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



Non-electronic active amplifiers
– an example is the torque amplifier shown here

Electronic amplifiers

● 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

Sources and loads

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

Modelling sources and loads

Modelling the input of an amplifier
– the input can often be adequately modelled by a simple resistor
– the input resistance

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

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





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

Equivalent circuit of an amplifier

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 14.1 in the course text):

Example: An amplifier has a voltage gain of 10, an input resistance of 1 kΩ and an output resistance of 10Ω . The amplifier is connected to a sensor that produces a voltage of 2 V and has an output resistance of 100Ω , and to a load of 50Ω .

What will be the output voltage of the amplifier (that is, the voltage across the load resistance)?

We start by constructing an equivalent circuit of the amplifier, the source and the load

From this we can calculate the output voltage:


The voltage gain of the circuit in the previous example is given by:

– 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

An ideal voltage amplifier would not suffer from loading
– it would have Ri = ∞ and Ro =0
– consider the effect on the previous example




– the effects of loading are removed (see Example 14.3)

Output power

The output power Po is that dissipated in the load resistor

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

Power gain

Power gain is the ratio of the power supplied to the load to that absorbed at the input

For numerical example see Example 14.5 in set text

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Frequency response and bandwidth

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


(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

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

Differential amplifiers

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



Equivalent circuit of a differential amplifier
  – one of the commonest forms of differential amplifier is the operational amplifier
  – discussed in later lectures

Simple amplifiers

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

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
● 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

Feedback systems

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A generalised feedback system


By inspection of diagram we can add values

Thus

This is the transfer function of the arrangement

Terminology:
   ● A is also known as the open-loop gain
   ● G is the overall or closed-loop gain

Effects of the product AB
– If AB is negative
   ● If AB is negative and less than 1, (1 + AB) < 1
   ● In this situation G > A and we have positive feedback

– If AB is positive
   ● If AB is positive then (1 + AB) > 1
   ● In this situation G < A and we have negative feedback
   ● If AB is positive and AB >>1


– gain is independent of the gain of the forward path A

Negative feedback

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Negative feedback can be applied in many ways
   – Xi and Xo could be temperatures, pressures, etc.
   – here we are mainly interested in voltages and currents

Is particularly important in overcoming variability
   – all active devices suffer from variability
     ● their gain and other characteristics vary with temperature and between devices
   – we noted above that using negative feedback we can produce an arrangement where the gain is independent of the gain of the forward path
     ● this gives us a way of overcoming problems of variability

Negative feedback – an example

Consider the following example (Example 15.1 in text) Example: Design an arrangement with a stable voltage gain of 100 using a high-gain active amplifier. Determine the effect on the overall gain of the circuit if the voltage gain of the active amplifier varies from 100,000 to 200,000.

We will base our design on our standard feedback arrangement

We will use our active amplifier for A and a stable feedback arrangement for B

Since we require an overall gain of 100 and

we will use B = 1/100 or 0.01

Now consider the gain of the circuit when the gain of the active amplifier A is 100,000

Now consider the gain of the circuit when the gain of the active amplifier A is 200,000

Note that a change in the gain of the active amplifier of 100% causes a change in the overall gain of just 0.05 %.
Thus, the use of negative feedback makes the gain largely independent of the gain of the active amplifier.
However, it does require that B is stable.
  – fortunately, B can be based on stable passive components

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