# Measurements

### Errors in measurement

When taking any measurements, the effect of inaccuracies in the meter used, ie the tolerances (which may be positive or negative) on the meter readings must be taken into account.

To take a simple case, suppose the input to a PA is measured as 15V at 10A, ie 150W. If both meters are reading low by say 5%, the actual input is (15V + 5%) = 15.75V at (10A + 5%) = 10.5A or 165W. This can be considered, as a worst case as it is unlikely that both meters will read low by this amount. The error in reasonably new good-quality meters should be less than 5%, while old meters of unknown history may be in error by more than 10%.

Tolerances are usually expressed as a percentage (eg ±2%), a value (eg ±0.3V or ±200Hz) or as so many 'parts per million' (eg ±100ppm). A number of tolerances affecting a reading may be added together, although this is likely to give a pessimistic total. As an example, consider the following sample examination question:

A transmitter operating in the band 21MHz to 21.450MHz has a frequency tolerance of 100 parts in one million and a radiated bandwidth of 6kHz when using emissions of type A3E. If the frequency checking equipment at the station has a frequency tolerance of 10 parts in one million, what is the lowest frequency a licensee can use that ensures no emission below 21MHz?

(a) 21,005.1kHz
(b) 21,053.1kHz
(c) 21,008.31kHz
(d) 21,005.31kHz

Fig 10.10. Diagrammatic solution of frequency-tolerance problem

The tolerance build-up is as follows:

    Band Edge ..................................................................................21,000.00kHz

    Frequency tolerance is 100ppm, ie 100Hz per megahertz ........................2.10kHz

    Frequency meter tolerance 10ppm .........................................................0.21kHz

    A3E bandwidth is 5kHz, ie carrier must be in centre of this band ..............3.00kHz

                                                                                                                ------------

                                                                                                       21,005,31kHz

and thus the lowest frequency which can be used is 21,005.31kHz. This is shown diagrammatically in Fig 10.10.

The DTI recommendations on frequency measurement in the amateur station in the booklet "How to become a Radio Amateur" should be studied.

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