 197

WW k 5.4)7.22(200)(basein Z

Find the transistor input impedance

WWW 4.5k ||2.2k ||k 10)( stagein Z

Next calculate the stage input impedance

W1.29k )( stagein Z

Calculate the stage input voltage

mV mV V k

k in 35.1226.1600

26.1 WW

W

So, mV mV V AV inout 266)35.1(197

Example: What is the output voltage of the following circuit if the input is 2mV?

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IES2012 Analogue Electronics:

CE Voltage Amplifier – Variation

Example: What is the output voltage if the transistor is replaced by one with a b = 50

We know from the previous example that r’ e = 22.7W and that the voltage gain, A = 197

WW k 1.1)7.22(50)(basein Z

b determines the base input impedance so,

WWW 1.1k ||2.2k ||k 10)( stagein Z

And also determines the stage input impedance

W 836)( stagein Z

This reduces the stage input voltage

mV mV V in

53.02683600

683 WW

W

And, in turn, the output voltage of the circuit reduces mV mV V AV inout 104)53.0(197

Because the input impedance of the stage is dependent on b, so is the output voltage of the circuit. This

circuit’s performance depends on the individual transistor used!

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Amplifier Output Impedance

cout R Z

The output impedance of an amplifier is the same as the amplifier’s Thevenin impedance looking

back into the output of the circuit. We can calculate this from the AC equivalent circuit

Thevenin’s theorem states that voltage and current

sources are replaced with thier internal resistance.

Therefore, the collector-emitter source is replaced

with an open circuit

Output Impedance of stage:

Output Impedance of circuit: Lcout R R Z ||

The choice of RC not only effects the gain

but also defines the output impedance of

the amplification stage

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Multistage Amplifiers

)||( 2C11 )in(stagec Z Rr

1

2C1

'

)||(

1e

) stagein(

r

Z R A

For the first stage:

)||( C22 Lc R Rr

2

C2

'

)||(

2 e

L

r

R R

A

For the second stage:

21 A A Atotal

Total voltage gain:

rc1 is effectively the output Z of the

first stage in parallel with the inputZ of the second stage

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Example: What is the output voltage of this amplifier circuit for a 1mV source voltage?

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Start with the first stage and calculate the input impedance.

This is the same as the previous examples so,

W 7.22' mA1.1mV25

er WWWW k Z stagein 29.14.5k ||2.2k ||k 10)(

Also, from previous examples,

mV

mV V k

k in

67.0

129.1600

29.1

WW

W

Example: What is the output voltage of this amplifier circuit for a 1mV source voltage?

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To calculate the output voltage of stage 1 we need to know the gain of the stage. This gain is

effected by the input resistance of the second stage

WWWW 1.01k 1.29k ||7.4||7.4 21 k Z k r )in(stagec

5.447.22

01.1'1

W

Wk r

r

e

c A

So the voltage at the collectorof the first transistor (the

output of the first stage) can

be calculated as

mV V

mV

V AV

C

inC

30

)67.0(5.44

1

11

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The ac collector resistance of the second stage is the collector resistor in parallel with the load

resistor, soWWW k 48.4100k ||7.42 k r c

1977.22

48.4'2 2

2

W

Wk r

r

e

c A

So the output voltage of the

circuit can be calculated as

V V

mV

V AV

out

cout

91.5

)30(197

12

Giving a gain of (As the stages are identical, so is r’ e)

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Transistor Troubleshooting

Transistor circuits can appear to be complex with many sources of error. To identify sources offaults in transistor circuits we need to analyse the expected voltages and currents in a circuit.

Fault finding usually makes use of ideal transistor models. Why? – Component tolerances,

such as 5% for resistance values, mean that no calculation will give a perfect answer but a

simple approximation will be close enough to identify an problem.

Most faults are due to short or open circuits.

Short circuits: Bad wiring, Damaged devices, Solder bridges between connections

Open circuits: Bad wiring, Component burn out, Poor solder connections

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Common Transistor Circuit Faults

Low collector voltage: Faulty power lead, Open collector resistor,

Power supply fault,

High Collector voltage: Poor wiring, Open base resistor, Open transistor

These simple faults will cause large variations in the transistor currents and voltages.

Circuit faults rarely cause small variations in transistor currents and voltages

Exceeding any transistor junction breakdown voltages, maximum currents and power

ratings can damage one or both diodes

Damaged transistors: Short circuits, Open circuits, High leakage currents,

Reduced gain

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Transistor TroubleshootingOut of circuit transistor tests

Measure collector-emitter resistance: Should be high resistance (several MW) as

diode are back to back. Reading of zero to

several kW indicate a short – replace transistor

Measure base-emitter resistance: Ratio of reverse to forward resistance should

Measure base-collector resistance: be 1000:1 or greater. If lower, the transistor is

damaged

Curve tracer : Measure Gain and leakage currents

In-circuit transistor tests

Measure VCE: Should be > 1V and < VCC (Transistor in Active region)

Measure VBE: Should be ≈ 0.7V (diode forward bias)

Short base-emitter, measure VC: Makes transistor cut-off, VC = VCC (Remove

diode forward bias)

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Summary

• Introduce AC amplifiers

• Discussed sources of signal distortion in bipolar transistors

• Discussed simple AC equivalent circuits for bipolar transistors

•

Introduced frequency limitations of bipolar transistors

• Discussed Common Emitter voltage amplifiers

• Introduced multistage amplifiers

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VB VE VC Fault

0.7V 0V 12V No error

15V 0V 0V RB short circuited –

transistor in saturation

0V 0V 15V VBB or RB open circuit

– transistor in cut-off 0V 0V 15V Base – emitter shorted

– transistor in cut-off

0.7V 0V 15V RC short circuited

0.7V 0V 0V VCC or RC open circuit

0.7V 0V 0V Collector – Emitter shortcircuit

0.7V 0V 9V β increase to 200

ies2012 lecture 7 & 8 - 2015(1)

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