Transcript Chapter 6

Amplification
Chapter 6
 Introduction
 Electronic Amplifiers
 Sources and Loads
 Equivalent Circuits of Amplifiers
 Output Power
 Power Gain
 Frequency Response and Bandwidth
 Differential Amplifiers
 Simple Amplifiers
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Introduction
6.1
 Amplification is one of the most common processing
functions
 Amplification means making things bigger
 Attenuation means making things smaller
 There are many non-electronic forms of amplification
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 Non-electronic amplifiers
– Levers
 Example shown on the right is a
force amplifier, but a displacement
attenuator
 Reversing the input and output
would produce a force attenuator
but a displacement amplifier
 This is an example of a
non-inverting amplifier (since the
input and output are in the same
direction)
A lever arrangement
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 Non-electronic amplifiers
– Pulleys
 Example shown right is a force
amplifier, but a displacement
attenuator
 This is an example of an
inverting amplifier (since the input
and output are in opposite
directions) but other pulley
arrangements can be non-inverting
A pulley arrangement
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 Passive and active amplifiers
– levers and pulleys are examples of passive amplifiers
since they have no external energy source
 in such amplifiers the power delivered at the output must
be less than (or equal to) that absorbed at the input
– some amplifiers are not passive but are
active amplifiers in that they have an external
source of power
 in such amplifiers the output can deliver more power than is
absorbed at the input
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 Non-electronic
active amplifiers
– an example is the
torque amplifier
shown here
A torque amplifier
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Electronic Amplifiers
6.2
 Can be passive (e.g. a transformer) but most are
active
 We will concentrate on active electronic amplifiers
– take power from a power supply
– amplification described by gain
Voltage Gain ( Av ) 
Vo
Vi
Current Gain ( Ai ) 
Power Gain ( Ap ) 
Io
Ii
Po
Pi
Circuit symbol
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Sources and Loads
6.3
 An ideal voltage amplifier would produce an output
determined only by the input voltage and its gain
– irrespective of the nature of the source and the load
– in real amplifiers this is not the case
– the output voltage is affected by loading
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 Modelling the input of an amplifier
– the input can often be
adequately modelled by
a simple resistor
– the input resistance
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 Modelling the output of a circuit
– all real voltage sources have an output resistance
– for example, a battery can be represented by an ideal
voltage source and a series resistance representing its
output resistance
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 Modelling the output of an amplifier
– similarly, the output of an
amplifier can be modelled
by an ideal voltage source
and an output resistance
– this is an example of a
Thévenin equivalent circuit
(we will return to such circuits
later)
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 Modelling the gain of an amplifier
– can be modelled by a controlled voltage source
– the voltage produced by the source is determined by
the input voltage to the circuit
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Equivalent Circuits of Amplifiers
6.4
 Having modelled the input, the output and the gain,
we can now model the entire amplifier
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 The use of an equivalent circuit
(see Example 6.1 in the course text):
Example: An amplifier has a voltage gain of 10, an input
resistance of 1 k and an output resistance of 10 . The
amplifier is connected to a sensor that produces a voltage of
2 V and has an output resistance of 100 , and to a load of
50 . What will be the output voltage of the amplifier (that is
the voltage across the load resistance)?
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 We start by constructing an equivalent circuit of the
amplifier, the source and the load
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 From this we can calculate the output voltage:
Vi 

Ri
Vs
Rs  Ri
1 k
2 V  1.82 V
100   1 k
Vo  AvVi
 10 Vi
RL
Ro  RL
50 
50 
 10  1.82
 15.2 V
10   50 
10   50 
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 The voltage gain of the circuit in the previous
example is given by:
Voltage gain ( AV ) 
Vo 15.2

 8.35
Vi 1.82
– note that this is considerably less than the stated gain
of the amplifier (which is 10)
– this is due to loading effects
– the gain of the amplifier in isolation is its
unloaded voltage gain
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 An ideal voltage amplifier would not suffer from
loading
– it would have Ri =  and Ro = 0
– consider the effect on the previous example
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 If Ri = , then
Ri
R
 i 1
Rs  Ri Ri
 Therefore
Vi 
Ri
Vs  Vs  2 V
Rs  Ri
Vo  AvVi
 10 Vi
RL
Ro  RL
50 
50 
 10  2
 20 V
0   50 
50 
– the effects of loading are removed (see Example 6.3)
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Output Power
6.5
 The output power Po is that dissipated in the load
resistor
Vo 2
Po 
RL
 Power transfer is at a maximum when RL = Ro
– maximum power theorem
– choosing a load to maximize power transfer is
called matching
– often voltage gain is more important than power
transfer
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Power Gain
6.6
 Power gain is the ratio of the power supplied to the
load to that absorbed at the input
Pi 
2
Vi
Ri
Vo 2
Po 
RL
 For numerical example see Example 6.5 in set text
 Gain often given in decibels
Power gain (dB) =10 log10
P2
P1
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 Sample gains expressed in dBs
Power gain Decibels (dBs)
Power gain Decibels (dBs)
100 20
0.5 -3
10 10
0.1 -10
1 0
0.01 -20
 Using dBs simplifies calculation in cascaded circuits
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 Power gain is related to voltage gain
P2
V22 / R2
Power gain (dB)  10 log10
 10 log10 2
P1
V1 / R1
 If R1 = R2
Power gain (dB)  10 log10
V22
V12
 20 log10
V2
V1
Power gain (dB)  20 log10 (Voltage gain )
 This expression is often used even when R1  R2
– see Example 6.7 and Example 6.8 in the course text
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Frequency Response and Bandwidth
6.7
 All real amplifiers have limits to the range of
frequencies over which they can be used
 The gain of a circuit in its normal operating range is
termed its mid-band gain
 The gain of all amplifiers falls at high frequencies
– characteristic defined by the half-power point
– gain falls to 1/2 = 0.707 times the mid-band gain
– this occurs at the cut-off frequency
 In some amplifiers gain also falls at low frequencies
– these are AC coupled amplifiers
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 (a) shows an AC coupled
amplifier
 (b) shows the same
amplifier – with gain in dBs
 (c) shows a DC coupled
amplifier – the gain is
constant down to DC
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 The bandwidth is the
difference between the
upper and lower cut-off
frequencies …
 … or the difference
between the upper-cut-off
frequency and zero in a
DC coupled amplifier
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Differential Amplifiers
6.8
 Differential amplifiers have two inputs and amplify the
voltage difference between them
– inputs are called the non-inverting input (labelled +)
and the inverting input (labelled –)
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 An example of the use of
a differential amplifier
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 Equivalent circuit of a differential amplifier
– one of the commonest forms of differential amplifier is
the operational amplifier – discussed in later lectures
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Simple Amplifiers
6.9
 Operational amplifiers are relatively complex circuits
 Amplifiers can also be formed using a ‘control device’
– circuit is similar to a potential divider with one resistor
replaced with a ‘control device’ typically a transistor
A potential divider
A simple amplifier
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Key Points
 Amplification forms part of most electronic systems
 Amplifiers may be active or passive
 Equivalent circuits are useful when investigating the
interaction between circuits
 Amplifier gains are often measured in decibels (dBs)
 The gain of all amplifiers falls at high frequencies
 The gain of some amplifiers falls at low frequencies
 Differential amplifiers take as their input the difference
between two input signals
 Some amplifiers are very simple in construction
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