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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