QRP Power Measurement

A couple of WorldRadio readers have written to ask about the voltage figures in the chart accompanying January ‘05’s QRP column on QRP power measurement.

They were determined some time ago by aligning voltages derived using the simple circuit described in the article with figures derived using test equipment.

The January figures do not necessarily align with results derived by using the traditional formula for power associated with Ohm’s Law. Previous experimentation owed those differences to variables and losses that the formula does not recognize.

I would be happy to hear from anyone who would like to run a similar comparison today – using the circuit from January’s column vs. lab-quality test gear. We could bring those results to readers in a future column.

Following are the voltage and associated power figures using the standard formula - which adjustments for a .1 diode voltage drop and converts peak readings to RMS readings for use in Ohm's Law:

P = [ ( V + .1 X .707) squared ] / R

The following chart shows: Power / Actual Meter Reading

10mW / 0.9000 volts
20mW / 1.3144
30mW / 1.6322
40mW / 1.9002
50mW / 2.1363
60mW / 2.3497
70mW / 2.5461
80mW / 2.7288
90mW / 2.9004
100mW / 3.0626
250mW / 4.9007
500mW / 6.9721
750mW / 8.5615
1W / 9.9014
1.25W / 11.0818
1.5W / 12.1492
2W / 14.0422
2.5W / 15.7137
3W / 17.2230
3.5W / 18.6110
4W / 19.9029
4.5W / 21.1164
5W / 22.2639

P = [ ( V + .1 X .707) squared ] / R

Read that: Power equals (voltage plus .1, multiplied by .707). Now square that figure. Then divide the resulting squared figure by resistance - which in this case is 50 ohms.

So, if your DVM's voltage reading is 2.7288, you're measuring 80mW:

P = (2.7288 + .1 X .707) squared / 50 = .079992 or .08 watts (80mW)

This formula can be used to determine the associated power with any DVM reading coupled to the QRP power measurement circuitry. If your DVM does not go to multiple decimal digits, simply round figures to make your calculations.