Pulse repetition frequency and pulse width sensitivity test to pulse phase noise

1 Introduction

Ultra-low phase noise is a common requirement for radar test equipment. In the field of aviation and aerospace, radar signals are mostly pulse systems, and pulse width and pulse repetition frequency directly affect the resolution of radar ranging and speed measurement. For example, early warning radars require signals with long pulse width and low pulse repetition frequency; while pulse Doppler radars (PD radars) require signals with narrow pulse width and high pulse repetition frequency. How to accurately measure the phase noise of pulse signals with different pulse widths and different pulse repetition frequencies is becoming more and more urgent. In the past, the pulse signal phase noise test system was very complex and expensive, and the reference pulse source and the measured source needed to be synchronized. In addition, the ability to measure phase noise with different pulse widths and different pulse repetition frequencies was limited by the number of PRF filters. Now this situation has become history. The R&S FSWP with the R&S FSWP-K4 option can complete these measurements with one click. It can record signals, automatically calculate all parameters such as pulse repetition frequency and pulse width, and automatically build PRF digital filters; demodulate signals and display phase noise and amplitude noise. The maximum offset frequency range and measurement calibration are automatically performed, and engineers do not need to worry about whether the correct parameters are set correctly. In any case, engineers can define pulse gate parameters to prevent the transient characteristics of the pulse edge from affecting the test results and thus improve sensitivity. It is also possible to use cross-correlation techniques to measure signal sources with good phase noise in order to compensate for the reduction in signal sensitivity due to pulse modulation.

The desired improvement in dynamic range is described in Equation 1 below:

ΔL = 5·log(n) [1]

ΔL: Improvement in phase noise sensitivity through cross-correlation technique (in dB)

n: number of cross-correlations

For example, if the number of cross-correlations is 10, the phase noise sensitivity is improved by 5 dB.

2. Theoretical analysis

The general method of generating a pulse modulated signal is to use a signal source to continuously perform amplitude modulation on the carrier and pulse waveform. Before modulation, several standard pulse terms are introduced. Figure 1 is the waveform of a pulse signal, and Table 1 shows several main parameters of the pulse signal.

Figure 1. Pulse waveform

Table 1. Standard terminology for pulse signals

In addition to knowing the time domain characteristics of the pulse signal, the frequency domain characteristics of the pulse signal are also very important. From the principle of amplitude modulation, we know that the generation of amplitude modulated signals is achieved by multiplying the carrier and the modulating signal, and the multiplication of the signal in the time domain is equal to the convolution of the signal in the frequency domain. When the signal is pulse modulated, the frequency spectrum density of the signal will change. Figure 2 is the frequency spectrum after pulse modulation. The frequency spectrum characteristics are discrete spectra with equal intervals according to the pulse repetition frequency PRF (pulse RepeTITIon Frequency), and the spectrum shape is a sinx/x lattice function. The reciprocal of the pulse width is the position of the zero crossing point.

Figure 2. Power spectrum of continuous wave after pulse modulation