RF power measurement
A source with an SWR of 1.5 and a sensor with an SWR of 1.2 leave an uncertainty of ±0.16 dB that no meter can correct: more than the error of many power meters.
01Why power is measured and not voltage
At radio frequency the voltage changes along a line with standing waves, and it depends on where it is measured. The power traveling toward the load, on the other hand, is well defined. That is why RF instruments measure power, in watts or in dBm, with a sensor that absorbs the signal and a meter that reads its output. The relationship between voltage, current and power on lines was covered in power on lines, in Transmission Media.
02The sensors
| Sensor | Principle | Typical range | Feature |
|---|---|---|---|
| Thermistor (bolometer) | The power heats a thermistor in a bridge, which is rebalanced with DC | −20 to +10 dBm | DC substitution: traceable, slow; today used in standards |
| Thermocouple | The power heats a thermoelectric junction | −30 to +20 dBm | Measures the true RMS value of any waveform |
| Diode | Rectifies the signal; in the square-law region the output is proportional to the power | −70 to +20 dBm | Very sensitive and fast; outside the square-law region it depends on the waveform |
Below about −20 dBm, the current of a detector diode is proportional to the square of the voltage, that is, to the power, for any modulation. Above that it begins to behave as a peak detector, and with modulated signals the result depends on the waveform. Modern diode sensors combine several paths or correct in software, and peak power sensors sample the envelope to measure radar pulses or bursts of digital communications.
03Calibration factor and mismatch uncertainty
No sensor absorbs all the power it receives: part is reflected and part is lost before reaching the sensing element. The manufacturer measures its calibration factor as a function of frequency, and the meter applies it. What cannot be corrected without measuring phases is the interaction between the source and the sensor: the multiple reflections between the two add or subtract depending on the phase, and leave a mismatch uncertainty:
The reflections between the source and the sensor. The chart shows the measured power relative to the true one as a function of the phase between the two reflections, which is not known: the band between the maximum and the minimum is the uncertainty.
The way to reduce it is to improve the match on whichever side can be improved: a 10 dB attenuator between the source and the sensor improves the match seen by the sensor, at the cost of level. Mismatch uncertainty also affects the uncertainty budget of any RF measurement.
04In the laboratory
Use a diode sensor to measure a continuous signal and a 100% AM-modulated one at several levels, and observe where the reading stops matching the true power.
Measure the power of a generator through a cable of variable length with a poorly matched load in the middle, and observe how the reading changes with the length.
Repeat the measurement with a 10 dB attenuator at the generator output and compare the scatter.
05Common mistakes
- Forgetting the calibration factor for the working frequency. It can change by several percent across the band.
- Measuring modulated signals with a diode outside its square-law region. The reading depends on the waveform.
- Ignoring the mismatch. It is often the largest source of uncertainty.
- Exceeding the maximum power of the sensor. Diode sensors are damaged a few dBm above their range.
06Self-assessment
What reflection coefficient corresponds to an SWR of 2?
1/3.
What is the mismatch uncertainty with an SWR of 2 at the source and 1.3 at the sensor?
\( |\Gamma_s||\Gamma_L| = 0.333 \cdot 0.130 = 0.043 \): from +0.37 to −0.39 dB.
Which sensor would you use to measure the RMS value of a heavily modulated signal?
A thermocouple, or a diode in its square-law region.
Why does an attenuator reduce the mismatch uncertainty?
Because the reflections returning toward the source pass through it twice and arrive attenuated: the sensor sees a better-matched source.
07Further reading
- Keysight Technologies. Fundamentals of RF and Microwave Power Measurements. Application Note 1449, in four parts, Keysight. The sensors, the meters and the calculation of the uncertainty.
- David M. Pozar. Microwave Engineering. 4th ed., Wiley, 2012. The reflection coefficient and mismatch in microwave networks.
- Clyde F. Coombs Jr. (ed.). Electronic Instrument Handbook. 3rd ed., McGraw-Hill, 1999. RF power meters and their sensors.