Spectrum analyzers must deliver wide dynamic range to keep pace with increasingly demanding requirements for evaluating third-generation (3G) wireless systems and their multicarrier power amplifiers (PAs). An analyzer's published adjacent-channel-power-ratio (ACPR) performance, however, can be misleading when the effects of measurement uncertainty are considered. By evaluating the measurement process and the influence of coherent and incoherent distortion, it may be possible to clarify the interpretation of spectrum analyzer ACPR dynamic range.

The wideband-code-division-multiple-access (WCDMA) ACPR¹ dynamic-range specification created by the Third Generation Partnership Project (3GPP) is of particularly interest for many engineers. The ACPR dynamic range is often used as a figure of merit for spectrum analyzers, even though instrument uncertainty can make comparisons of different instruments difficult. Many factors contribute to an instrument's overall ACPR measurement uncertainty, including display fidelity, frequency response, and the effects of its internally generated noise and distortion. For measurements requiring high dynamic range, the most substantial source of error is typically a combination of the instrument's internally-generated noise and distortion and the noise and distortion present in the measured signal.

The dynamic range chart of Fig. 1 shows the noise, phase noise, and third-order intermodulation distortion (IMD) of the instrument as a function of its mixer level.² The curve labeled "Instrument ACP" is a summation of the other curves, and yields the spectrum analyzer's internal ACP. The optimum (lowest) ACP of −74.5 dB occurs at a mixer level of −13.5 dBm.

In practice, a level of −74.5 dB would never be measured because the ACP of the DUT will add with the ACP of the instrument to produce another value.³ In this case, the DUT ACP performance of −74.5 dB will add with the analyzer's ACP power and, in the best case (when the signals are completely incoherent), the displayed result will be −71.5 dB.

To avoid errors caused by reduced signal-to-noise and signal-to-distortion ratios, the common rule is that the analyzer should have 10 to 15 dB greater dynamic range than the DUT to be measured. However, as this example shows, this may not be an adequate way to ensure an acceptable amount of measurement uncertainty.

Third-Order IMD
The noise-like nature of digital signals makes it seem reasonable that the third-order IMD generated by the instrument will be incoherent with the third-order IMD generated by the DUT. However, this is generally not the case. The distortion is in fact coherent and will add as voltage rather than power, resulting in higher-than-expected measurement uncertainty.

One way to understand distortion coherence is to visualize the envelope of a test signal. Nonlinearities in the DUT and in the front end of a spectrum analyzer will usually compress the peak envelope excursions. If both the DUT and the spectrum analyzer compress the peaks at the same instant, the effects will add coherently as voltage errors and the distortion products will add (or subtract depending on the phase of the signals).¹

How does this affect the measurement? If incoherence is assumed, then the most logical way to make the measurement is to set the input attenuator to achieve a mixer level at the minimum point on the ACP curve. The error caused by incoherent addition will always be positive, so it is reasonable to obtain the optimum measurement setting by simply adjusting the attenuator until the best (minimum) reading is observed. Unfortunately, the characteristics of coherence complicate the matter. This is because coherent addition can be positive or negative (depending on the unknown phase relationship), so adjusting the mixer level to achieve the best reading can result in an optimistic but erroneous result.

Consider the ACPR measurement of −60 dB in Fig. 2 that was achieved at a mixer level of −13.5 dBm. For the incoherent case, this would be the optimum mixer level setting, and the resulting error caused by the internal ACP of the analyzer would be +0.15 dB, resulting in a reading of −59.85 dB. However, if coherent distortion is present, as it is likely to be, the total error could be +1.00 dB to −1.05 dB, producing a measurement range of −59.0 to −61.05 dB.

Larger Errors
Larger errors will result from measurements made close to the coherent distortion curve than from measuring close to the incoherent noise curve (see Figs. 1 and 2). The optimum measurement setting is determined by increasing the attenuation, which lowers the spectrum analyzer's mixer level, as illustrated in Figure 2. Assuming the distortion and noise curves follow a straight line on the dynamic range chart as theoretically predicted, the optimum amount that the mixer level should be shifted depends on the level of DUT ACPR, and can be estimated using the equation:

While the distortion curve of all spectrum analyzers varies somewhat from an ideal value, it varies significantly in some instrument models. It is the basic reason why an instrument with high specified dynamic range does not always produce better measurement results than a unit with lower specified performance. This does not mean that more dynamic range is not always desirable for making better measurements, but that the instrument's optimum settings for a specific measurement are the ones of significance, rather than the dynamic range it achieved with the optimum settings specified in data sheets and other literature.

To illustrate this point, consider the measured third-order-intercept (TOI) surface plots of Figs. 3a and 3b comparing two spectrum analyzers. By definition, TOI is the theoretical point where the third-order IMD curve resulting from two tones will intercept the axis (0 dBc). The graphs show TOI as a function of mixer level and tone separation.