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.
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 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.
Theoretically, the surface plots should be flat. In reality, they vary depending on the mixer level and tone separation. While analyzer A has the best maximum TOI, it does not have the best TOI for all mixer levels and tone spacing. A single TOI specification may not tell the full story of the instrument's distortion performance. In addition, instrument makers may choose different settings to qualify their specification, taking either aggressive or conservative approaches. Consequently, comparing instruments specification for specification can be an unreliable way to evaluate them.
Third-order spectral regrowth generated by a digitally-modulated signal can be loosely correlated to two-tone, third-order IMD. The spectrum analyzer's distortion curves for an ACP measurement of a digitally modulated signal will therefore exhibit similar behavior with the performance varying depending on the measurement bandwidth, which is directly related to the noise level and optimum mixer level, and adjacent-channel spacing.
Assuming that the spectrum analyzers in Figs. 3a and 3b have similar internal noise levels, analyzer A will have better minimum ACPR for measurements with the wider measurement bandwidths and channel spacing typically used for WCDMA because of its higher noise floor and therefore higher optimum mixer levels. Analyzer B would perform better measuring the narrower bandwidths and close channel spacing typically used for cmda2000, multicarrier GSM, and multi-tone signals, because of its lower noise floor and therefore lower optimum mixer levels. However, even for tests with wide measurement bandwidths, the effective dynamic range of analyzer A may not be better for an actual measurement.
For a wide-bandwidth ACPR measurement, the ACP third-order spectral regrowth curve for the two spectrum analyzers might look like the example in Fig. 4. While the distortion of analyzer B is relatively predictable, the distortion of analyzer A degrades significantly at lower mixer levels. Although analyzer A would have better minimum ACPR performance, its effective dynamic range from an accuracy perspective is limited once the mixer level is optimized for better measurement uncertainty.
The larger-than-expected uncertainty effects caused by distortion may particularly affect the measurement if noise correction is used. Many modern spectrum analyzers have an automated noise correction function that if performed properly can dramatically reduce measurement uncertainty and extend the instrument's effective dynamic range. The noise-correction technique makes the analyzer measure its internal noise, calculates its error contribution to the measurement, and subtracts the error out of the final result.
The effectiveness of noise correction depends on how accurately and repeatably the instrument can measure its own noise relative to the ACP measurement. Although some uncertainty is introduced into the measurement from the noise-correction algorithm, an accurate spectrum analyzer will ensure this uncertainty is generally small compared to the error caused by the noise and distortion (Fig. 2).
Noise correction reduces the total measurement error in two ways. First, noise error is corrected by subtracting it out of the measurement. Second, the effects of the distortion can be minimized by an additional reduction of mixer level because the noise floor is no longer limiting the measurement.
However, Fig. 4 shows that further reduction in mixer level may not be as effective as anticipated depending on the behavior of the analyzer's distortion. In other words, once the analyzer's attenuator (mixer level) is tuned to minimize the measurement uncertainty, analyzer A no longer has the advantage over spectrum analyzer B because the distortion performance is not as good at lower mixer levels.
In short, because of the unexpected behavior of third-order spectral regrowth, a better ACPR specification for one format does not necessarily predict better performance for other ACPR measurements. In addition, the effect of coherence dictates that better minimum ACPR performance may not translate directly into more accurate measurements, especially when noise correction is used.
Taking all of this information into account, a reasonable question is how best to evaluate a spectrum analyzer's ACPR performance. The minimum ACPR dynamic range specification should not be disregarded altogether, but a closer examination should be made to substantiate it.
The First Step
The first step is to see if ACP performance is included in the specifications guide or data sheet for the instrument. ACP performance included in brochures and marketing literature is sometimes not substantiated by solid specifications. If possible, compare the ACPR accuracy specification based on a required measurement level. If the accuracy specification is not available, ask the vendor to supply it for incoherent and coherent scenarios.
It is also beneficial to compare the dynamic-range specifications for other ACP measurements including other formats or test setups. This can indicate the consistency of the analyzer's distortion performance. Checking the instrument's TOI specification may also be a good indicator, in particular the mixer levels and tone spacing to which the TOI specification applies. Running a side-by-side comparison of two instruments making measurements using different formats, measurement bandwidths, channel spacing, and tone spacing, can be revealing as well.
Overall, it is important to remember that the requirement for more dynamic range is really a requirement for better measurement uncertainty and repeatability. It is not which analyzer has the better dynamic-range specification that counts, but which analyzer can make the required measurements more accurately.
- David Kurtz, Philip Stepanek, and Joe Gorin, "Coherent Addition of Intermodulation Distortion in Spectrum Analyzer," IEEE Microwave Theory & Techniques Symposium, Philadelphia, PA, June 8-13, 2003.
- Application Note 150, 1212, "Spectrum Analyzer Basics," Agilent Technologies, Santa Rosa, CA, June 1, 2000.
- Application Note 5966-4008E, "AN 1303 Spectrum Analyzer Measurements and Noise," Agilent Technologies, Santa Rosa, CA, May 2002.