Electronic Instrumentation — Multimeter, Function Generator and CRO

By the end you should be able to: Draw the block diagrams of an electronic instrumentation system, a digital multimeter and a function generator, and use a CRO to measure amplitude, frequency and phase, including by Lissajous patterns.

The generic instrumentation system

Measurand → Transducer → Signal conditioning → Processing → Display/Record

Transducer converts the physical quantity — temperature, pressure, strain — into an electrical signal.
Signal conditioning amplifies, filters and linearises it. Most of the engineering is here, because transducer outputs are typically small, noisy and not quite linear.
Processing converts to digital and computes.
Display or recording presents the result.

The digital multimeter

Block diagram: Input → Attenuator/Amplifier → Function selector (AC-to-DC converter, current shunt, or ohms source) → A/D converter → Decoder/Driver → Digital display.

Everything is converted to a DC voltage first, because the A/D converter measures only DC voltage. That is the organising idea:

AC volts — rectified and converted to an equivalent DC level.
Current — passed through a precision shunt resistor; the voltage across it is measured.
Resistance — a known constant current is driven through the unknown resistor and the resulting voltage is measured.

Advantages over analogue: no parallax error, unambiguous reading, higher input impedance (typically 10 MΩ, so it disturbs the circuit less), auto-ranging and auto-polarity.

One real limitation, worth knowing because it produces wrong answers that look right: a cheap DMM measures AC by rectifying and applying the form factor of 1.11, which is correct only for a sine wave. On the distorted waveforms drawn by electronic loads and dimmers, the reading is simply wrong. A true RMS meter computes the actual RMS value and costs more for exactly this reason.

The function generator

Block diagram: Frequency control → Integrator → Comparator/Schmitt trigger → (feedback loop) → Wave-shaping circuits → Output amplifier and attenuator.

The classic topology generates all three waveforms from one loop:

A constant current charges a capacitor linearly, producing a ramp — the integrator output.
When the ramp reaches a threshold, a comparator flips and reverses the current, so the ramp falls. The result is a triangular wave.
The comparator's own output, flipping between two levels, is a square wave.
A shaping network of diodes and resistors rounds the triangle into an approximate sine wave.

So one oscillator produces triangle, square and sine simultaneously, which is why function generators offer exactly that set.

The cathode ray oscilloscope

Block diagram: Vertical (Y) amplifier and attenuator → CRT vertical plates; Trigger circuit → Time base generator → Horizontal (X) amplifier → CRT horizontal plates; plus the CRT with electron gun and the power supplies.

What each part does.

Electron gun produces and focuses a beam.
Vertical deflection plates deflect it in proportion to the input signal.
Time base applies a sawtooth to the horizontal plates, sweeping the beam left to right at a known rate, then flying back. This makes the horizontal axis a time axis.
Trigger starts each sweep at the same point on the waveform, so successive traces overlay and the display appears stationary. An untriggered trace drifts across the screen — the commonest complaint from a first-time user, and it is a trigger problem, not a fault.

Measurements.

V_{p-p} = (\text{vertical divisions}) \times (\text{volts/div})

T = (\text{horizontal divisions}) \times (\text{time/div}), \qquad f = \frac{1}{T}

Lissajous patterns

Feed one signal to Y and another to X, with the time base switched off. The spot traces a closed figure whose shape depends on the ratio of frequencies and their phase difference.

The frequency rule:

\frac{f_Y}{f_X} = \frac{\text{number of tangencies to a horizontal line}} {\text{number of tangencies to a vertical line}}

Count where the figure just touches a horizontal line drawn across the top, and a vertical line drawn down the side.

A circle or ellipse means 1:1.
A figure of eight means 2:1.
A straight diagonal line means 1:1 and in phase (or antiphase).

Phase measurement at 1:1, from the ellipse:

\sin\phi = \frac{y_1}{y_2}

where $y_1$ is the y-intercept of the ellipse and $y_2$ its maximum y-extent. A straight line means 0° or 180°; a circle means 90°.

Lissajous figures were the practical way to compare an unknown frequency against a standard before digital counters existed. They remain a standard exam question, and they are still the quickest way to see a small phase difference.