Operational amplifiers
An operational amplifier (op-amp) is an integrated circuit with two inputs, the inverting (−) and non-inverting (+), and one output. It has a very high gain, very high input resistance and very low output resistance. Its output is limited by the supply voltages (saturation). With negative feedback from the output to the inverting input, an op-amp gives stable, predictable gain.
| Circuit | Gain | Use |
|---|---|---|
| Inverting amplifier | G = −R_f ÷ R_in | Amplifies and inverts a signal |
| Non-inverting amplifier | G = 1 + R_f ÷ R₁ | Amplifies without inverting |
| Voltage follower (buffer) | G = 1 | Matches a high-resistance source to a low-resistance load |
| Comparator (no feedback) | Output saturates | Switches high or low depending on which input is larger: light and temperature switches |
Choose the input voltage and the two resistors. Find the gain and the output voltage (the supply is ±12 V, so the output cannot go beyond that).
Digital electronics
Digital circuits use two levels, 0 and 1. The basic gates are AND, OR and NOT; NAND and NOR are universal gates: any circuit can be made from NAND gates alone. Boolean algebra describes them: Q = A·B (AND), Q = A + B (OR), Q = Ā (NOT). De Morgan’s laws: (A·B)‾ = Ā + B̄ and (A + B)‾ = Ā · B̄. A flip-flop is a circuit that stores one bit; counters and memories are made from flip-flops.
| A | B | AND | OR | NAND | NOR | XOR |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 0 | 0 | 0 |
Analogue and digital signals; rectifiers; transistors
An analogue signal varies continuously; a digital signal has only two levels, so it is less affected by noise. An analogue-to-digital converter (ADC) samples a signal and gives it a number; sampling at least twice the highest frequency (the Nyquist rule) keeps the information. A bridge rectifier with a smoothing capacitor makes d.c. from a.c.
Communication systems
| Stage | Job |
|---|---|
| Transducer (microphone) | Turns sound into an electrical signal |
| Amplifier | Makes the signal bigger |
| Modulator | Puts the signal on a carrier wave (AM, FM, digital) |
| Transmission channel (radio, cable, optical fibre) | Carries the signal; noise and attenuation add errors |
| Receiver and demodulator | Recovers the signal |
| Loudspeaker | Turns the signal back into sound |
Key terms
- Operational amplifier
- A high-gain differential amplifier used with feedback.
- Negative feedback
- Feeding part of the output back to the inverting input to stabilise the gain.
- Universal gate
- A gate (NAND or NOR) from which any logic circuit can be built.
- ADC
- A circuit that converts an analogue signal to digital numbers.
Summary
- Op-amps with negative feedback: inverting gain −R_f/R_in; non-inverting gain 1 + R_f/R₁.
- Boolean algebra and De Morgan’s laws; NAND and NOR are universal.
- Analogue signals are converted to digital by ADCs.
- A communication system has transducer, amplifier, modulator, channel and receiver.