key word : pulse phase noise, pulse width, pulse repetition frequency, digital IQ phase demodulation
abstract In the measurement of pulse signal phase noise using digital phase demodulation and amplitude demodulation technology, pulse width and pulse repetition frequency will affect the test results. This paper first introduces the generation mechanism and characteristics of the pulse signal, and combines the principle of FSWP digital phase demodulation, and then gives the impact analysis of the pulse phase noise test results.
1 Introduction
Ultra low phase noise is a general requirement for radar test equipment. In the aviation and aerospace fields, radar signals are mostly pulse systems, and pulse width and pulse repetition rate directly affect the resolution of radar ranging and speed measurement. For example, early warning radar needs signals with long pulse width and low pulse repetition rate; However, pulse Doppler radar (PD radar) needs signals with narrow pulse width and high pulse repetition rate. How to accurately measure the phase noise of pulse signal under different pulse width and pulse repetition frequency becomes more and more urgent. In the past, the pulse signal phase noise testing system was very complex and expensive, and needed to synchronize the reference pulse source and the measured source. In addition, the ability to measure phase noise under different pulse widths and pulse repetition rates was limited by the number of PRF filters. Now this situation has become a 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 rate and pulse width, and automatically build a PRF digital filter; Demodulate the signal and display the phase noise and amplitude noise. The maximum offset frequency range and measurement calibration are carried out automatically. Engineers do not need to worry about whether the correct parameters are set correctly. In any case, engineers can define the parameters of the pulse gate to avoid the impact of the transient characteristics of the pulse edge on the test results and thus improve the sensitivity. The cross correlation technique can also be used to measure the signal source with better phase noise in order to compensate for the decrease in signal sensitivity caused by pulse modulation.
The following equation 1 describes the expected increase in the dynamic range:
ΔL = 5 ∙ log(n) [1]
Δ L: improvement of phase noise sensitivity through cross correlation technology (unit: dB)
n: Number of cross-correlation
For example, if the number of cross-correlation is 10, the sensitivity of phase noise is increased by 5dB
2. Theoretical analysis
The general method to generate pulse modulated signals is to use signal sources to continuously amplitude modulate the carrier and pulse waveforms. Before modulation, first introduce the standard terms of several pulses. Figure 1 is the waveform of the pulse signal, and Table 1 shows several main parameters of the pulse signal.
Fig. 1 Pulse waveform
Table 1 Standard Terminology of Pulse Signal
In addition to knowing the time-domain characteristics of the pulse signal, the frequency-domain characteristics of the pulse signal are also very important. According to the amplitude modulation principle, the generation of the amplitude modulation signal is realized by multiplying the carrier wave and the modulation 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 shows the frequency spectrum after pulse modulation. The frequency spectrum characteristic is a discrete spectrum with equal interval according to the pulse repetition frequency (PRF), and the spectrum shape is a sinx/x Singer function. The reciprocal of pulse width is the position of zero crossing.
Fig. 2 Power spectrum of continuous wave after pulse modulation
2.1 Influence of pulse width and pulse repetition frequency on phase noise
The horizontal position in the figure below shows the change of pulse repetition frequency (PRF) while changing pulse width (τ) pulse frequency spectrum. The vertical position shows the change of pulse width (τ) while changing pulse repetition frequency (PRF) pulse frequency spectrum.
Figure 3 Sideband fc Spectrum with Phase Noise
It can be seen from Figure 3 that the pulse modulation carrier frequency spectrum has the following characteristics: when the pulse width is fixed, the noise of fc is inversely proportional to the pulse repetition frequency (PRF) (low pulse repetition frequency corresponds to high spectral line density and noise, on the contrary, high pulse repetition frequency reduces the noise of fc). In addition, when the pulse repetition frequency is constant, increasing the pulse duty cycle will reduce the noise of fc, which is due to the narrowing of the pulse envelope and the reduction of the spectral line density. As for the noise increase of fc, assuming that the noise contributions of all spectral lines are the same, the fc noise will increase in the worst case:
Noise change ≤ Log ten (The number of spectral lines is calculated from the first zero crossing in sinx/x)
2.2 Automatic detection of FSWP pulse signal and automatic construction of PRF filter
Figure 4 shows the signal flow of FSWP, and the shaded part shows the digital processing part of pulse signal. FSWP can automatically detect the pulse signal through the pulse detection module, generate a mark at the beginning of the pulse and generate a pulse gate to feed back to the pulse hold measurement module. When the pulse is in the OFF state, the pulse hold measurement module will lock the pulse signal, thus eliminating the noise of all plates during the pulse off period and improving the dynamic range of the system. Next is the digital filter module, which is a digital low-pass filter in FPGA. Its function is to filter out the components whose frequency is greater than PRF/2. Compared with the traditional method, this is one of the main advantages of FSWP in measuring pulse phase noise. In the traditional phase detector method for measuring pulse phase noise, there is no suitable PRF filter, It is usually necessary to manually connect different PRF filters to measure the phase noise of pulse signals, but FSWP can automatically build appropriate filters to greatly simplify the measurement process.
Another advantage of FSWP pulse detection and processing based on digital signal is that it avoids the transient interference generated by pulse switch. FSWP generates a pulse gate at the beginning of pulse, and the real measurement starts in a very clean area near the pulse center.
Figure 5 FSWP pulse signal setting
The setting of the pulse signal is shown in Figure 5. The blue strip area below the pulse signal represents the delay time starting from the pulse gate, and the pulse gate is represented by the purple strip area, which is the area where the FSWP really starts to measure the pulse phase noise. Generally, the width of the pulse gate is 75% of the total pulse width automatically detected, Advanced users can test the pulse phase noise in a specific pulse area by adjusting the width and delay of the pulse gate.
3 Test verification
First, connect the pulse signal source and FSWP as shown in Figure 6, set the carrier frequency of the pulse source to 1GHz, pulse repetition period to 100us, and pulse width to 10us.
Figure 6 Connection diagram of FSWP measurement pulse phase noise
Press the (MEAS CONFIG) button on the front panel of the FSWP, select the (Pulsed Phase Noise) menu from the pop-up dialog box, and the FSWP enters the pulse phase noise measurement mode.
3.1 Change the pulse repetition frequency while keeping the pulse width unchanged
When the pulse width is fixed, increasing the pulse repetition rate reduces the noise of fc, which is due to the decrease of spectral line density in the pulse envelope. As shown in Figure 7, if the carrier frequency of the pulse source is 1GHz, the pulse width is 10us, the pulse repetition frequency of Trace1 is 100kHz, and the pulse repetition frequency of Trace2 is 10kHz, the spectral line density of Trace1 will be 1/10 lower than that of Trace2. It can be seen from the formula that the noise change is ≤ 10 * Log ten (1/10)=-10dB。
Figure 7 Measurement Curve of FSWP Pulse Phase Noise with Different Pulse Repetition Frequencies
It can be seen from the test results that the pulse phase noise of Trace1 is - 9.3 dB lower than that of Trace2 near PRF/2, which is basically consistent with the theoretical value.
3.2 Change the pulse width while keeping the pulse repetition frequency unchanged
When the pulse repetition frequency is fixed, increasing the pulse duty cycle will reduce the noise of fc, which is due to the narrowing of the pulse envelope and the reduction of spectral line density. As shown in Figure 15, if the carrier frequency of the pulse source is 1GHz, the pulse repetition period is 100us, the pulse width of Trace1 is 10us, and the pulse width of Trace2 is 50us, the spectral line density of Trace2 will be 1/5 lower than that of Trace1. It can be seen from the formula that the noise change is ≤ 10 * Log ten (1/5)=-6.9dB。
Figure 8 Impulse Phase Noise Measurement Curve of FSWP with Different Duty Cycle
It can be seen from the test results that the pulse phase noise of Trace2 is - 5.23dB lower than that of Trace1 near PRF/2, which is basically consistent with the theoretical value.
4 Summary
To sum up, advanced digital phase demodulation and amplitude demodulation technologies are adopted, FSWP can easily measure the phase noise of the pulse signal. The measurement frequency offset of the pulse phase noise is automatically limited to the PRF/2 range. Changes in pulse width and pulse repetition frequency will change the spectral line density within the envelope, which will affect the pulse phase noise. The pulse phase noise is basically unchanged near the carrier, and near the PRF/2, The impact of pulse phase noise will be very obvious.
