AQA A-Level Physics: Electronics

An operational amplifier (op-amp) is connected as an inverting amplifier. The input signal is applied through an input resistor $R_{in}$Rin​ to the inverting ($-$−) input, the non-inverting ($+$+) input is held at 0 V, and a feedback resistor $R_f$Rf​ is connected from the output back to the inverting input.

Explain how this circuit works as an inverting amplifier. Your answer should refer to:

• the assumptions that the op-amp draws negligible input current and has a very large open-loop gain;
• why the inverting input behaves as a virtual earth sitting at approximately 0 V;
• how the negative feedback through $R_f$Rf​ leads to a voltage gain of $G = -\frac{R_f}{R_{in}}$G=−Rin​Rf​​.

(6 marks)

An op-amp is wired as an inverting amplifier and powered from supply rails of $+15$+15 V and $-15$−15 V. The resistor values are listed below.

Quantity	Value
Input resistor $R_{in}$Rin​	22 kΩ
Feedback resistor $R_f$Rf​	220 kΩ
Supply rails	$\pm 15$±15 V

(a) Calculate the voltage gain of the amplifier. (1 mark)

(b) A steady input of $+0.80$+0.80 V is applied. Calculate the output voltage, and state whether the output is within the range of the supply rails. (2 marks)

(c) The input is now increased to $+2.0$+2.0 V. Calculate the output voltage the gain formula predicts, explain why the actual output cannot reach this value, and state the actual output voltage. (3 marks)

A temperature-warning circuit uses a potential divider made from a negative-temperature-coefficient (NTC) thermistor in series with a fixed 10 kΩ resistor, across a 5.0 V supply. The voltage measured across the fixed resistor is fed to the non-inverting ($+$+) input of an op-amp comparator. The inverting ($-$−) input is held at a fixed reference of 2.5 V. The comparator is powered from $\pm 15$±15 V rails.

The thermistor's resistance at two temperatures is given below.

Condition	Thermistor resistance
Cold (5 °C)	30 kΩ
Hot (60 °C)	2.5 kΩ

(a) Calculate the voltage at the non-inverting input (across the 10 kΩ resistor) when the thermistor is cold, and state the comparator output voltage ($+V_s$+Vs​ or $-V_s$−Vs​). (2 marks)

(b) Repeat the calculation for the hot condition and state the comparator output. (2 marks)

(c) State, with a reason, whether this circuit switches its output high when the surroundings get hot or when they get cold. (1 mark)

A designer is building an automatic security light that must switch on in darkness. A light-dependent resistor (LDR) is connected in series with a fixed 10 kΩ resistor across a 6.0 V supply, and the voltage across the LDR is fed to the non-inverting ($+$+) input of an op-amp comparator. The comparator output drives a transistor that switches a relay, and the relay turns the lamp on when the comparator output is high ($+V_s$+Vs​). The LDR resistance varies as shown.

Condition	LDR resistance
Bright daylight	1.0 kΩ
Darkness	100 kΩ

(a) Calculate the voltage at the non-inverting input in bright daylight and in darkness. (2 marks)

(b) The reference voltage on the inverting input is set to 3.0 V. Explain how the system responds as it gets dark, and explain why a reference of 3.0 V is a sensible choice. (3 marks)

A microphone pre-amplifier uses an op-amp connected as a non-inverting amplifier, powered from $\pm 15$±15 V rails. The feedback resistor is $R_f = 90 \ \text{k}\Omega$Rf​=90 kΩ and the resistor from the inverting input to earth is $R_{in} = 10 \ \text{k}\Omega$Rin​=10 kΩ.

(a) Calculate the voltage gain of the amplifier. (1 mark)

(b) A signal of amplitude $0.50$0.50 V is applied at the input. Calculate the amplitude of the output signal. (1 mark)

(c) Express the voltage gain of the amplifier in decibels, using $G_{dB} = 20\log\left(\frac{V_{out}}{V_{in}}\right)$GdB​=20log(Vin​Vout​​). (2 marks)

Real operational amplifiers are often analysed by treating them as ideal op-amps.

State three properties of an ideal operational amplifier. (3 marks)