# Frequency counter accuracy and resolution

### RF Frequency Counter Tutorial

Frequency counters are widely used for the accurate measurement of frequency of radio frequency, RF, signals, or for that matter the frequency of any repetitive electronic signal.

Frequency counters are widely available for comparatively low prices and within an electronic repair or development laboratory a wide variety may be available. Additionally frequency counters are widely available from electronic measuring equipment stockists. Accordingly it is necessary to choose the best counter for a given applications.

The accuracy and resolution of frequency counters are two important elements of the overall specification. The resolution and accuracy are two completely different aspects of the performance of the frequency counter although they are often equated with each other.

In order to be able to interpret the readings of a frequency counter, it is necessary to have an understanding of the difference between accuracy and resolution.

## Frequency counter resolution

The resolution of a frequency counter is its ability to differentiate between two signals that are close to each other. It is a measure of the number of digits in the reading of the signal frequency.

Most frequency counters are what are termed direct reading counters, and the resolution is determined by the gate time. This is the time for which the counter is counting the number of pulses or transition crossings.

As the number of crossings in a second is equal to the frequency, a one second gate time will enable frequencies to be read down to a resolution on 1 Hz. It can be seen that for other gate times, a 0.1 second gate time will allow a resolution of 10 Hz to be achieved, whereas a 10 second gate time will enable a resolution of 0.1 Hz to be achieved.

Thus it can be seen that for a direct reading frequency counter, the resolution is a function of the gate time.

## Frequency counter measurement error

The accuracy of a frequency counter is a little more difficult to determine as it is a function of a number of factors. There are several categories of measurement error that can occur some of which affect the counter timer when making different types of measurement. These inaccuracies can be summarised as follows:

• The ± count error:   One of the forms of frequency counter error occurs with the way exact timing of the gate open and closure with respect to the incoming waveform. Sometimes it is possible for the time base to open so that there is one more count than at other times. The ambiguity occurs because of the non-coherent relationship between the time base clock and the incoming waveform.

Frequency counter ± count error

The time base gate is open for the same amount of time in each case, but in the first case only one positive going edge is counted, whereas in the second case, two are counted. The reason for this is the relative timing or phasing between the two signals.
• Time base error:   Although the time base will be accurate, its actual accuracy being dependent upon the type of clock oscillator used, its accuracy will have a direct impact on the overall frequency counter accuracy. The oscillator accuracy is the sum of the various oscillator errors:

• Mains / line voltage variations:   Variations in the power input voltage will cause variations of the voltages to the crystal oscillator. The level of the variation will depend upon the effectiveness of any voltage regulators, but there is always some small voltage variation. This can result in small errors in the crystal oscillator voltage that will be reflected in the frequency counter timer errors.
• Temperature stability:   Temperature stability of the crystal oscillator used for the clock or timebase is one of the main sources of error or inaccuracy. The short term stability is generally quoted in parts per million over a temperature range. Often when wanting to make accurate measurements, it is wise to allow the test instrument to warm up and for the temperature to stabilise over a period of a few hours before the measurement is taken. Oven controlled crystal oscillators may reach their specified accuracy sooner, but experience generally indicates allowing a frequency counter, or any other test instrument to warm up and stabilise over a a few hours before making any accurate measurements.
• Long term stability:   This form of crystal oscillator frequency error occurs over time. While many high grade crystal oscillators are pre-aged, these errors still occur to some degree. Typically they are expressed in parts per million over a month. A period this long is taken because the effects of ageing are masked by the short term effects over much shorter periods of time. The errors resulting from ageing of the frequency counter timer clock can be reduced by periodic recalibration of the test instrument.
• Short term stability:   The short term variation include elements such as the short term frequency variations including phase noise / phase jitter. If phase noise is high it can mean that the gate period could vary or jitter by an amount that could cause fewer or more pulses to be gated than the exact gate time would allow through.
• Trigger error:   Trigger errors on a frequency counter are those errors that occur on a time interval counter as a result of noise on the incoming signal that result in the input gate being opened or closed to soon or too late. They cause the cause one limit of the hysteresis window of the input trigger to fire at the wrong time, thereby introducing a timing measurement error. This error can be made worse by increasing he sensitivity of the input circuitry and thereby allowing noise to have a greater effect.
• Systematic error :   This form of measurement error on a test instrument occurs as a result of a mismatch between the start and stop channels. It may result of differences in channel rise or fall times, or the propagation delay differences.

By understanding the errors in a frequency counter, it is possible to use them more effectively, knowing what can and cannot be achieved. It is also possible to better define a frequency counter when one is to be bought.

By Ian Poole

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