The use of a spectrum analyzer for pulse measurements requires a good knowledge and understanding of the parameters of the pulsed signal, as well as the operation of the spectrum analyzer to make valid and correct measurements. One of the main objectives of pulsed measurement techniques has been the precise measurement of radar signals. Advances in pulse type and pulse train information may improve the use of radar; however these advances will increase the complexity of the measures. Automatic pulse measurements have been introduced in modern spectrum analyzers to greatly simplify the challenge of these new measurements. This article shows pulse measurements using a typical spectrum analyzer with a traditional sweep architecture, discusses some of the advantages in radar waveforms, and reviews some important considerations to reduce measurement uncertainty on these pulsed signal analyzer architectures. more modern spectrum.
Basic pulse measurements
The main advantage of using a spectrum analyzer is that it can be used to analyze frequency-dependent power components with a wide dynamic range. Simple measurements, such as analyzing the symmetry of the pulse spectrum, can validate the radar transmitter. An asymmetric spectrum can lose power, generate unwanted spurious emissions, and degrade overall radar performance.
When making measurements using a spectrum analyzer, particularly on signals with short duty cycles, one needs to be familiar with the expected pulse parameters and important spectrum analyzer settings such as resolution filter (RBW). Span, and the sweep time to display the results.
Figure 1 shows the traditional sweep architecture of a spectrum analyzer. A signal is filtered and converted to an IF intermediate frequency, where various resolution and video filters are applied to the signal while the local oscillator sweeps a span of frequencies. The resulting frequency and energy are displayed on the screen.
Because a pulsed signal is not constantly present, the energy will not completely “fill” the spectrum in a single sweep. Figure 2 shows the spectrum characteristics of a pulsed RF signal with pulse width T and pulse repetition interval t. The amplitude of the spectral lines is determined by the envelope curve over the center frequency f0.
When measuring the spectrum using a spectrum analyzer, it is possible to display the individual spectral lines or the envelope curve depending on the settings of the measuring instrument. The Resolution Bandwidth (RBW) should be set to a value considerably less than the Pulse Repetition Frequency (= 1/T). The line spacing is equal to the pulse period (pulse repetition interval) and is independent of the sweep time setting on the analyzer. The height of the spectral lines is also independent of the RBW. The highest spectral line shown in the spectrum is lower than the actual pulse amplitude due to the pulse desensitization factor (PDF). The PDF depends on the ratio of the pulse width between the period:
PDF = 20 * log(t/T)
Using the spectrum, the power of the pulsed signal can be calculated by placing a marker on the highest spectral line (as shown in Figure 3):
Peak Power = marker reading – PDF = marker reading – 20*log(t/T)
When using the peak detection method, if the RBW of the analyzer increases such that it is greater than the reciprocal of the pulse period (but less than the reciprocal of the pulse width), the spectrum analyzer will display the spectrum envelope. The envelope amplitude increases linearly with the RBW, so doubling the RBW produces a 6dB increase in amplitude.
By continuing to increase the RBW to a value greater than the reciprocal of the pulse width, the spectrum analyzer can approximate the peak power of the pulsed signal within the resolution bandwidth limitations of the traditional spectrum analyzer.
To demonstrate this limitation, Figure 4 shows the capture at zero span of three different pulse widths using a 10MHz RBW resolution filter. While pulse widths of 500 and 200 ns durations are accurately represented, when the signal pulse width decreases to 100 ns, the peak amplitude becomes smaller due to the bandwidth of the resolution filter. Since the pulse width is shorter, the limitations of the traditional spectrum analyzer have an effect on the measurement uncertainty.
Radar complexity increase
Many types of modern radar have advantages beyond traditional range detection functions to improve resolution, mitigate performance limitations, and improve functionality. The impact of these types of modern radars increases the complexity and performance requirements of the traditional spectrum analyzer. Pulse Doppler radar provides radial velocity information about the target in addition to range and direction. Using a typical coherent transmitter and receiver, velocity information can be extracted from pulse-to-pulse variations in the received signal. The pulse-to-pulse transmitter stability verification test is increasingly demanded in the operation of measurement equipment as phase information, not contemplated in a traditional spectrum analyzer. Pulse compression radars are used to improve range resolution. Pulse Frequency Modulation (FMOP) and Pulse Phase Modulation (PMOP) can substantially improve the ability to resolve multiple targets at long ranges. A 2GHz bandwidth FM chirp can resolve targets less than 10cm apart. Some of the typical FMOP/PMOP techniques include: Linear Frequency Modulation (FM Chirp); nonlinear frequency modulation; coded pulse phase modulation (eg Barker codes); and time-frequency coded modulation. Not only doing pulse compression tends to increase the need for analysis bandwidths with reduced pulse widths and fast rise times, but also to analyze transmitter stability requires different types of waveform analysis not available in traditional spectrum analyzers. To collect the necessary phase information, a baseband IQ conversion is required to perform the type of analysis necessary to validate this type of radar transmitters.
An example of an advanced radar technique might be the use of a stepped pulse repetition interval (PRI). This technique is used in most modern radars to overcome the limitations of a constant PRI. Constant PRI frequency radars are susceptible to jamming and false target identification due to double echo. Figure 5 shows the analysis of a multi-rate PRF transmitter. It is not only the PRI that varies in this case, but also the pulse widths. This type of analysis in a traditional spectrum analyzer would not be possible as well as many of the measurements described above that require a constant and stable PRI.
Modern spectrum analyzer architecture for advanced radar analysis
Performing analysis of modern radar signals requires a spectrum analyzer architecture that goes beyond the traditional swept spectrum analyzer. Modern spectrum analyzers incorporate an FFT acquisition or vector signal analysis mode. This class of spectrum analyzers is also called a signal analyzer. Real-time spectrum analyzers also use a similar acquisition architecture.
As shown in Figure 6, the vector signal analyzer has a front-end similar to that of a traditional swept spectrum analyzer with filtering and frequency conversion. However, once the signal has been placed at an IF frequency, the full spectrum of the converted signal is digitized by an A/D converter and stored in memory. The time sampled data can then be converted using FFT and waveform processing where phase, spectrum and time information can be retained for analysis. With the vector signal analyzer, the analysis bandwidth is not limited by the maximum resolution bandwidth like the sweep analyzer, but by the maximum IF bandwidth. IF bandwidth is defined by the A/D converter, sample rate, and associated IF filtering. Typical vector signal analyzers have bandwidths of 40 MHz, 80 MHz, and up to 160 MHz to enable analysis of much faster pulse widths with a higher degree of certainty as shown in Figure 7.
Acquisitions are captured without loss of information in memory and then FFT and waveform analysis is performed on the acquired signals.
Important considerations for pulse-pulse measurements
The representation of information in individual pulses and pulse trend information requires advanced analysis in modern spectrum analyzers. Figure 8 shows a single pulse analysis of a linear FM chirp. The display shows the pulse train for multiple pulses and tabulated analysis (green) for individual pulses. The individual pulse analysis (blue) for the linear FM chirp is expressed in Frequency, Amplitude, and Phase vs. Time using Pulse Analysis.
Define pulse parameters
As shown in Figure 9, the vector signal analyzer provides a number of time domain displays and measurement results that are not available on a traditional swept spectrum analyzer. To understand the importance of the measurement uncertainty associated with the results, it is important to define the pulse parameters. Rise and fall times are typically measured between 10-90% excluding the “Overshoot” and “Droop” parameters associated with the pulse. The pulse width is typically measured at 50% rising and falling edge measured in linear units. The selection of the trigger point and the phase reference point for pulse-to-pulse measurements have a direct relationship on the measurement results.
When measuring the pulse-to-pulse performance of a radar transmitter, it is important to understand the variables that can affect the measurement system uncertainty for accurate Doppler measurements, including:
Signal to Noise Ratio
Signal Bandwidth and Filtering
Reference clock (or time base) stability and trigger Jitter.
Phase Noise Buildup
The same variables can also contribute to the uncertainty in the signal generator when analyzing the receiver circuit and the Doppler measurement uncertainty.
Analysis of the variables
Signal to Noise Ratio:
As a general rule, the higher the signal-to-noise ratio, the lower the uncertainty due to the noise contribution. While this is not typical when measuring a stable pulse, the uncertainty can increase if the pulse train goes into a power ramp mode of operation. A power ramp may also be observed when making a measurement over the air, if the measurement is located in a fixed position while the radar antenna rotates (eg Air Traffic Control Radar). It is also important what is related to the measurement bandwidth of the instrument with respect to the bandwidth of the signal of interest. Too much bandwidth can increase the noise power relative to the signal.
Signal Bandwidth and Filtering:
The bandwidth of the IF acquisition system must be sufficient to accurately represent the rise time of the pulsed signal. As previously mentioned, too high an IF bandwidth can increase noise. However, if the bandwidth is artificially reduced to filter out the pulse width of the signal, pulse-to-pulse measurements could be artificially reduced by measurement instrumentation. Applying filtering to prevent the overshoot parameter of the rising and falling edges of the pulse can substantially improve the reproducibility of the signal. It is important that the selection of the pulse-to-pulse measurement point, or the adjustment of the measurement points, is long enough to detect the edges of the pulse.
Applying a Gaussian filter to smooth the pulse can improve the pulse-to-pulse measurement uncertainty. It must be taken into account that the filtering used to make the pulse measurement stable will have an impact on other measurements such as rise time and spectrum occupancy. Parameter settings should be ensured for each measurement to ensure reproducibility and precision of results.
Reference Clock (Time Base) Stability and Trigger Jitter:
When measuring a radar signal, it is important to link the time base of the radar synthesizer to the measurement equipment. However, this is not always possible, especially when measuring signals over the air. Some radars, such as "bistatic" or "multistatic" have receivers located at a great distance from the transmitter and require synchronization using the reference clock (GPS). Between the short-term stability of the clock and the errors associated with trigger circuit synthesis, phase ambiguity can give rise to pulse-to-pulse errors.
Phase Noise Accumulation:
The impact of phase noise on the measurement uncertainty is directly proportional to the measurement time and the phase noise performance at different frequency offsets. Phase noise accumulation occurs in the interval between the reference measurement pulse and the pulse to be measured. The longer the period, the greater the accumulation of phase noise. Therefore, the phase noise performance at nearby frequency offsets may be one of the most important variables in pulse-pulse measurements.
Summary
Simple radar signals have traditionally been measured using swept spectrum analyzers. However, modern radar signals that now include phase and frequency modulation techniques or stepped PRI cannot use a simple architecture to obtain meaningful results. Modern spectrum analyzer architectures, such as the vector signal analyzer, are required to make measurements of advanced pulsed radar signals.
It is important to select the vector signal analyzer with sufficient bandwidth to achieve reproducible results.
Vector signal analyzers, such as the Rohde & Schwarz R&S FSW with Option K6, are now available with advanced signal analysis software to provide accurate scalar and vector measurements of pulsed signals.
