# Arbitrary Function Generator, AFG

## The Arbitrary Function Generator, AFG, is a subgroup of arbitrary waveform generators, using a direct digital synthesizer as the basis of its operation.

Arbitrary Waveform Generators includes:
Arbitrary waveform generator     Arbitrary function generator     Variable clock AWG

Signal generator types:     Signal Generator Basics     RF signal generator     Function generator     Pulse generator

Direct digital synthesizer, DDS technology lends itself to being used within arbitrary waveform generators, AWGs. Those AWGs that use DDS technology are often referred to as arbitrary function generators, or AFGs.

The reason for being called arbitrary function generators is that they often appear as an extension of the function generator test instruments that are available.

Arbitrary waveform generators using direct digital synthesis technology are able to benefit from the technology, while not adding unwanted additional complexity and cost. DDS technology has developed considerably in recent years and this makes them a very attractive option to form the basis of a waveform generator. As a result arbitrary function generators are relatively widely used.

## Arbitrary function generator basics

As mentioned, this type of arbitrary waveform generator is based around the DDS types of frequency synthesizer, and sometimes it may be referred to as an Arbitrary Function generator, AFG.

The arbitrary function generator uses integrated circuits intended for direct digital frequency synthesizers, but enables an arbitrary waveform generator circuit to be created relatively easily and for an economic price.

To look at how an arbitrary function generator works, it is necessary to look at the operation of a direct digital synthesizer.

This circuit operates by storing the points of a waveform in digital format, and then recalling them to generate the waveform. These points can be on any form of repetitive waveform that is required. The rate at which the DDS completes one waveform governs the frequency. The basic block diagram of the DDS based arbitrary waveform generator is shown below.

The operation of the DDS within the arbitrary function generator can be envisaged by looking at the way that phase progresses over the course of one cycle of the waveform.

The phase is often depicted as a line of phasor rotating around a circle. As the phase advances around the circle, this corresponds to advances in the waveform. The faster is progresses, the sooner it completes a cycle and the hence the higher the frequency.

The direct digital synthesizer operates by storing various points of the required waveform in digital format in a memory. These can then be recalled to generate the waveform as they are required.

To simulate the phase advances a phase accumulator is used. This takes in phase increment information, and clock pulses from a clock. For each clock pulse, the phase will advance a certain amount. The greater the increment, the larger the phase advance, and hence the higher the frequency generated.

At each clock pulse the phase information is presented to the memory and the relevant location is accessed, proving the waveform information for that particular phase angle.

It can be seen that any waveform can be loaded into the memory; although a sine wave is shown on the diagram, the actual waveform could be anything.

While it is possible to load certain preset waveforms into the memory, it is also possible to load user generated ones in as well. These make the test instrument an arbitrary waveform generator or arbitrary function generator rather than a standard function generator.

While the arbitrary function generator or DDS based version of the arbitrary waveform generator, has many advantages, there are also some disadvantages that should also be taken into account when choosing what type of signal generator to use.

• Sub Hz frequency resolution:   By using a long word length phase accumulator in the phase accumulator of the DDS, it is possible to achieve sub-Hertz frequency resolution levels.
• Down sampling:   Waveforms are automatically truncated by sampling to allow repetition rates above the clock frequency.
• Digital modulation:   It is possible to add digital modulation words to the phase accumulator to provide a means of providing digital modulation.

• Waveform jitter:   Waveform jitter is an issue with arbitrary function generators because frequencies are up-sampled or down-sampled and this results in missing samples and hence jitter. Only frequencies equal to the clock frequency divided by the waveform length and its sub multiples are not sampled and therefore they do not suffer from this problem
• Single waveform capability:   It is only possible to generate a single waveform at a time because memory segmentation and waveform sequencing is not possible using a DDS arbitrary function generator

The arbitrary function generator is the ideal instrument where a variety of programmed waveforms are required without the added flexibility and complexity of the more expensive variable clock arbitrary waveform generator. For most laboratory applications, the arbitrary function generator is an ideal choice.