# Arbitrary Function Generator, AFG

### - tutorial details of the arbitrary function generator, a direct digital synthesis version of an arbitrary waveform generator, sometimes called a DDS waveform generator.

### In this section

The arbitrary waveform generators that use direct digital synthesis techniques as the basis for their operation are often called just arbitrary function generators because 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.

## 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.

**Block diagram of a DDS based arbitrary function generator**

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.

**Phase relationship for a signal**

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.

## Advantages and disadvantages of AFG

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.

**Arbitrary function generator advantages**

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.*Sub Hz frequency resolution:*Waveforms are automatically truncated by sampling to allow repetition rates above the clock frequency.*Down sampling:*It is possible to add digital modulation words to the phase accumulator to provide a means of providing digital modulation.*Digital modulation:*

**Arbitrary function generator disadvantages**

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*Waveform jitter:*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*Single waveform capability:*

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.

* By Ian Poole*

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