In the electronic warfare milieu, one of the most common RF applications is that of radar systems. Radar, which uses RF energy to determine the range, angle, and/or velocity of objects, detects aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain, among other things. An oscilloscope's demodulation math function is very helpful in analysis of radar signals, so let's look at a couple of examples of how to approach such measurements. Figure 1. Radar pulses are acquired with an RF carrier frequency of 1 GHz. Pulse repetition frequency (PRF), pulse repetition interval (PRI), and transmitter-on time are calculated automatically using parameters 2 through 5.

First, we'll consider a radar pulse signal with an RF carrier frequency of 1 GHz (Figure 1). The waveform contained in the upper grid is the acquired RF pulse, consisting of a series of short bursts separated by long electrical idle times. In this example, several math operators are also in use. The first operator is the demodulation of the input RF signal (math trace F1), which produces the envelope of the amplitude modulation on the input. The next math operator used is the demodulation operator applied to the zoom trace, shown as the pink math trace (F2) superimposed over zoom trace Z1. Trace Z1 is zoomed onto a single RF pulse from the input waveform (the zoomed area appears highlighted in the upper grid). Finally, the lower grid of Figure 1 contains a Fast Fourier Transform (FFT) of the zoom trace (F3 in blue), revealing the frequency spectral content of the RF pulse.

Across the bottom of Figure 1, below the display grids, is an array of measurements taken on the demodulated pulse, including timing parameters of both the carrier and the demodulated signal. Bountiful information can be extracted from an RF signal once it's been demodulated. Note that there are two frequency measurement parameters enabled within the measurement parameter table. The first frequency measurement (P1) operates on the input signal and reports a precise RF carrier frequency of 1.0033 GHz. We’ve applied a second frequency measurement (P2) to the demodulated signal F1, which measures the pulse repetition frequency (PRF) of the radar signal. Note that the measured PRF reported by parameter P2 characterizes the switching rate at which the radio signal is powered on and off, as measured in pulses per second. The 10-kHz PRF of the radar signal is two orders of magnitude lower than the carrier frequency of 1 GHz. Although parameters P1 and P2 are both using the frequency measurement parameter, the frequency information reported by the two parameters describes very different phenomena present in the radar signal.

Continuing with the measurement results of Figure 1, we calculate a period measurement as parameter 3. If we had applied the period measurement to the input signal, it would have simply reported a 1-ns period corresponding to the 1-GHz carrier. However, the period measurement takes on new meaning when applied to the demodulated waveform F1. It now reports the PRI (pulse repetition interval), which is the distance in time between subsequent radar pulses. Parameter 4 measures width, but not that of the carrier’s oscillations. With the width parameter applied to the demodulation waveform, it calculates the duration of the transmitter’s power-on time for each pulse. Lastly, the duty cycle of parameter 5 reports the power-on time of the transmitter in terms of percentage. PRF and PRI, along with pulse width and duty cycle, are defining characteristics of a radar system, and see extensive use in the fields of radar and electronic warfare. In the past, this type of analysis required manual intervention (such as placing cursors by hand to measure the burst time), but can now be performed automatically by redirecting oscilloscope measurement parameters to the demodulated math operator rather than the carrier, providing new insight quickly.

#### Linear Frequency Modulation Chirp

Another example of a radar signal is a linear frequency modulation chirp (Figure 2). The demodulated RF envelope (trace F1) reveals the chirp in the signal, indicating frequency modulation throughout the pulse. The frequency rises in a linear ramp. In this case, the demodulation is from the frequency perspective to extract the modulation profile. The frequency demodulation (trace F2 in pink) plots frequency as a function of time, while the FFT (trace F3 in blue) displays frequency vs. magnitude. Note that the FM scale is 1 MHz/div, and the demodulation is plotted with frequency on the Y-axis and time on the X-axis, where the time scaling of the demodulated chirp is identical to the time scaling of the acquired RF burst. The linearity of the FM chirp is observable from both the smooth ramp shape of the demodulated waveform in the time domain, as well as the flat spectral plateau in the frequency domain.