Page 410 - Physics Coursebook 2015 (A level)

398
Cambridge International A Level Physics
WORKED EXAMPLE
4 In the circuit shown in Figure 25.20, Rin = 4 kΩ and Rf = 20 kΩ. Calculate:
a the output voltage when the input voltage is 0.5 V
b the maximum input voltage if the supply voltage
is ±12 V
c the input resistance of the amplifier.
The solutions can be found using the formula for gain G.
Step1 CalculatethegainG = − Rf = −20 =−5 Rin 4
Step 2 Calculate Vout = gain × Vin = −5 × 0.5 = −2.5 V Step3 Theop-ampbecomessaturatedwhen
The two resistors R1 and R2 form a potential divider. The total voltage across R1 and R2 is Vout and the voltage across R2 alone is Vin.
The current in the two resistors can be written as:
Vout = Vin (R1 + R2) R2
The gain is calculated from:
G = Vout = (R1 + R2) = 1 + R1 Vin R2 R2
Vout = −12 V, so:
Vin=Vout =12=2.4V
R2
For a non-inverting amplifier, the output is in phase with the input. When the input voltage is positive, so is the output voltage.
G5
Step4 PointPisat0V,sotheinputresistanceisjust
QUESTIONS
17 The circuit shown in Figure 25.19 is a non- inverting amplifier. What are the values of R1 and R2? Show that the gain of the amplifier is 1.
18 Draw the circuit of a non-inverting amplifier with a gain of 10. Explain whether the input resistance is very high or very low.
19 Suppose that the non-inverting amplifier in Figure 25.21 has R1 = 50kΩ, R2 = 5kΩ and Vs = 10 V.
a Calculate the gain.
b Calculate the output voltage when the input
Thus for a non-inverting amplifier the gain is given by: G = 1+ R1
caused by Rin = 4 kΩ.
The non-inverting amplifier
Figure 25.21 shows the circuit for a non-inverting amplifier. The input voltage is applied to the non-inverting input; part of the output voltage is fed back to the inverting input.
+Vs –
+
–Vs
R2
voltage is: i −0.10V
ii +1.0V.
Vin
R1
Vout
Output devices
The output voltage of an op-amp may be used to operate a device according to the changing input voltage. We will now look at three types of output device.
The relay
Although the output resistance of an op-amp is low, a typical op-amp can only provide a maximum output current of 25 mA. The maximum voltage output from an op-amp is also limited to the supply voltage, typically 15 V. To switch on larger currents and larger voltages the op- amp is connected to a relay.
Figure 25.21 A non-inverting amplifier.
As long as the op-amp is not saturated, the potential difference between the inverting (−) and non-inverting inputs (+) is almost zero. So V − = V +.
Since the non-inverting input (+) is connected to the input voltage, V + = Vin. Thus V − = Vin.