# Improved resolution of relative power measurement using a directional wattmeter

Measurement of RF power is prone to errors, and instruments with high absolute accuracy are very expensive, and beyond the means of most experimenters.

There are times though when increased resolution of relative power measurements is very useful, without necessarily demanding extreme absolute accuracy. This article describes a method of improving the resolution of power measurements with suitable directional wattmeter, for reasonably accurate relative power measurements.

The detector voltage of common directional wattmeters is related to the RF power level, and by measuring the detector output (DC) voltage with a digital voltmeter, higher resolution measurements are possible. The link that is needed is a mechanism of relating the detector voltage to the RF power level.

## Cubic spline interpolation

One method is to make a series of observations of indicated RF power and detector output voltage at various power levels. The observations can then be used to create a cubic spline interpolation of any arbitrary measured detector voltage (with high resolution), and the RF Power level calculated.

Fig 1:
Pin (W) Vout Vin
10 2.0550 22.3607
20 3.0620 31.6228
30 3.8000 38.7298
40 4.3600 44.7214
50 4.8600 50.0000
60 5.4400 54.7723
80 6.3000 63.2456
100 7.0000 70.7107

For example, the RF power and detector output voltage at various power levels of a Revex W560 forward detector were measured, and RF input voltage calculated and are tabulated in Fig 1.

From this data then, Vout=7.3V corresponds to Pin=109.3W. The spreadsheet W560.xls contains the framework for creating the cubic spline interpolation, and then calculating Pin for some measured Vout.

## Linear regression

An alternative approach is to create a linear regression on the Vout and Vin, and obtain a simple expression relating Pin to Vout. This technique is not as accurate because the relationship between Vout and Vin is not perfectly linear due to diode characteristics. For situations where Vout is much greater than the diode threshold, accuracy may be reasonably good for many applications.

The spreadsheet W560.xls also contains a linear regression model for the Revex W560 data. It can be seen from the graph that it does not coincide exactly with the cubic spline interpolation and the original data points, and is worse when extrapolated… though extrapolation is an issue for both methods. The relationship from the linear regression is that Pin=(1.963318268+9.774563829*Vout )^2/50.

The spreadsheet also contains a sheet for a MFJ949E detector, and it can be seen to be less accurate, the Standard Error is almost double that of the W560.

## Implementation

This technique works best when the raw detector voltage can be sample, the higher the voltage, the less error introduced in measuring it with a DMM. In the case of the Revex W560, the detector voltage is about 10V at full scale, much better than 42mV meter voltage of a Bird 43 at full scale.

The cubic spline method with well chosen sample data will give better accuracy than a linear regression.

Some instruments have poor calibration accuracy in the first place (eg the MFJ949E) and are less suited to this method of extending resolution.

An example of practical application of the technique is the measurements used for the article A test of Zs on an IC7000 .