Function Generators

Intuition

A signal you specify rather than find

Most test work needs something going in. A filter with nothing at its input is a set of components; the same filter fed a sine of known size and frequency starts telling you what it does. That is the job of a function generator: it produces a waveform whose shape, size, rate and resting level you set, so that everything downstream can be compared against something known.

Four controls do nearly all of it. Shape picks between a sine, a square, a triangle and usually a few more. Frequency sets how many cycles a second. Amplitude sets how big the swing is. Offset slides the whole waveform up or down without changing its size, which is what a circuit running on a single positive supply needs.

Before you touch any of them, know this: the amplitude control is calibrated against an assumption. Most generators are built to drive 50 Ω, and their display reads the amplitude you would get if a 50 Ω load were connected. Connect something else and the reading and the reality part company: an oscilloscope input, which draws almost nothing, sees twice the displayed figure.

A volume control on an amplifier does the same thing in a smaller way. Marked in watts, it means those watts into the loudspeaker impedance the maker assumed. Fit a different loudspeaker and the marking is a rough guide rather than a measurement. The generator's amplitude display is the same kind of number, and Layer 3 shows exactly how far out it can be.

Practitioner

Getting the amplitude you asked for

A generator is quick to set up and easy to set up wrongly, so follow the order below.

1. Decide what the circuit under test can survive before setting anything. A generator will happily present ten volts to a three-volt logic input.
2. Set the shape, then the frequency, then the amplitude, then the offset. Offset last, because on many instruments the sum of amplitude and offset is limited and the generator will quietly clip if you exceed it.
3. Tell the generator what it is driving. Instruments with a load setting need it set to high impedance for a scope input and to 50 Ω for a matched load; get this wrong and every amplitude is out by a factor of two.
4. Connect the ground clip first, and to the circuit's own reference rather than to a convenient piece of metal.
5. Enable the output, and confirm on a scope what the generator claims it is producing. This step catches the load setting, a clipped offset and a dead lead in one go.
6. Change frequency in decades first, then close in. Sweeping slowly through the whole range hunting for a response wastes more time than two coarse steps.

The instrument's own arithmetic is short. Period follows from frequency:

and the average level of a rectangular output follows from its duty:

Engineer

Source resistance and the load that changes your settings

Behind the output socket is a source and a resistance in series with it, and that resistance is deliberate. A defined output resistance, almost always 50 Ω, matches the cables used at radio frequencies and stops reflections from a mismatched far end coming back and confusing the measurement.

It also means the socket cannot deliver its internal voltage to anything. The internal source and the load form a divider:

so the generator's designers set the internal amplitude to twice the number on the display. Ask for 2.00 V peak to peak and the source behind the resistance is really producing 4.00 V. Into a matched 50 Ω load, half of that is dropped internally and the load receives 2.00 V, exactly as promised.

Attach something else and the arithmetic moves. A 600 Ω load takes 3.69 V. A 1 kΩ load takes 3.81 V. An oscilloscope input takes so little that the whole 4.00 V appears, which is double what the panel says and the single most common surprise a beginner meets on a bench.

Four numbers for one waveform

Amplitude has more than one meaning and instruments disagree about which they show. Take the matched case, a sine of 2.00 V peak to peak. Its peak is 1.00 V, half the swing. Its RMS value is smaller again:

giving 0.707 V, which is what an AC meter reports and what sets the heating this signal would produce. The mean of its magnitude, which is what a rectifier-and-average circuit actually collects, is 0.637 V, smaller still. Amplitude measures sets out the family properly.

Radio-frequency benches use a fifth: power referred to 1.00 mW, written dBm, which is only meaningful once the resistance is stated.

That sine into 50 Ω delivers 10.0 mW, which is 10.0 dBm. The zero of that scale, 1.00 mW into the same resistance, corresponds to 224 mV RMS.

The edges are not vertical

A square wave is drawn with vertical sides and no instrument produces one. The generator's own bandwidth sets how fast its output can move, and a single-pole response makes that relationship simple:

A generator specified at 25.0 MHz cannot do better than 14.0 ns between the ten and ninety per cent points, an exponential of 6.36 ns rather than a step. On the 3.30 V swing above, that means the output passes 330 mV and 2.97 V that far apart.

At a kilohertz that is invisible: fourteen nanoseconds out of a millisecond changes nothing you could see or measure. Testing the rise time of a logic gate is another matter, because the generator's own edge would then be slower than the thing being measured, and the result would describe the generator instead of the gate.

The same limit shows up in a subtler way well below the top of the range. A square wave is a fundamental plus a series of odd harmonics, and the generator rolls off the ones above its bandwidth, so a square wave whose fundamental gets close to the specified bandwidth loses its higher harmonics and rounds at the corners, well before the fundamental itself reaches the limit. Harmonics explains where those components come from, and the practical rule that falls out of it is to keep the fundamental at least a decade below the instrument's rating whenever the shape of the edge matters, which keeps enough of the harmonic series intact that the rounding this section describes stays out of sight.

Professional

Generators that are not function generators

The instrument described so far builds its waveform from a stored table and a clock, which is why the same box will produce a sine, a square and a triangle without any change of circuit. That construction leaves fingerprints. The output is a staircase before filtering, its steps set by the sample clock, and a sine near the top of the instrument's frequency range is assembled from fewer points than one near the bottom. Distortion figures therefore vary across the range in a way a dedicated sine oscillator's does not.

Arbitrary waveform generators extend the same idea by letting you supply the table. Anything you can describe as a list of samples becomes an output, which is how a sensor's real signal, a fault condition or a modulated carrier gets replayed into a circuit repeatably. The limits are the sample rate, the memory depth and the reconstruction filter, and all three are stated on the datasheet.

Several instruments on a bench are not function generators at all and are worth telling apart. A signal generator in the radio sense produces a very pure sine of accurately known amplitude, usually with modulation, and is specified on phase noise and level accuracy rather than on shape. A pulse generator produces edges far faster than a function generator can, with independent control of width and delay. A bench power supply produces a constant level and nothing else. Choosing the wrong one usually shows up as a measurement limited by the source.

Two features on a modern generator repay learning early. A sweep runs the frequency across a range while a trigger output marks the start, which turns a filter measurement from twenty manual readings into one trace. A burst emits a counted number of cycles on command, which is how a resonant circuit's ringdown or a receiver's acquisition behaviour gets exercised without a continuous drive.

Synchronising two instruments matters too. Most generators have a reference input and output so several boxes can share one clock, and a trigger or sync output that emits a clean edge once per cycle. Feeding that sync to an oscilloscope trigger input gives a rock-steady display of a signal the scope would otherwise struggle to lock on to, which is often the difference between a measurement and an argument with the trigger controls.