# Fractional N Frequency Synthesizer Tutorial

### - fractional N frequency synthesizers provide a method of enabling small step sizes or channel spacing while maintaining a high comparison frequency for improved synthesizer performance.

Fractional n frequency synthesizers utilise a method of changing the division ratio within a digital PLL synthesizer to provide frequencies that are not integral multiples of the comparison frequency.

Using a traditional PLL frequency synthesizer, the output frequency is an integral multiple of the comparison frequency. If the division ratio of the divider in the loop is set to a number 'N', then the output frequency will be N times the comparison frequency.

For applications where small step sizes are required, for example in situations where almost continuous tuning is required, and step sizes of around 100 Hz or so are needed, fractional n synthesis becomes an attractive option.

## Fractional n synthesis need

A fractional n synthesizer uses the basic digital PLL loop. It has a VCO, phase detector, loop filter, divider and could even utilise a mixer within the loop as well.However to explain its operation, the case will be used of a simple digital loop with a divider only added to the basic PLL.

**Basic digital frequency synthesizer**

Using this loop the phase detector will compare the two signals entering, i.e. the reference and the divided VCO signal. The loop will lock when the two signals entering the detector are of the same frequency. This means that the VCO will be operating at a frequency equal to the division ratio times the phase comparison frequency.

To achieve small steps between channels of frequencies, while still offering a reasonable operating frequency requires a very high division ratio. For example a loop operating at 10 MHz and requiring a 100 Hz step size will need a division ratio of 100 000. This perfectly feasible, but it does impact the loop performance. As the loop bandwidth must typically be around a tenth of the reference comparison frequency, this would mean, for the above example figures a loop bandwidth of only 10 Hz. This results in loss of performance:

- Slow PLL frequency switching time
- Large passive component sizes
- High phase noise at frequencies close to the carrier, i.e. within loop bandwidth and VCO phase noise not reduced further out

Another option is to use a multiple loop synthesiser, but this has significant cost implications.

A much cheaper option, while still retaining a general high level of performance is to use a fractional n frequency synthesizer.

## Fractional n synthesis concept

The concept behind fractional n synthesis, is very much as the name indicates: the divider takes on a fractional division ratio rather than an integer one that would be normally expected. To achieve this, the divider alternatives between division ratios. Typically it will change between N and N+1 - the proportion of the various division ratios determined to give the required frequency. The division ratio range of N and N+1 gives frequencies between the two division ratios. Also switched modulus counters giving counts between N and N+1 are available.

The advantage of using fractional n synthesis is that the step frequency can be small while still allowing a high comparison frequency and loop bandwidth to improve the overall synthesizer performance.

**Fractional N Frequency Synthesizer Block Diagram**

When using a dual modulus divider it is easy to calculate the overall effective division ratio. To determine the effective division ratio, it is necessary to know the two division ratios and the number of VCO cycles for which each division ratio is effective. Therefore the effective division ratio can be calculated from the formula:

**Where:**

Neff = overall division ratio

A = number of cycles divided by N

B = number of VCO cycles divided by N+1

## Fractional N synthesis spurious emissions

It can be imagined that the change in division ratio over the period of the VCO cycles causes some disruption to the system. This results in close in spurious emissions that appear on the output of the factional N synthesiser.

The periodic modulus changes causes a phase error accumulation which accumulates over N reference cycles of the divider. This phase error translates into periodic disturbances in the VCO control voltage and in turn this results in the generation of spurious signals that are relatively close in to the wanted carrier.

This phase accumulation occurs because the average of the feedback frequency is equal to the reference frequency. As a result, the phase error will accumulate over N reference cycles before being reset.

There are a number of ways of reducing the effects of these spurious signals. The accumulating phase error can be cancelled out - a method that was patented by Racal in a scheme they referred to as Digiphase. Alternatively the modulus switching can be accomplished randomly so that the sidebands are masked as noise. This reduces the distinct sideband levels in favour of a higher overall sideband noise level.

* By Ian Poole*

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