Topic 8 – Amplifier Basics

In the exam you are expected to:

·        Describe voltage gain and phase relationships between input and output voltages;

·        Know about bandwidth in terms of voltage gain and power;

·        Know about input and output impedances;

·        Know about positive feedback and how it leads to instability and oscillation;

·        Describe how negative feedback reduces the gain but increases the bandwidth.

Analogue electronics involves a continuously varying signal that can have any value, positive or negative; the only limit is the value of the power supply.  The diagram below compares analogue and digital signals

Notice that digital signals do not fall below 0 V.

Analogue systems are widely used in:

·        Radio broadcasting

·        Telephony

·        High Fidelity music reproduction.

In effect, any use where we need to hear things.  Our ears respond to analogue signals, not digital.

Question 1  Compare digital and analogue signals.  ANSWER

The output voltage from an input device such as a microphone, or tape head in a cassette recorder is very small, in the order of millivolts.  The loudspeaker takes a voltage of 20 V.  Therefore there needs to be a way of boosting the voltage to a level at which it can be used.  A transformer is no good, because, as the voltage is increased, the current is reduced.  We have to find a way of increasing the current as well as the voltage.  This is done using an amplifier.

The extent to which the amplifier increases the voltage, current, or power is called the gain.  It is the ratio of the output voltage (or current, or power) to the input voltage (or current, or power):

                                    Gain = Output voltage

                                                Input voltage

In this section of work we will consider the voltage gain.

Question 2  The output voltage of an amplifier with gain of 1000 is 20 V.  What is the input voltage?  ANSWER

Let us now look at what happens when we apply a sinusoidal voltage to the input of an amplifier and see its effect on the output voltage.

Notice that the phase of the wave is changed by 180^o (p radians). 

If the average level of the input signal too large, we will get distortion.

Question 3  Use the diagram above to explain why the output of the amplifier is distorted.

ANSWER

Notice that the peaks and troughs of the waves are cut off.  This is called clipping and results in a noticeable distortion.  Bad clipping can make an audio signal at best unpleasant to listen to, at worst unintelligible.

Bandwidth

The frequency response of an amplifier is the range of frequencies that an amplifier can amplify.  The human ear can detect frequencies in the range 20 Hz to 20000 Hz and an ideal audio amplifier would do the same at a power gain of a constant value.  That doesn’t happen in practice.  The graph of gain against frequency is like this:

The bandwidth of the amplifier is the range of frequency at which the power is at least half the maximum power.

If a loudspeaker provides a constant load, we can say that a voltage rise of Ö2 times gives a doubling of power.  This is because the current will also go up Ö2 times.  Therefore we can define the bandwidth as:

the frequency in which the voltage gain is not less than 1/Ö2 times the maximum value, about 70 %.

Question 4  An amplifier gives out a voltage of 15 V to drive an 8 ohm loudspeaker.  Its bandwidth is from 30 Hz to 15 kHz.  What is the output voltage and power at these two extremes?   ANSWER

Feedback

Feedback is a term that electronic engineers use in which a fraction of the output is taken back to the input.  Negative feedback is widely used in amplifier circuits that reduces the gain.  It also makes the amplifier more stable.  Amplifiers without negative feedback tend to be rather unstable.  This can arise due to:

·        Temperature differences

·        Stray inductance and capacitance effects

·        Noise within the components or from poor soldering.

·        Fluctuations from the power supply.

The effect of an unstable amplifier is that the output becomes distorted in an unpredictable and random way.

Positive Feedback

Positive feedback is not used in amplification.  The diagram shows the principle:

The microphone picks up some sound and this goes with the input signal to be amplified.  This makes the sound louder, so the input to the microphone gets larger, which gives a larger output… 

The result of this is a feedback loop or howl round.  The amplifier becomes unstable and will oscillate.   Whatever you call it, it sounds the same, an ear shattering boom or screech.

Positive feedback is used constructively in circuits such as the Schmitt Trigger or oscillator circuits.

Question 5  Explain why positive feedback is not a desirable thing in an audio amplifier.

ANSWER

Negative Feedback

Negative feedback reduces the gain, but increases the stability by feeding a small fraction of the output to the input. The phase is changed.  This reduces the input so that the output is reduced as well.  Therefore the amplifier is much easier to control.

The principle of negative feedback is best shown with an op-amp circuit

The output is fed into the inverting input, and the phase will be changed by 180^o.   This will reduce the output.

Question 6  Why is negative feedback a good thing in an audio amplifier?

ANSWER

Input Impedance

The input device such as a microphone is connected to the input of an amplifier through a capacitor.  Many microphone have a battery in them so the capacitor prevents a dc offset, which is a small dc voltage that gets amplified by the amplifier itself.  The dc offset that has been amplified can lead to an unacceptable waste of power.

Question 7  How does the capacitor prevent the dc offset?   ANSWER

The diagram shows how a microphone is connected to an amplifier:

We can treat the input to any amplifier, however complicated as a simple capacitor and resistor in series, with an output voltage to the amplifier.  The input impedance is the vector sum of the reactance of the capacitor C and the resistance R2.

It is important for best performance that the impedance is matched with the value of R1.  So if the impedance of the microphone is 10 kilohms, then the input impedance should be about 10 kilohms or more.

Output Impedance

Any amplifier, however complex can be treated as a simple perfect battery in series with an internal resistor.  This is called Thévinin’s Theorem.  To prevent dc offsets from wasting power, an output capacitor may be placed in the output line to the loudspeaker.  Therefore the amplifier has an output impedance.  So we can represent the amplifier like this:

We treat the circuit like the cell with an internal resistance.  It’s a perfect source in series with an internal resistor and a capacitor.

The most effective power transfer occurs when the output impedance is the same as the impedance of the loudspeaker. (The loudspeaker has a resistance and inductance, which is beyond our scope).

As before reactance of the capacitor is given by

And the impedance is given by

Question 8 An amplifier has an internal resistance of 6 ohms and an output capacitor of value 1000 mF.  The no load output voltage is 12 V rms.  It is connected to a loudspeaker of resistance 8 ohms and negligible inductive reactance.  At what frequency does the maximum power transfer occur?  What is the maximum power output?

ANSWER

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