Averaging is a common technique for reducing the measurement uncertainty inherent in all measurements. Performing the same measurement a number of times and averaging the results can reduce the randomness of the experimental result. Averaging is an automatic function available in most instruments. Rather than returning noise-ridden results, an instrument may make 100 measurements, calculate the average, and return just that average as the measured result. But power averaging in spectrum analyzers may actually provide misleading data as the following experiments intend to show.

The experiments involved correlating the power measurements of two spectrum analyzers from different vendors. However, the issues discussed are generic in the sense that they apply to any spectrum-analyzer power measurement with some form of post-detection averaging.

One of the first incorrect assumptions regarding power averaging in spectrum analyzers is averaging the root-mean-square (RMS) power will yield the average power of a zerospan trace or portion of the trace. Perhaps to understand the problem with this assumption, it may help to view averaging mathematically, as in Eq. 1. It shows M_AVE as the average of a series of individual measurements taken over N trials of an experiment, where each of those measurements is denoted as M_i:

In this instance, the task was to verify that one instrument (instrument A) correlated with a second instrument (instrument B) to within some level of accuracy (for example ±1 dB). All measurements were performed in zerospan (ZS) mode, a common spectrum-analyzer approach for measuring power at a specific frequency. The use of ZS is irrelevant to the problems with averaging, because the same kinds of averaging issues occur in traditional frequency-domain spectrum analysis.

In both cases, the ZS technique was used for adjacent-channel-power-ratio (ACPR) measurements. This measurement capability is common to modern analyzers with digital intermediate-frequency (IF) filters, allowing the instrument to perform multiple power measurements at varying offsets from the center frequency without retuning.

Figure 1 shows a real ZS measurement of a pulsed GSM signal. The blue curve represents the actual GSM pulse envelope. The measurement performed here is the “Output RF Spectrum (ORFS) due to modulation,” which is simply an ACPR measurement.

It is possible to calculate a number of useful results from the trace, such as the maximum peak power, minimum power, and average power. Finding the trace maximum power and minimum power is conceptually straightforward— the analyzer performs a maximum peak and minimum peak search on the entire trace and returns the results.

The simplest (and correct) way to calculate average power is to average across all the points between the red lines. Equation 2 accomplishes this, where N is the number of trace points between the red lines, and Pith point is power in the

Unfortunately, instrument manufacturers don’t always agree on power averaging approaches. One of the instruments averaged powers as in Eq. 2, while the other instrument first converted each power point to a voltage, took the average of all of these voltages, and then used the average voltage to calculate the average power. Equation 3 shows this calculation:

It was not a trivial exercise to prove that one instrument was using Eq. 2 and the other was using Eq. 3 since the difference between the two reported average power levels wasn’t that large. It was necessary to pull multiple traces out of both instruments and calculate the average every conceivable way until good fits were found. In the example in Fig. 1, the difference between the “true” average power (subsequently referred to as the RMS power) and the average voltage power is 0.25 dB (RMS power is 0.25 dB greater). This could have been written off as a simple measurement difference (error) between the two instruments. While 0.25 dB may not seem like much, when the requirement is for ±1 dB of correlation (accuracy), 0.25 dB looms as a significant amount. If the difference in power levels over the whole burst is examined, the delta widens to ~1 dB (again, RMS power registering higher than average voltage power). In this case, the difference is equal to the level of accuracy one is trying to obtain.