Evaluating the performance of an advanced radar system depends upon the capabilities of both the operator and the test equipment. The test gear must be properly specified to achieve accurate results for a number of key measurements, including rise time, frequency error estimation, and pulse-to-pulse phase measurements. Matching the capabilities of the test equipment to the expected performance of the radar system can ensure accurate and repeatable results.

One of the key measurements required for evaluating an advanced radar system is pulse rise time. The short-duration pulses typically used in radar systems occupy extremely wide signal bandwidths, requiring test equipment that can process that bandwidth. Essentially, the narrower the pulse, the wider the RF bandwidth must be to avoid distortion of the pulse. Wider RF bandwidths, however, bring with them increased noise power, adversely affecting sensitivity to small signals. For each application, one must consider the correct balance between measurement bandwidth, signal fidelity, and noise performance.

To illustrate the effect of measurement bandwidth, examine the differences in rise time between a 110- MHz measurement bandwidth and one with 55-MHz bandwidth (Fig. 1). For this example, a pulse with less than 3-ns rise time was created, so that the system rise time of the test instrument, a real-time spectrum analyzer (RTSA), could be seen. The resultant 7-ns measurement (top of Fig. 1) is due primarily to the system rise time of the RTSA. However, some overshoot can be seen in this measurement, a result of the flat-top bandpass filter used in the RTSA. Reducing the measurement bandwidth to 55 MHz with an internal, user-selected Gaussian filter (bottom) reduces the overshoot, but increases the pulse's measured rise time.

The overshoot present in the 110- MHz measurement bandwidth is due to a combination of overshoot in both the pulse and the measurement-path. In this case, the measurement-path consists primarily of the filter in the RTSA's intermediate-frequency (IF) section, combined with the digital filters used to correct for the amplitude and phase errors in the instrument. The combination of these filters not only produces very good amplitude flatness and phase linearity in the 110 MHz measurement bandwidth, but also results in pre-shoot and overshoot ringing in the measurement. For this reason, a set of Gaussian filters can be applied to the measurement path to control pre-shoot and overshoot effects.

Gaussian filters with as much as 55 MHz 3 dB bandwidth can be applied in certain RTSA models. When the Gaussian filter shape is combined with that of the IF and digital correction filters, the resultant filter has a 55 MHz bandwidth with a Gaussian response to approximately 12 dB. This combination of filters provides predictable phase and amplitude characteristics in the passband and more significant attenuation outside of the passband.

In order to accurately measure the characteristics of a pulse train, the frequency of the pulses must be known. In many cases, a system reference signal may be available that can be used to lock the reference of the RTSA to the device-under-test (DUT) reference. In this case, the manually entered frequency error is zero, because the measurement tool and the DUT references are locked together. When the pulse frequency is not precisely known, a RTSA uses three selectable methods of frequency error estimation to determine the difference between the center frequency of the RTSA and the pulse frequency. The method, as selected by the user, depends upon the frequency and phase characteristics of the pulse.

The frequency and phase characteristics of radar pulses may be defined as having constant phase, changing phase, or linear frequency chirp behavior. In each case, the phase of the pulses is estimated over time in order to determine any phase difference from the measurement phase and to use this difference to estimate the frequency change or error between the pulse train and the instrument's center frequency. The frequency of a pulsed signal with constant phase (such as a pulsemodulating a CW signal) can be estimated by determining the phase of each pulse relative to the phase of a reference signal. Signal-processing algorithms built into an RTSA use an in-phase/quadrature (I/Q) representation of the signal to be measured. The phase is calculated from the I/Q waveform where:

Phase (φ) = arctan(Q/I)

The calculated phase of each pulse is then used to calculate the slope of the phase difference vs. time, and the resultant frequency error relative to the analyzer frequency is obtained (Fig. 2). To minimize overshoot and ringing effects caused by filtering when determining the phase of the pulse, I and Q samples are taken from the center 50 percent of each pulse.

For signals that have constant frequency with changing phase (such as created by turning a fixed-frequency oscillator on and off), there is no simple phase relationship between pulses. That is, while the frequency of each pulse is the same, the phase of each pulse may vary. In this case, the frequency of each pulse must be determined. By determining the phase slope of each pulse relative to the reference signal, it is possible to calculate the frequency error of each pulse. The center 50 percent of each pulse's on-time is used for this calculation. The resulting frequency values for all pulses in the analysis period are then averaged together to determine frequency error from the measurement frequency.

For signals that contain a repeating linear frequency-modulated (FM) chirp, the phase changes in a parabolic fashion over the duration of the pulse's on-time. In this case, an estimation of the frequency error can be made by fitting a line tangent to each of the parabolic phase calculations.

Pulse-to-pulse phase measurements are frequently an important metric for advanced radar systems. Along with the need to accurately measure the pulse frequency, pulse-to-pulse phase measurement accuracy is dependent on four principle factors: phase noise, total measurement time, pulse edge definition and measurement point, and signal-to-noise ratio (SNR). The phase noise from both the signal under test and the measurement instrument can affect measurement accuracy. The amount of uncertainty created by phase noise is determined by the total measurement time. For example, a measurement time of 1 ms will result in the integrated phase noise limit of integration beginning at approximately a 1 kHz offset from the carrier and extending out to the measurement bandwidth.

Greater pulse-to-pulse measurement stability can be obtained by minimizing the time between the reference pulse and the measured pulse. Another important factor in accurate phase measurements is the estimation of where the rising edge of the pulse actually begins and how long it takes for phase ringing to diminish. Pulseto- pulse phase measurements of the RF carrier are made at a defined offset from the rising edge of the pulse. Poorly defined or poorly measured rising edges can cause inconsistent offsets from the reference pulse and degrade accuracy. The use of interpolation methods when measuring rising and falling edges can help to minimize this uncertainty.

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It is useful to specify the measurement point relative to the rising edge of the pulse. To account for ringing, pulse-to-pulse phase measurement accuracy is specified for any point greater than t = 10/ (measurement bandwidth) from either the rising or falling edge of the pulse. For example, pulse-to-pulse phase measurements using a 55 MHz measurement filter are within specifications for measurement points greater than 10/(55 x 106), or approximately 182 ns from the rising or falling edge of the pulse. Figure 3 shows a pulse trace view on the RTSA, illustrating placement of the phase measurement point.

Finally, the SNR is an important factor in accurate pulse-to-pulse measurements. A high-end RTSA's typical pulse-to-pulse phase measurement uncertainty at 2 GHz with a 20 MHz bandwidth is 1.7 deg., dropping to 2.0 deg. for a 110 MHz bandwidth. At 10 GHz, the accuracy for a 20 MHz bandwidth is 3.2 deg., increasing to 5.0 deg. for a 110 MHz bandwidth. This increase in uncertainty is primarily due to the higher phase noise and noise level present in the analyzer at higher frequencies.

TROUBLESHOOTING RADARS
Advanced radar systems increasingly employ digital processing, making them more difficult to troubleshoot. With increasing bandwidth and speed capabilities offered by high-performance field-programmable gate arrays (FPGAs), digital-to-analog converters (DACs), and analog-to-digital converters (ADCs), modern radar systems are replacing traditional analog triple-frequency-conversion radar front ends with digitally implemented filtering, modulation, signal processing, and upconversion to IF. These digital signal paths have reduced the number of test points available, so that the designer must get the most information possible from each point in the system. Here are some points to consider when using an advanced RTSA to diagnosis complex radar issues.

Determining basic pulsed radar operating parameters is greatly simplified with an automated test suite (such as the pulse measurement capability of Option 20 Advanced Signal Analysis for the RSA6100A series of RTSAs from Tektronix). To demonstrate basic pulsed radar characterization with such a test solution, a typical pulse train was captured and a selection of measurements performed, as shown in the Pulse Table of Fig. 4. As it shows, each measured pulse is numbered, with each selected measurement for the pulse listed in one row. In the example of Fig. 4, some of the displayed measurements are shown in a zoom view for ease of readability. This view of the measurements can be used to get an overview of all of the signal characteristics to quickly discover large differences between pulses that occur over the analysis period. The pulse trace display is used for detailed examination of any pulse present in the pulse results table. Any measurement on a selected pulse can be examined in the pulse view, and a user can automatically scale the measurement to zoom in on the detail.

The pulse statistics display performs a combined analysis on a series of pulses, offering either a measurement trend view or a Fast Fourier Transform (FFT) of measurement results. The pulse measurement trend view graphs a measurement result for each pulse, versus its pulse number, automatically eliminating the variable dead time between pulses. This enables easy inspection of the trend of a measurement over time.

Unintentional phase or amplitude modulation of radar pulses can be a problem. For example, insufficiently filtered aircraft power supplies that convert 400 Hz AC power to a highvoltage DC power source can unintentionally modulate the microwave power amplifier used in the radar system's transmitter, causing pulse amplitude variations that occur at the rate of the AC power source. Quickly isolating a power supply modulation problem from a myriad of other possibilities can be difficult. With a conventional swept-tuned spectrum analyzer, it would be necessary to try to discern low-level narrow-band modulation on a broadband pulse in the frequency domain. But the RTSA's pulse statistics view can greatly simplify the task of finding 400 Hz modulation of a pulse spectrum that is several megahertz wide.

Figure 5 shows a trend of averageon power measurements, scaled to reveal small variations in the pulseto- pulse amplitude. In this example, the variations are very small, about 0.2 dB peak-to-peak, and might even go unnoticed unless they were plotted as a trend. These amplitude variations are also periodic in nature. It is possible to detect that there is a dominant frequency to these variations, but the rate of these variations must still be determined.

Conversion of the trend data to the frequency domain allows easy viewing of the nature of the modulation and hence key information about its source. The RTSA's spectral view can show if the modulation occurs at a single frequency or contains several frequencies. The RTSA is used to perform a FFT to the trend of measurement results, providing a spectral view of the amplitude trend data that clearly shows the 400 Hz (powersupply) modulation. The ability of the pulse measurement suite to convert time-domain statistical analyses to the frequency domain provides a useful capability to discover and isolate problems from pulsed signals.

Elaborate test systems are usually required to characterize complex radar signals. The transient nature of pulsed radar signals, along with liberal use of modern pulse compression schemes, makes such characterization difficult even with sophisiticae RF/ microwave test equipment. In addition, achieving high measurement accuracy usually calls for measurement equipment with exceptional performance. Fortunately, the frequency coverage, bandwidth, and dynamic range of RTSAs along with advanced measurement algorithms help address many of the key measurement challenges faced by radar designers.