Voltage and Power Add Differently: Understanding Signal Power Measurement

Blog Post created by benz on Apr 10, 2017

  The difference can be anything from 0 dB to infinity

Most RF engineers are aware that signal measurements are always a combination of the signal in question and any contributions from the measuring device. We usually think in terms of power, and power spectrum has been our most common measurement for decades. Thus, the average power reading at a particular frequency is the result of combining the signal you’re trying to measure plus any extra “stuff” the analyzer chips in.

In many cases we can accept the displayed numbers and safely ignore the contribution of the analyzer because its performance is much better than that of the signal we’re measuring. However, the situation becomes more challenging when the signal in question is so small that it’s comparable to the analyzer’s own contribution. We usually run into this when we’re measuring harmonics, spurious signals, and intermodulation (or its digital-modulation cousin, adjacent channel power ratio, ACPR).

I’ve discussed this situation before, particularly in spurious measurements in and around the analyzer’s noise floor.

Graphic explanation of addition of CW signal and analyzer noise floor. Diagram of apparent and actual signals, actual and displayed signal-to-noise ratio (SNR).

Expanded view of measurement of a CW signal near an analyzer’s noise floor. The analyzer’s own noise affects measurements of both the signal level and signal/noise.

It’s apparent that addition happens between the power of the signal and that of the analyzer’s internal noise. For example, when the actual signal power and the analyzer noise floor are the same, the measured result will be high by 3 dB.

However, it’s essential to understand that the added power is in the form of noise, which is not coherent with the signal—or anything else. The general incoherence of noise is a valuable assumption in many areas of measurement and signal processing.

We can get tripped up when we unknowingly violate this assumption. Consider the addition of these CW examples in the time domain, where the problem is easier to visualize:

Graphic explanation of addition of two equal-amplitude CW signals, showing effect of relative phase. In-phase addition produces a total power 6 dB greater than an individual signal, while out-of-phase addition results in zero net power.

The addition of coherent signals can produce a wide range of results, depending on relative amplitude and phase. In this equal-amplitude example, the result can be a signal with twice the voltage and therefore 6 dB more power (top) or a signal with no power at all (bottom).

I’ve previously discussed the log scaling of power spectrum measurements and the occasionally surprising results. The practical implications for coherent signals are illustrated by the two special cases above: two equal signals with either the same or opposite phase.

When the signals have the same phase, they add to produce one with four times the power, or an amplitude 6 dB higher. With opposite phase the signals cancel each other, effectively hiding the signal of interest and showing only the measurement noise floor. Actual measurements will fall somewhere between these extremes, depending on the phase relationships.

This coherent addition or subtraction isn’t typically a concern with spurious signals; however, it may arise with harmonic and intermodulation or ACPR measurements in which the analyzer’s own distortion products might be coherent with the signal under test. Some distortion products might add to produce a power measurement that is incorrectly high; others could cancel, causing you to miss a genuine distortion product.

I suppose there are two lessons for RF engineers. One: some measurements may need a little more performance margin to get the accuracy you expect for very small signals. The other: be careful about the assumptions for signal addition and the average power of the result.

In a future post I’ll describe what we learned about how this applies to optimizing ACPR measurements. Until then, you can find more information on distortion measurements at our signal analysis fundamentals page.