What does signal conversion cover in WJEC A-Level Electronics?

Signal conversion covers turning analogue signals into digital form and back. Analogue-to-digital conversion involves sampling at a regular rate, the Nyquist criterion (sample at least twice the highest frequency) and aliasing, quantisation into $2^n$ levels for an $n$-bit converter, resolution as the full-scale voltage divided by $2^n$, and quantisation error. Digital-to-analogue conversion covers the weighted-resistor summing DAC, the R-2R ladder DAC, and reconstruction with a low-pass filter.

What is the Nyquist criterion and what is aliasing?

The Nyquist criterion states that a signal must be sampled at a rate of at least twice its highest frequency component for it to be reconstructed faithfully. If the sampling rate is too low, aliasing occurs: high frequencies appear as false lower-frequency signals that were never present, corrupting the reconstruction. An anti-aliasing low-pass filter is placed before the ADC to remove frequencies above half the sample rate first.

How does the number of bits affect an ADC?

An $n$-bit ADC divides the input range into $2^n$ levels, so the resolution (the voltage represented by one step) is the full-scale voltage divided by $2^n$. More bits give more levels, smaller steps, finer resolution and a smaller quantisation error, the unavoidable rounding error of at most half a step. For example, going from 8 to 10 bits increases the levels from 256 to 1024 and cuts the step size by a factor of four.

Why is an R-2R ladder DAC often preferred over a weighted-resistor DAC?

A weighted-resistor DAC needs binary-weighted resistors spanning a very wide range of values, all precisely matched, which is hard and expensive to manufacture for many bits. An R-2R ladder DAC uses only two resistor values, R and 2R, repeated, which are far easier to match precisely, especially on an integrated circuit. It therefore scales to many bits with good accuracy. Both produce a stepped output that a low-pass filter smooths into a continuous waveform.

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WJEC A-Level Electronics Signal Conversion: analogue-to-digital and digital-to-analogue conversion explained

A deep-dive WJEC A-Level Electronics guide to Signal Conversion. Covers analogue-to-digital conversion (sampling, the Nyquist criterion and aliasing, quantisation, resolution, the number of bits and quantisation error) and digital-to-analogue conversion (the weighted-resistor summing DAC, the R-2R ladder DAC and reconstruction with a low-pass filter).

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What the signal-conversion section demands
Analogue-to-digital conversion
Digital-to-analogue conversion
How signal conversion is examined
The topics, dot point by dot point
For the official specification

What the signal-conversion section demands

The world is analogue but electronics increasingly processes signals digitally, so conversion in both directions is essential. The WJEC specification treats the two converters with their key calculations, and the topic rewards clear understanding of sampling, resolution and reconstruction.

This guide walks through the two topics in specification order, then sets out the exam patterns WJEC repeats. Each topic has a matching dot-point page with worked exam questions; this overview ties them together.

Analogue-to-digital conversion

Sampling measures the signal at regular intervals; the Nyquist criterion requires the sample rate to be at least twice the highest frequency, or aliasing produces false lower frequencies. Quantisation rounds each sample to the nearest of $2^n$ levels for an $n$ -bit converter, so the resolution (one step) is $\frac{V_{full}}{2^n}$ . More bits mean smaller steps, finer resolution and smaller quantisation error, the rounding error of at most half a step.

Digital-to-analogue conversion

A weighted-resistor DAC feeds each bit into the virtual earth of a summing amplifier through a binary-weighted resistor, so the bit currents add in the ratio of the place values; its drawback is the wide range of precisely matched resistors needed. The R-2R ladder DAC uses only two resistor values, $R$ and $2R$ , which match easily and scale to many bits. The stepped output is smoothed by a low-pass reconstruction filter into a continuous waveform.

How signal conversion is examined

Expect resolution calculations from the number of bits and full-scale voltage, the Nyquist criterion with an aliasing example, the binary-weighting argument for a DAC, and the comparison of weighted-resistor and R-2R designs with the role of the reconstruction filter. These are reliable, formula-driven marks.

The topics, dot point by dot point

Each topic has a dot-point answer page with worked exam questions and cross-links. Browse them from this overview and the subject hub.

For the official specification

WJEC Eduqas publishes the full specification, past papers and mark schemes at eduqas.co.uk. Always revise from the current specification and the board's own past papers, because question style is board-specific.

Sources & how we know this

WJEC Eduqas GCE A-level Electronics specification — WJEC Eduqas (2017)