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Pulsed signals employed in radar systems are difficult to characterize because the pulse width and pulse repetition frequency are not constant and depend on the radar mode, which effectively eliminates the RF power meter as a tool for calculating pulsed-signal peak power from mean power. In addition, many parameters must be measured in order to effectively characterize a pulsed signal, including peak and average power, pulse shape, and a pulse profile that includes rise time, fall time, pulse width, and pulse period. Other measurements include carrier frequency, occupied spectrum, carrier on/off ratio, pulse repetition frequency, and phase noise. Spectrum analyzers offer engineers the best solution for measuring pulse width, peak power, phase noise, and many other key parameters.

A pulsed signal consists of many spectral lines across a wide frequency range (Figure 1). Depending on the parameters of the pulse and resolution bandwidth (RBW), the results can be displayed three ways. If the RBW is smaller than the spacing of the spectral lines, changing it does not change their measured level. With a narrower bandwidth than the spacing of the first null in the envelope (1/pulse width), an envelope spectrum can be displayed. Finally, if the bandwidth is wider than the null spacing, the entire spectrum falls within the bandwidth, which means that the spectrum of the signal cannot be displayed. With a further increase in bandwidth, the response approaches the time domain function of the pulse. Depending on the pulse parameters, the pulse-desensitization factor can also be calculated, which is the reduction of the level measured within the pulse bandwidth of the spectrum analyzer. In this case, the marker reading plus the desensitization factor equals the peak power.

The RBW value is important for pulsed-signal measurements, because a change in RBW produces changes in the measured level. The pulse-desensitization factor depends on the pulse parameters and the RBW if the bandwidth is greater than the spacing of the spectral lines, and the measured amplitude depends on the number of lines within the bandwidth and the total signal bandwidth. The RBW correction factor is driven by the shape of the filter in the instrument because the shape of the bandwidth reflects the power within the filter bandwidth. If the RBW is too wide, the line or envelope spectrum changes to a time domain spectrum and the impulse response of the RBW filter becomes apparent.

Using a spectrum analyzer in the time domain, it is possible to obtain a direct measurement of pulse width. The peak marker allows measurement of peak power, while the delta markers allow measurement of parameters such as rise time, fall time, pulse-repetition interval, and overshoot. With a wide RBW and video bandwidth (VBW), the spectrum analyzer can track the envelope of the RF pulse so the impulse response of the pulse can be seen. The maximum RBW/VBW limits the spectrum analyzer's capability to measure narrow pulses, and a general rule has long been that for the shortest pulse that can be measured, the pulse width is greater than or equal to 2/RBW.

Radar systems generally use modulation within the RF pulse. Understanding the power characteristics of this modulation is important because radar range is limited by the power available within the pulse. Conversely, a longer pulse length will lead to limited resolution. Modulation formats can range from simple FM (chirp) to complex digital modulation formats, which modern spectrum analyzers can support. Spectrum analyzers can also measure traditional analog modulation in pulse (AM, FM, and phase modulation). Additionally, they can perform analysis functions involving demodulation of many digital modulation formats such as Barker code BPSK modulation within the RF pulse, and pulse-to-pulse phase measurement.

Testing output power is one of the important measurements on radar transmitters, and several different types of measurements can be made. Average power is usually made as a mean-power measurement with a power meter. Another important value is peak power, and if the pulse repetition frequency (PRF) and the pulse width are known, the power of the measured mean power can be calculated.

The waveform of a signal in the time domain is displayed on a spectrum analyzer using a raster-scan CRT display (or an LCD). The number of pixels in these displays in the amplitude axis as well as in the time (or frequency) axis is limited. This leads to limited resolution for both amplitude and frequency or time. To display the full amount of measurement data taken in a sweep, detectors are used to compress the data samples into the allowable number of displayed pixels.

For the measurement of peak power, spectrum analyzers have a peak detector that can display the highest power peak within a given measurement interval. However, for the mean power measurement of amplitude-modulated signals, such as pulse-modulation signals, the peak detector in spectrum analyzers is not appropriate because the peak voltage is not related to the power of the signal. However, these instruments also provide either a sample detector or rms detector.

A sample detector checks the envelope voltage once per measurement point and displays the result, but this can cause total loss of signal information because it is limited to the number of pixels available in the x-axis of the screen. An rms detector samples the envelope signal at the full sample rate of the ADC, and all samples within the range of one pixel are used for the rms-power calculation. As a result, the rms detector displays a greater number of measurement samples than a sample detector.

The rms detector measures the power of the spectrum represented by a pixel by applying the power formula to all samples. For higher repeatability, the number of samples per pixel can be controlled by the sweep time. With longer sweep times, the time interval for the integral of the power of each pixel increases. In the case of pulsed signals, repeatability is dependent on the number of pulses within the pixel. For a smooth, stable rms-trace result, the sweep time must be set to a value long enough to capture several pulses within one pixel. The rms detector calculates the rms value of all samples linearly represented by a single pixel on the screen.

For accurate measurement of peak and mean power on pulse-modulated signals, the instrument's IF bandwidth and ADC converter sampling rate must be high enough so they do not influence the pulse shape. With the 10 MHz resolution bandwidth and 32 MHz sampling rate available in the Rohde & Schwarz (R&S) FSP spectrum analyzer, for example, it is possible to measure pulse-modulated signals with pulse widths as narrow as 500 ns with high accuracy.

For the measurement examples in this article, the R&S SMU signal generator is used to create a simulated radar signal and the output signal is an AM-modulated RF carrier. The broadband AM modulation is generated by an arbitrary waveform generator to create a sequence of pulses with 500 ns pulse width and a 1 kHz PRF. The pulse level is changed over time to simulate the effect of antenna rotation for the long-term average power measurement.

For measuring peak power, the spectrum analyzer must be set to an RBW and VBW wide enough to settle within the pulse width. In this measurement, the RBW and VBW are set to 10 MHz. The spectrum analyzer is set to zero span and displays the power over time. The sweep time is set to a value that allows a single pulse to be investigated. The spectrum analyzer uses a video trigger to show a stable display of the pulse shape. The pulse width is varied, and three measurements are plotted with pulse widths of 100 ns, 200 ns, and 500 ns to investigate the effect of the resolution filter settling time. The three results of a typical peak power measurement are shown in Figure 2.

The blue dotted trace is measured with 500 ns pulse width and shows a flat response on the top of the pulse. The green, dashed trace is measured with a 200 ns pulse width. This value is equal to the calculated settling time. The peak level in this measurement just reaches the value measured with the 500 ns pulse. Marker 1 (T2) is set to the peak value and shows 9.97 dBm. This pulse width is the minimum value that can be accurately measured with the 10 MHz resolution bandwidth. The red, solid trace is measured with a 100 ns pulse width that is shorter than the settling time of the resolution filter. In this plot, the delta marker reading “Delta 2 (T3)” is set to the peak value and shows a loss of about 3 dB vs. the nominal pulse level.

The next step is a measurement of pulse width, which is usually defined as the point at which the signal level is at 50% of its average voltage across the pulse length (Figure 3). This point is 6 dB below the peak level in a logarithmic level grid typically used on a spectrum analyzer. For the measurement of pulse width, a marker is set to 6 dB below the average pulse power on the rising edge, and a delta marker is placed on the point 6 dB below the average power on the falling edge of the pulse.

The level reading of the delta marker in this case should be 0 dB. Because of the limited resolution of the measured points, a small level difference must be accepted. The reading of the delta marker “Delta 2 (T1)” in this measurement shows a pulse width of 508 ns. The accuracy of this measurement is influenced by the ADC converter sampling rate that defines the positions within the trace at which real measurement values are available. In between these points, the trace data is interpolated to generate the displayed points of the trace. The sampling rate of the ADC converter is 32 MHz, leading to measurement samples spaced by 31.25 ns.

The pulse modulation of the output signal of a radar transmitter is spread across a wide bandwidth, which can be seen on a spectrum analyzer as the well-known (sin (x))/x spectrum shape. The individual spectral lines do not allow direct calculation of the peak or mean power. Without knowing modulation parameters like pulse width or PRF, the calculation of power is not possible. For channel power measurement, most modern spectrum analyzers provide software routines for calculating power within given channels. These routines calculate the power by integrating the power represented by the displayed trace pixels within the frequency range of the channel bandwidth.

Measuring mean power requires an rms detector. When evaluating a radar signal, integration over several side lobes allows calculation of mean power, since most of the energy is contained in the main and adjacent side lobes of the (sin (x))/x spectrum. By using a channel bandwidth broad enough to capture the main and several side lobes of the signal, the mean power can be measured.

Figure 4 shows the measurement result of a channel power measurement. The channel bandwidth is set to a value of 10 MHz to capture the main lobe and both adjacent side lobes. The same measurement with 50 MHz channel bandwidth captures a bit more than 10 side lobes on each side (Figure 5). The measurement result of -23.01 dBm channel power agrees with the calculated mean power of the pulse signal. Even the measurement with 10 MHz shows good agreement with the target value, since most of the power is concentrated in the main and the first adjacent side lobes. For this method of measuring mean power, no knowledge of the pulse modulation parameters is necessary, and it is usable for pulse signals with continuously changing pulse parameters.

Modern spectrum analyzers are extremely well suited for making a wide array of power measurements on the pulsed signals employed by radar systems. However, the unique properties of pulsed and modulated pulsed signals make it important to understand how a spectrum analyzer's features can best be used. With this knowledge, these instruments can provide a complete picture of a pulsed signal's characteristics, which can help designers optimize a radar system's performance.

Kay-Uwe Sander is senior application engineer for spectrum analyzers and measurement receivers at Rohde & Schwarz in Munich, Germany. His prior work includes more than 18 years with the company developing spectrum analyzers. He has extensive experience with microwave receivers and headed the development of several Rohde & Schwarz spectrum analyzers.