Instantaneous Phase Measurements of Wideband Active Electronically Scanned Arrays (AESA)
By Bill Accola, Business Development Engineer, Agilent Technologies

The process of aligning, characterizing and testing electronically controlled multi-element radar arrays can pose significant challenges. One example is the creation of larger assemblies that contain hundreds or thousands of individual transmit/receive (T/R) modules. In such cases, mutual coupling effects can play havoc with array behavior under real-world operating conditions. What’s more, the ability to achieve proper antenna patterns for transmission and reception requires the adjustment of individual elements.

Inevitably, multi-channel measurements of instantaneous phase are required but, fortunately, there are several well-established test methods. Many of these utilize spectrum analyzers, performance network analyzers and high-speed scopes—all of which are central to the ongoing effort to advance the state of the art of these measurements.

In a recent case, a novel time-domain approach based on wideband multi-channel high-speed digitizers was considered. The proposed test method and setup of this case are examined here, along with its strengths and limitations. This method is applicable to array configurations tested under either factory or range conditions.

Measuring Phase Using Digital Intra-Pulse Modulation
The unit-under-test is an array consisting of 64 elements arranged in an 8x8 grid. This is broken down into four logical sub-array clusters consisting of 16 elements each in a 4x4 grid of T/R elements.

Each T/R module undergoes unit testing, which covers every state associated with various combinations of phase and amplitude. Screening is then performed for characteristics such as intermodulation distortion (IMD), noise factor and isolation. It is reasonable to assume that any T/R module that passes exhibits the expected phase and amplitude characteristics.

Typically, the next step involves integration of the T/R modules, their support structure and an RF manifold. Before completion of this assembly step, adjustment of each element is required to reduce or eliminate mutual coupling effects. The often dynamic nature of the interaction makes it necessary to perform this measurement in the transmit mode using a pulsed carrier with intra-pulse modulation. These requirements contain both a challenge and a unique opportunity: Whether the system uses extremely narrow transmitter pulses or modern pulse-compression schemes, the result is the same: signals with wider bandwidths. Additionally, it is necessary to measure the phase of the signal in the presence of realistic neighboring-element excitation. The method and apparatus described here have the frequency coverage, bandwidth and time-base stability to address this key measurement challenge.

There are two key assumptions in this example: the instantaneous bandwidth (IBW) requirement is about 1 GHz (common for modern radar) and the required phase accuracy is better than ±1.0 degree. As a point of reference, consider that at 450 MHz, 1 degree of phase corresponds to slightly more than 6 ps, about 0.05 inch, or a 1.2 mm length of RG-59 coax.

Outlining a Pragmatic Test Method
Prior to the first measurement, the test system (Figure 1) is calibrated across the 1 GHz bandwidth of interest. This provides a known amplitude and phase response for each measurement channel. The three main items in the system—downconverter, digitizer and interface test adapter—are a matched set.

A common RF source drives the T/R modules at their respective transmitter ports, and transducers mounted to an XY fixture sense the individual element outputs. The method of coupling is largely dependent on the physical construction of the array.

Waveforms are downconverted to baseband and the baseband outputs are sampled by an Agilent digitizer (U1065A). A trigger initiates time-correlated sampling on each channel.

Amplitude and phase control for each T/R module is set using a control bus. The external RF source is set to drive the four elements-under-test through a 1:4 power splitter.

An accurate relative phase measurement across any two elements—one element relative to any other—depends primarilly on the stability of the common time base (see next section for details) and the total measurement time. Because pulse-to-pulse phase is not being measured, error sources such as pulse-edge definition and the measurement point within each pulse are not a factor. Using this setup, the effect of phase noise can also be ignored because it is common to each measurement channel.

To determine the total measurement time (i.e., sample window) it is necessary to first consider the maximum frequency of the test pulse and then determine the worst-case number of periods required to obtain the desired level of precision. The analysis below assumes a corner case of 1 GHz bandwidth sampled at 2 GSa/s.

To ensure adequate margin, the measurement period should always be a pessimistic estimate of the acquisition time period required to resolve phase with at least the specified precision, constrained by the desire to perform the entire measurement within a single pulse. As a result, the measurement time is effectively the minimum pulse width of the RF source. Faster is better because it equates to a shorter pulse width. Longer pulse widths do offer improved precision for a given IBW; however, this luxury is rare.

Enhancing Time-Base Stability
Relative phase can be defined only for those situations in which a single common external frequency (CEF) signal is being measured. When measuring a frequency with a digitizer, for example, this implies that the sampling clocks used for the individual channels must also be at the same sampling frequency (SF). This can be ensured with extremely close coorelation between the measurement channels—and this is indeed the case with Agilent U1065A digitizers. If more than four channels are required, multiple U1065A digitizers can be synchronized in a multi-instrument configuration using the Agilent Acqiris auto-synchronous (AS) bus.

The frequency-dependent phase characteristics of the RF chain must be characterized and nullified from the interface test adapter to the digitizer input ports (see data presented below). The uncertainty of any phase measurements associated with variations in signal amplitude from channel to channel represent a second-order (minor) effect.

The internal calibration of the U1065A digitizer adjusts the delays of each ADC in each channel. Prior to each group of measurements, the system automatically adjusts for the relative difference in internal propagation time between signal paths for ADC clocks, the input signals leading to the ADC, and internal ADC mismatches. Without this critical step, these uncertainties would combine to contribute errors approximately one full order of magnitude greater than the required precision. Two important points must be noted:

• The stability of the inter-channel time delay or phase mismatch is very high, assuming only small ambient temperature variations (e.g., a few degrees Celsius). This implies that many measurements can be done without having to repeat the internal or test-system calibrations.

• The calibration compensates for the absolute time delay or phase error between channels. The precision of the calibration, as with the measurement itself, is a function of the number of aquired points or measurement time. Increasing the number of acquired points improves the accuracy of the measurement.

Analyzing the Results
A least-squares-sine-wave fit is applied to a time series of digitized data covering the measurement period. (This technique is preferred over the nearly equivalent Fourier phase analysis, which requires carefully chosen measurement periods.) This approach includes an implicit assumption that the CEF and SF are stable over the measurement period. Thus, a four-parameter fit should be performed on data from each channel. The fitted frequency should not be allowed to move away from the known input frequency. This constraint may be necessary because the number of data points per cycle is low. If desired, the fits could be performed with the additional constraint that the frequency be the same for all channels; however, this should not have a significant effect.

A worst-case RMS phase error is equal to 50 ps RMS on one cycle (1 ns, two points, at 1 GHz and 2 GSa/s). This conservative estimate of digitizer performance is equivalent to a phase error of 18 degrees (5% of the cycle) and implies an amplitude change from 0 to 30% of the full amplitude.

Fortunately, the statistical part of the RMS error will improve with the square root of the number of cycles acquired (stochastic process). From this, it is necessary to aquire only 18x18 or 324 cycles (650 points) at 2 GSa/s to achieve an RMS phase error of less than ±1 degree.

Validataing the Test Method
The test configuration was as follows:

• Input frequency: 996.1 MHz
• Sampling Interval: 500 ps
• Number of Samples: 1000
• 5000 iterations per run (the unit is calibrated once per run)

The input signal was split into channel 1 and channel 2; the two cables were not verified as having exactly the same length. The sine-fit method was used to calculate the phase values, with no constraint on the fitted frequency. The results of –0.4 degree and +0.5 degree are shown in Figure 2, where each of the 5,000 points represents a sine-fit for a 1,000-point record. One note: The repeatable 19.4-degree difference between channels 1 and 2 measured during the group of calibration measurements was removed during the final measurements.

As further validation of the digitizer’s stability, the full-scale range of the RF source was varied from 60% to 90% of the digitizer’s full-scale range. The results are outlined in Table 1. Note that the mean and standard deviation values of the phase difference are neglible, and the delta results in approximately ±0.4 degree.

Conclusion
As shown by the data, precise measurements of wideband instantaneous phase can be achieved by applying a few steps that manage uncertainty in the RF instrumentation and the test setup. By using very conservative estimates for noise and performing a simple system alignment to cancel out intrinsic errors, this method can obtain better than ±1 degree relative phase measurement precision up to 1 GHz bandwidth using roughly 1,000 sample points at 2 GSa/s (a 500-ns measurement period). The precision of the sine-fit is proportional to the measurement time, and channel-to-channel amplitude variation has negligable influence. This approach is scalable in number of channels as well as precision.

Oscilloscopes such as Agilent’s 90000 Infiniium scopes are a good choice for bandwidths greater that 1 GHz. When analyzing the details of dynamic intra-pulse coupling phenoma, the next logical step is to extend the analysis using vector signal analysis software, which is compatible with many Agilent digitizers and scopes. More information is available online from www.agilent.com/find/radar and www.agilent.com/find/digitizers.

Author Biography
Bill Accolla is a business developement engineer with over 20 years of experience working with and developing novel embedded data conversion components, circuits and systems in appllications ranging from commercial/industrial to aerospace/defense test and measurement. He has been with Agilent Technologies since 2006. He holds four US and international patents. Bill studied material science and engineering at SUNY StonyBrook.

Agilent Technologies
www.agilent.com
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