Page 408 - Physics Coursebook 2015 (A level)

Cambridge International A Level Physics
sensing device (thermistor)
comparator (op-amp)
heater
396
Negative feedback
What happens when the op-amp in Figure 25.17 is connected to a heater which warms the air around the thermistor? The op-amp senses when the room is cold and switches on the heater. The heater then warms the room and this information is fed back to the thermistor, which then senses that the room is now warm enough and switches off the heater. This process is known as feedback and keeps the room at a reasonably constant temperature.
The effect is shown in Figure 25.18.
Figure 25.18 Feedback keeping temperature constant.
There are many examples of feedback. Your body temperature is remarkably constant because of a number of feedback mechanisms. When your skin senses that
you are cold, a signal is sent via the nerves to your brain which closes down some of the blood vessels in your skin to reduce energy loss. If you are very cold the brain makes muscles contract and expand uncontrollably as you shiver. This will make the core of your body warm again and
the effect is fed back to the brain, which switches off the shivering.
Electrical feedback is also very important. Consider the circuit shown In Figure 25.19. In this circuit Vin, the input to the op-amp, is connected to the non-inverting input
(+). The whole of the voltage output Vout is fed back to the inverting input (−) of the op-amp. How does the op-amp behave with this feedback loop?
The potential V − at the inverting input (−) is always the same as Vout because they are connected by the feedback loop. We will assume that the open-loop voltage gain is
infinite and that the op-amp is not saturated. In this case V– must be equal in value to V+ , and this is an important principle.
Suppose the system starts with both Vin and Vout as
0 V and then the input voltage Vin changes to +0.1 V. The op-amp multiplies the potential difference between V + and V − by the open-loop voltage gain to produce Vout . The gain is very high so Vout increases quickly. What does Vout become? As Vout is ‘fed back’ to V− , the value of V− increases and this reduces the difference between V − and V +. Very quickly this difference becomes zero again and
Vout = Vin. + −
We know that Vout = G0 × (V − V ), where G0 is the
open-loop voltage gain. Since Vout = V − and Vin = V + we have:
Vout =G0(Vin−Vout)
Vout(1 + G0) = G0Vin
The closed-loop gain G is given by:
G = Vout = G0 Vin (1 + G0)
Because G0 is very high, about 105, there is little difference between G0 and (G0 + 1), so the closed-loop gain is very nearly 1. Since the input voltage was +0.1 V the output voltage is also +0.1 V. This analysis is true as long as the output voltage is smaller than the supply voltage, in this case as long as Vout is between −6 V and +6 V.
This may seem strange. We have taken an op-amp with a gain of 105 and turned it into a device with a gain of 1, so the input voltage and output voltage are equal. This is hardly an amplifier, but it is useful. The op-amp draws very little current from the input, yet it can supply a reasonable current from its output. This circuit is often used as a buffer between electronic circuits. If something happens to one circuit it does not affect the other circuit.
A piezo-electric microphone has a high internal resistance and cannot supply much current. If it is connected to the input of the op-amp in Figure 25.19, the same voltage is output but the current can be larger.
Another advantage is that it does not matter whether the frequency of the input signal is high or low; the gain
is the same. So the output signal is exactly the same as the input signal and there is no distortion. This is only true when the open-loop voltage gain is high. At very high frequencies the open-loop voltage gain falls and eventually the closed-loop gain falls. The bandwidth, the range of frequencies for which the gain is constant, is increased by using negative feedback.
+6 V –
+
V –6 V in
Vout
0V
Figure 25.19 An op-amp with the output connected to the inverting input.