Publication date: 23 June 2009
Several test methods are well established. Spectrum analyzers, performance network analyzers and high-speed scopes are central in the ongoing effort to advance the state of the art. 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 from this case are examined, along with its strengths and limitations. This method is applicable to array configurations under factory or range conditions.
Consider an array consisting of 64 elements arranged in an 8 by 8 grid. Each element and its associated Transmit/Receive (T/R) module groups into four logical sub-array clusters consisting of 16 elements each (in a 4 by 4 grid).
Each T/R module goes through unit test, which covers every state associated with various combinations of phase and amplitude. Then it is screened for IMD two tones (IP3), noise factor, isolation, etc. Assume that T/R modules that successfully pass have defined phase and amplitude characteristics.
Typically, the next step involves incorporation of the T/R modules, support structure and a RF manifold. Before this assembly step is completed, each element is checked and adjusted as required to reduce or eliminate mutual coupling effects. The often dynamic nature of the interaction compels us to make this measurement in the transmit mode using a pulsed carrier with real world intra-pulse modulation.
Herein are the challenge and the unique opportunity represented by these requirements. Whether your system uses extremely narrow transmitter pulses or modern pulse compression schemes, the result is the same – wider bandwidth. Add to this the need to measure both the phase of and 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.
Let us assume the instantaneous bandwidth (IBW) requirement is ~1 GHz (not uncommon in modern radar), and the phase must be measured with better than +/- 1.0-degree accuracy. As a point of reference, consider that at 450 MHz, 1 degree of phase corresponds to a little over 6 picoseconds, about 1/20 inch, or 1.2mm length of RG-59 coax.)
Prior to getting started, the test system illustrated in Figure 1 is calibrated across the 1 GHz bandwidth of interest. This ensures a “known” amplitude and phase response on each measurement channel. The N5280A down converter, U1065A digitizer and interface test adapter items are a matched set.
The T/R modules are driven at their respective transmitter port from a common RF source. The individual element outputs are sensed by a series of transducers mounted to a XY fixture. The method of coupling is largely dependent on the physical construction of the array.
Waveforms are down-converted to baseband using the new Agilent 4-channel Down Converter (N5280A). Baseband outputs are applied to an Agilent digitizer (U1065A) to be sampled). A suitable trigger initiates a time-correlated sampling on each channel.
Each T/R module amplitude and phase control is set via a control bus. The external RF source, in this case Agilent’s microwave signal generator, is set to drive the four elements under test through a suitable 1-to-4 power splitter.
An accurate relative phase measurement across elements (one element relative to any other) depends primarilly on the stability of the common time base (see below for details) and the total measurement time. Since we’re not measuring pulse-to-pulse phase, error sources like 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, since it’s common to each measurement channel.
To determine the total measurement time, or sample window, we need to consider the maximim frequency of the test pulse and determine the worst case number of periods required to obtain the desired precision. The analysis below assumes a corner case of 1 GHz bandwidth sampled at 2 GS/s.
To ensure plenty of 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, constrainted by the desire to perform the measurement in a single pulse. So the measurement time is effectively the minimum pulse width of the RF source. Faster is better, because it translates to a shorter pulse width. Longer pulse widths do offer improved precision for a given IBW, but this luxury doesn’t always exist.
Relative phase can only be defined for situations where a single common external signal frequency (CEF) is being measured. In the case of a measurement of a frequency with a digitizer, this implies that the sampling clocks used for the different channels must also be at the same sampling frequency (SF).
This is ensured by the extremely close coorelation between U1065A measurement channels. If more than 4 channels are required, which is often the case, multiple U1065A digitizers can be synchronized together in a multi-instrument configuration using the Agilent Acqiris Auto-synchronous (AS) Bus.
The frequency-dependent phase characteristics of the RF chain from the interface test adapter to the digitizer input ports must be characterized and nullified; as we’ll see from the data presented below. The uncertainty of our phase measurements associated with variations in signal amplitude from channel to channel are a minor (second order) effect.
The U1065A digitizer’s internal calibration 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 approximately one order of magnitude greater error than the required precision. But…1. The stability of the time delay or phase mismatch between channels is very high, assuming only small ambient temperature variations (a few °C). This implies that many measurements can be done without having to redo the internal or test system calibrations. 2. The absolute time delay or phase error between channels is compensated for in the calibration. The precision of the calibration, like 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.
A least-square-sine-wave fit is applied to a time series of digitized data covering the measurement period. This includes an implicit assumption that the CEF and the SF are stable over the measurement period. We prefer this technique to the almost equivalent Fourier phase analysis which would require carefully chosen measurement periods.
Thus a four parameter fit should be done to each channel’s data. The fitted frequency should not be allowed to move away from the known input frequency. This constraint may be needed since the number of data points/cycle is low. If desired, the fits could be done with the additional constraint that the frequency be the same for all channels. However, this is not expected to have a significant effect.
A worst case RMS phase error on one cycle (1 nanosecond, 2 points, at 1 GHz and 2 GS/s) is equal to 50 picosecond RMS. This conservative estimate of digitizer performance is equivalent to a phase error of 5% of the cycle or 18° 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). So, to obtain less than a +/-1° RMS error, we need only acquire 18x18 = 324 cycles or 650 points at 2 GS/sec.
• 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 is split into channel 1 & channel 2. The two cables are not certified to have exactly the same length. The sine-fit method is used to calculate the phases – with no constraint on the fitted frequency. The results of -0.4 degrees and +0.5 degrees are shown in Figure 2, where each of the 5,000 points represents a sine-fit for a 1,000-point record.
Note the repeatable 19.4 degree difference between channel 1 and channel 2 measured during the group of calibration measurements, is removed during the final measurements.
As further validation of the digitizer’s stability, the full scale range of RF source was varied from 60% to 90% of the digitizer’s full scale range . The results are outlined below. Note that the mean and standard deviation of the phase difference are neglible, and the delta results in approximately +/- 0.4 degrees.
Varying Input Signal Amplitude:
The data shows that by following a few steps to manage uncertainty in the RF instrumentaion and setup, precise wideband instantaneous phase measurements are achievable. 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 ~ 1k sample points at 2 GS/sec.
This is 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 preceision. Oscilloscopes such as Agilent’s Infiniium scopes would make a great fit for bandwidths greater that 1 GHz. Extending the analysis using vector signal analysis software tools, which both the digitizers and scopes support, is the logical next step to analyzing the details of dynamic intra-pulse coupling phenomena.
Mr. Accolla is a Business Developemnt Engineer with over twenty years 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.
For more information, go to http://www.agilent.com/find/radar.
Mr. Wubbena is a marketing manager with over fifteen years focused on bringing engineering software to market. He has been with Agilent / HP since 1983. Hob is published in over a dozen publications in the US, Europe & Asia and holds three patents relating to displaying instrumentation, system verification and synchronous test. He has a MBA from the University of Denver and a BS in Engineering from the University of Wisconsin.
For more information, go to http://www.agilent.com/find/digitizers.
