Tutorial 7 B - More Operational Amplifier and Amplifier Basics

Learning Objectives

• In the exam, you are expected to:

• recall the properties of an ideal op-amp;

• recall that for a real op-amp, the product of voltage gain and bandwidth is a constant;

• recall that negative feedback is used to reduce the overall voltage gain of an op-amp amplifier subsystem.

Analogue Signals

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.  Digital signals have a maximum value of about 5 V, and minimum of 0 V. Operational amplifiers work with analogue signals.

Analogue systems are widely used, for example, in:

• Telephony;

• High Fidelity music reproduction.

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

 What is the difference between analogue and digital signals? Amplifier Gain

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.

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 180o (p radians).  This means that the output wave is upside down compared to the input wave.

 Are visual signals digital or analogue? If the average level of the input signal too large, we will get distortion. 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 graph of power gain against frequency for many amplifiers 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 root 2 times gives a doubling of power.  This is because the current will also go up root 2 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.

This is about 71 %. An amplifier has a gain of 200.  The input voltage is 75 mV, what is the output voltage? 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 as it 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 idea: 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.  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.

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. This is what happens:

• The output is fed into the inverting input,

• The phase will be changed by 180o.

• This will reduce the output.

• This is added to the input wave, reducing the size of the input.

The graph shows this: How does negative feedback reduces the input to an amplifier? Think about the phase changes. Operational Amplifiers

The operational amplifier was originally devised in the 1960s for use in analogue computers.  These are nowadays almost completely obsolete, although a few have some very special applications.  However the operational amplifier still has many uses in control and instrumentation electronics.  Although the original circuits used discrete components and were very expensive, miniaturisation has enabled op-amps to be made as integrated circuits, available for a few pence. Operational amplifiers require a dual power supply, which means having a central 0 volts rail, and a + 15 V rail and a – 15 V rail.  The full circuit diagram is shown below, but generally we will ignore the power supply. What is meant by a dual rail supply? Notice that the op-amp has two inputs and one output.  It is a difference amplifier and amplifies the difference between the inverting input and non-inverting input.  Be careful not to confuse the symbol with a non-inverting gate.  We need to be aware of some definitions to do with op-amps:

• Open-loop voltage gain – ratio of the input to the output voltage with no feedback applied.  It is the D.C. gain of the amplifier or the gain at a frequency of 1 Hz.

• Closed loop voltage gain – the voltage gain with feedback.

• Bandwidth is the frequency range in which the output does not fall by more than 3 dB from its maximum value.

The ideal op-amp should have the following characteristics:

• Infinite open loop gain

• Infinite input impedance so that no current is drawn

• Zero output impedance so that maximum current can be transferred to the load.

• Very wide bandwidth.

In practice the maximum open loop gain is 200 000.  Beyond that limit the amplifier goes into saturation which means that the voltage cannot go any higher.  The voltage is limited, of course, by the supply voltages.  In practice the limits are rather lower than this, about 1.5 to 2 V below the value of the supply.  Suppose the supply voltage was 15 V.  The maximum output voltage would be 15 – 1.5 = 13.5 V

 Question 6 Compare the real op-amp with the ideal op-amp. The behaviour of the op-amp is shown in this graph.  Notice that the horizontal axis is marked difference in voltage.  The op-amp is a difference amplifier. The graph tells us:

• The op-amp amplifies the difference between the two input voltages

• When the difference exceeds the limits X and Y, the output is saturated.

• In between the limits the graph is linear, so there is little distortion in these regions.

The characteristic of real op-amps makes them unsuitable for use as amplifiers in open loop form, as clipping will occur and this will distort the signal.  Therefore some of the output is returned to the amplifier by a feedback loop.  This reduces the gain and makes the amplifier more stable.  The amplifier can be used in open loop form as a voltage comparator (Click if you want to revise.)

 What would the input voltage be to give an output voltage of  ± 13.5 V?  What is the voltage swing needed to go from negative to positive saturation? The open loop frequency response of the op-amp is not very good: We can see that the gain starts to fall away quite dramatically above a frequency of only 5 Hz, which is not very high.  It would be quite useless as an audio amplifier.  However the gain can be improved by reducing the gain with the use of negative feedback. We can see from this graph that the more negative feedback that we apply, the wider the bandwidth.  There is a useful relationship for op-amps:

bandwidth × gain = constant

The constant is often called the unity gain bandwidth.  This is the bandwidth at which the gain of the amplifier is 1. Links Stanford University presentation (.pdf) Applet for basic op-amp Circuit Simulator Video tutorial