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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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› Non-electronic active amplifiers – an example is the torque amplifier shown here A torque amplifier Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 ) Io Ii Power Gain ( Ap ) Po Pi Circuit symbol Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› Modelling the input of an amplifier – the input can often be adequately modelled by a simple resistor – the input resistance Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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) Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› Equivalent Circuits of Amplifiers 6.4 Having modelled the input, the output and the gain, we can now model the entire amplifier Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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)? Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› We start by constructing an equivalent circuit of the amplifier, the source and the load Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› An ideal voltage amplifier would not suffer from loading – it would have Ri = and Ro = 0 – consider the effect on the previous example Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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) Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› (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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 –) Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› An example of the use of a differential amplifier Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› Equivalent circuit of a differential amplifier – one of the commonest forms of differential amplifier is the operational amplifier – discussed in later lectures Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#› 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 Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 6.‹#›