Page 406 - Physics Coursebook 2015 (A level)

Cambridge International A Level Physics
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only produce outputs between +9 V and −9 V. When the output voltage reaches either supply voltage, the highest or lowest value that it can achieve, the amplifier is said to be saturated.
The properties of an ideal op-amp
The ideal op-amp has the following properties.
Infinite open-loop voltage gain
This means that when an op-amp is used on its own, with no feedback loop, then a small input signal will be amplified to an ‘infinite’ output signal. Clearly this is not physically possible (the output cannot exceed the supply voltage) and at its maximum output the amplifier is saturated with output value +Vs or −Vs. However, when a feedback loop is applied, the overall gain of the circuit is reduced to a realistic value. Infinite open-loop voltage gain means that signals of a wide range of frequencies have equal gain before the feedback is applied. An actual op-amp may have an open-loop gain of 105 but this can be much higher.
Infinite input resistance (or impedance)
The input to an op-amp is a voltage. If, for example, a piezo-electric microphone is connected to the op-amp, then the microphone is acting as the voltage supply. It acts just like an electrical battery but the voltage it produces changes with time. Any voltage supply has an internal resistance. You may remember that one of the effects
of this is to reduce the terminal p.d. when a current is supplied. The infinite input resistance of an ideal op-amp means that no current is drawn from the supply, there are no ‘lost volts’ and the input voltage to the op-amp is as large as possible. The resistance for an alternating voltage is known as impedance, so the ideal op-amp has infinite impedance and no current passes into the input terminals. The input impedance of an actual op-amp may be as high as 1012 Ω, but 106 Ω is typical.
Zero output resistance (or impedance)
The output from an op-amp is a voltage. The op-amp is itself acting as a voltage supply to the next part of a circuit. An ideal op-amp has zero output resistance and so it acts just like an electrical battery with zero internal resistance. This means that there will be no ‘lost volts’ when current is supplied by the op-amp. An actual op-amp typically has an output resistance of around 75 Ω.
Infinite bandwidth
The bandwidth of an op-amp is the range of frequencies that are amplified by the same amount. An ideal op-amp will amplify signals of all frequencies and should therefore
have an infinite bandwidth. However, in actual op-amps the bandwidth can be as low as a few kilohertz.
Infinite slew rate
An ideal op-amp should change the output instantaneously as the input is changed. The slew rate of the op-amp is the factor that affects this time delay. An infinite slew rate means there is no time delay.
Zero noise contribution
Any signal includes a small amount of noise. The ideal op-amp does not produce any noise itself, although it will amplify any noise that is present in its input.
The op-amp as a comparator
The op-amp shown in Figure 25.16 is connected to two power supplies. One battery of 9 V is connected between the zero volt line and the +9 V positive supply terminal of the op-amp and the other between the zero volt line and the negative power supply terminal. These batteries are not shown. + −
The output voltage is given by Vout = G0 ×(V −V ), where G0 is the open-loop voltage gain. Notice that all of these voltages are measured with reference to the zero volt line, which is often connected to earth.
+9V –
+
–9 V Vout
0 V line (earth)
Figure 25.16 An op-amp used as a comparator. Suppose that G0 = 105 and that V + = 0.15 V and
V − = 0.10 V. The equation then gives: Vout = 105 ×(0.15−0.10) = 5000V
Clearly this is impossible. The op-amp is therefore saturated and Vout will be close to one of the power supply voltages, in this case +9 V because V + is bigger than V −. In fact:
■■ If V + is slightly greater in magnitude than V −, then Vout will have a magnitude equal to the positive power supply voltage.
■■ If V + is slightly smaller in magnitude than V −, then Vout will have a magnitude equal to the negative power supply voltage.
The op-amp is serving as a comparator, comparing V + and V −. If these two voltages are slightly different, then the output voltage tells us which one is larger. It is unlikely that the voltages will be exactly the same.
V–
V+