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Characterizing distortion is essential when evaluating multicarrier power amplifier (MCPA) performance. Traditional two-tone tests for intermodulation distortion (IMD) or single-carrier adjacent channel power ratio (ACPR) measurements are not sufficient to evaluate MCPAs. These amplifiers must instead be evaluated using multiple carriers as the stimulus, which more realistically simulate conditions the amplifiers will encounter in service. However, the test set-up for multicarrier ACPR measurements typically requires multiple sources along with other components.

As an alternative to multiple carriers, multiple tones with the proper phase relationships can be used to accurately represent multicarrier signals. By using new digital multitone signal generation techniques, and following prudent measurement methodologies, these complex amplifiers can be evaluated more easily, at less cost, and with high repeatability.

In digital communications systems, a digitally modulated signal with the appropriate signal format is used as the stimulus in an amplifier measurement system. ACPR is the ratio between the transmit power in the desired channel and the undesired power it has “splattered” into an adjacent channel.

The power statistics of some digital modulation schemes can vary depending on the signal's configuration. In CDMA systems, for example, the peak-to-average power ratio statistics of the signal vary with the number of code channels, and code channel number assignments. These power statistics can be depicted by the complementary cumulative distribution function (CCDF) curve, which directly affects ACPR measurement results.

Multicarrier signals have more demanding CCDFs than single-carrier signals and require MCPAs with more linear performance. For example, the spectrum measurement and CCDF of a GSM signal with 16 carriers that have random phases and data shows that while the peak-to-average power ratio of a GSM signal is close to zero, the CCDF of a 16-carrier GSM signal approaches a 10 dB peak-to-average power ratio for a 0.001 percent probability.

Since ACPR is influenced by peak-to-average power ratio, single-carrier ACPR measurements cannot provide a realistic measure of the real performance of MCPAs, and, instead, multicarrier signals are needed. However, because of the high cost and the complexity of a multicarrier measurement setup (often requiring several sources, as well as combiners, isolators and band stop filters), multitone IMD measurements are often used as an alternative to multicarrier ACPR measurements.

There are two basic ways to generate multitone signals. The analog approach, which has been widely used, requires one signal source for each tone. Each source can be independent, or all sources can be orchestrated with a controller. Obviously, the latter approach is preferred, since controlling so many sources manually is a frightening prospect.

In contrast, the digital approach generates multiple tones from a single source. The digital technique allows pre-distortion to be used to improve the dynamic range of the source, and provides very repeatable measurements.

There are two possible ways to generate analog signals. In the first, separate analog sources are used and LO drifting of the different sources is leveraged to create the phase randomization necessary to create spectral distribution similar to that of additive white gaussian noise (AWGN). This approach is viable, but it means long measurement times as the carriers slowly drift and build the CCDF curve.

An alternate method is to use analog sources within a system in which the phase can be set to random and the rate of phase change of each tone can be controlled to produce the randomization necessary to obtain an AWGN distribution in a reasonable time. However, this still does not provide a very repeatable signal, and multiple measurements still must be averaged to provide repeatable results.

In contrast, the digital technique employs a digital signal generator in combination with signal studio for enhanced multitone software or signal studio for NPR software, and a spectrum analyzer.

The signal generator can produce thousands of tones with random phase distribution at high spectral density to approximate the CCDF of AWGN or the CCDF of the multicarrier signal of interest. The multitone signal must be configured with a notch that has hundreds of tones that represent one of the channels.

Signals with a lower number of tones can also be used if a random phase set that provides the CCDF of interest (typically close to the CCDF of the multicarrier signal or of AWGN) is carefully chosen.

The test is made by measuring the distortion in the frequency band of interest. Integrating the distortion power over the band of interest basically provides the averaging of all the distortion tones in the notch, which reduces the measurement variance.

Averaging the distortion over several measurements can also be used to further improve repeatability. In addition, since the stimulus signal is generated digitally, and it has a certain period, the measurement is much more repeatable than analog techniques.

An example of the stimulus configuration using the digital approach is shown in Figure 1. In this case, the device under test is a GSM MCPA with 15 carriers (14 carriers with one carrier off in the center) and 600 kHz separation. The signal generator produces 3,000 tones with a tone spacing of 3 kHz over a frequency range of 9 MHz. Each carrier is represented by 200 tones (600 kHz). The notch is created over 600 kHz, so it covers 200 tones, and represents one of the carriers.

The distortion in the notch must be integrated (equivalent to averaging the distortion in the 200 tones), which will reduce the measurement variance. This is because the IMD at a single frequency consists of the vector sum of all the third-order two-tone and three-tone terms at that frequency.

The large number of tones used at the same amplitude makes it possible to assume that for each IMD tone in the notch there will be the same number of third-order two-tone and three-tone terms. However, the phases of the fundamental tones are random, so the third-order terms will add as vectors in a different way for each IMD tone. As a result, their amplitudes will vary. Placing many tones in the notch allows all possible phases to be integrated over frequency.

The second challenge in multitone distortion tests is how to make the measurement with enough dynamic range to avoid measurement uncertainty caused by instrument distortion. The measurement dynamic range is limited by both the source and the signal analyzer, as shown in Figure 2. Although, for the purpose of illustration, the distortion from each device has been placed linearly on top of the distortion of the following device, the distortion from the different devices will not necessarily add in-phase.

Digital signal source generation allows pre-distortion to be used so the dynamic range can be improved by measuring and compensating for the IMD generated by the source and any booster amplifier used.

The measurement is performed in two stages. In the first “calibration” stage, shown in Figure 3, the baseband signal (which has no distortion) and the distortion from the source (generated by the RF section) and booster amplifier are measured.

The attenuation in the signal analyzer is set so its distortion does not contribute to the distortion from the source and booster amplifier it is measuring. The distortion measured by the signal analyzer is used to pre-distort the stimulus signal.

The baseband pre-distorted signal will then consist of the initial wanted tones and 180-degree out-of-phase distortion products intended to cancel the source and booster amplifier distortion. The calibration cycle must be repeated until the required dynamic range (the level of distortion relative to the level of the fundamental) is reached at the output of the booster amplifier or at the output of the source, if no booster amplifier is used. Pre-distortion also corrects for the power levels of each fundamental tone, which enhances the measurement repeatability.

In the measurement phase, shown in Figure 4, the 180-degree out-of-phase distortion products at the output of the source and booster amplifier subtract from the distortion generated by the source and booster amplifier.

Now the resulting stimulus signal has the required dynamic range at the output of the booster amplifier. The attenuation in the spectrum analyzer is set to minimize distortion generated within the analyzer. The effectiveness of calibration is demonstrated in Figure 5, which shows the improvement in the stimulus signal used earlier (3,000 tones, 200 tones in the notch). The spectrum shows part of the notch before and after calibration.

From a spectrum analysis point of view, the best dynamic range will be obtained by choosing the optimum mixer level for the measurement.

The two-tone case is the simplest case to analyze. Figure 6 shows a spectrum analyzer's dynamic range chart example for two-tone IMD. The absolute maximum dynamic range occurs when the IMD is nearly equal to the displayed average noise level (DANL). However, this might not be the best mixer level to use because the analyzer's IMD will be coherent to the DUT's IMD and the DANL will be incoherent. The coherent distortion has a larger effect on measurement uncertainty than incoherent distortion.

To achieve 1 dB of uncertainty (for example, 0.9 dB of error from the spectrum analyzer's generated IMD and 0.44 dB of error from its DANL), the analyzer's IMD must be at least 20 dB below the DUT's IMD, while the DANL must be only about 4 dB below the DUT's IMD.

To calculate the maximum useable dynamic range for 1 dB uncertainty, and the optimum mixer level for 1 dB uncertainty, the IMR and DANL lines must be offset by 20 dB and 4 dB respectively, as shown by the dotted lines in Figure 6. The coherence-versus-incoherence phenomenon moves the optimum mixer level to the left (lower mixer level) and effectively reduces the available dynamic range.

To ensure to maximum dynamic range, a good operating point is to have an error budget in which 90 percent of the error is allocated to the coherent distortion (such as the spectrum analyzer's IMD) and the remainder of the error budget is allocated to the incoherent distortion (such as the spectrum analyzer's DANL). The contribution to dynamic range from the analyzer's phase noise might also be of concern if the measurement is made at frequency offsets close to the main tones.

The analyzer's dynamic range chart for a multitone IMD measurement can be built from the two-tone measurement dynamic range chart (Figure 7).

An offset must be added to the two-tone IMR line (IMR₂) to obtain the IMR line for N tones (IMR_N). The offset is the ratio between the n-tone IMD power at the frequency of interest and the two-tone IMD power.

For example, for the three-tone case (assuming independent and random phases with uniform distribution), the power level of the IMD at the frequencies immediately above and below the main tones is five times (7 dB) greater than the two-tone case.

Therefore, an offset of 7 dB should be added to the two-tone IMR line to obtain the three-tone IMR line for the IMD at the frequency immediately above or below the frequencies of the main tones.

The phase relationship among the tones will affect the peak-to-average power ratio and offset level. In general, the higher the peak-to-average power ratio, the higher the IMD, and, therefore, the higher the offset for the IMR line.

If the frequency of interest is not a discrete frequency offset, but it has a certain bandwidth, the offset will be a function not only of the frequency offset, but also of the bandwidth over which the distortion power needs to be integrated.

The resulting offset could also be negative (the IMR line could be below the two-tone IMR line) if the IMD integration bandwidth falls out of the area with the highest distortion. When integrating across a bandwidth, the DANL line will increase by about 2.5 dB plus 10 times the log of the ratio of the bandwidth of integration to the noise bandwidth in which DANL is measured.

As is probably obvious from discussions in this article, the designer faced with characterizing the performance of an MCPA has a considerably more difficult task than when characterizing single-channel amplifiers used in the past.

Not only are simple two-tone tests inadequate, but the choice of the signal used to stimulate the amplifier under test must simulate the conditions the amplifier will experience in service as accurately as possible. Two-tone CW signals used for this purpose have proven to deliver results that, in some cases, allow amplifiers to be deployed that simply cannot perform adequately when stressed.

Generating multicarrier signals or multiple tones, when performed with multiple signal sources, can be expensive and produce a test system with a maze of cables and connections that must be switched. Generating multitone signals digitally dramatically reduces this complexity, allows pre-distortion to be used to improve dynamic range, enables an appropriate time-domain profile to be established, and creates an overall stimulus environment that is extremely realistic and repeatable, as well as highly configurable.

Marta Iglesias holds a B.S.E.E. degree from the Universitat Politecnica de Catalunya in Spain. She has performed technical support for RF and microwave spectrum analyzers, and currently is a wireless applications marketing engineer for Agilent Technologies Inc. (www.agilent.com), where she is responsible for understanding the test needs of the wireless communications industry. She can be reached at marta_iglesias@agilent.com.

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