Advanced topics on RF amplitude and phase detection for low-level RF systems

TL;DR: In this paper, different sampling strategies and demodulation algorithms have been developed for low-level radio frequency (LLRF) systems, including accurate RF transient measurement, wideband RF detection, and detection with an asynchronous trigger, local oscillator, or clock.

About: This article is published in Nuclear Science and Techniques.The article was published on 2019-10-01 and is currently open access. It has received 8 citations till now. The article focuses on the topics: Radio frequency & Local oscillator.

Summary

1 Introduction

• The asynchronous sampling scheme does not require deterministic phase relations between the trigger, LO, clock and RF signals but places difficulties in the design of demodulation algorithms.
• There are already quite a few articles to discuss the RF signal detection focusing on the accuracy, precision and latency requirements described above [24] [25] [26] [27] [28] .
• For these special requirements, different demodulation algorithms are needed based on the common RF detector architecture in Fig. 1 .The following topics will be discussed: 1) RF transient detection with non-IQ: some RF signals may have transients with fast changing amplitude or phase which need to be measured accurately by the RF detector.

2.1 RF Transient Detection with non-IQ

• If the kth sample of the IF signal is denoted as xk, the in-phase (I) and quadrature (Q) components of the RF envelop vector can be calculated with the last n samples as EQUATION where the phase step.
• The non-IQ demodulation algorithm (2) can filter out the harmonics and DC offset in the IF samples [21] , [22] with a reasonable latency if n is not too large.
• When the IF amplitude or phase change fast like in the transients of an RF pulse, the second term will not vanish and appear as a systematic error with its spectrum centered at twice the IF frequency.
• Due to the fact that the clock frequency is synchronized with the IF frequency, a moving-average Finite Impulse Response (FIR) filter can also provide an accurate notch at double of the IF frequency.
• The moving-average FIR filter with 3 taps has been applied to SwissFEL LLRF system and resulted RF pulse baseband signal and spectrum have been shown as dotted-line plots in Fig. 2 and Fig. 3(a) .

2.2 Wideband RF Detection

• The non-IQ demodulation algorithm requires n samples of the IF signal to do the demodulation which reduces the bandwidth of the sampling.
• Let's assume that the ADC data is collected after a trigger and the first sample corresponds to a phase φ0 of the IF signal, see Fig. 4 below.
• This situation can happen if the phases of the IF and clock signals are aligned at some time point, when the clock samples a point close to the zero-crossing of the IF signal.
• The frequency responses of the non-IQ demodulation algorithm with n = 6 and the wideband detection algorithm (9) are compared in Fig. 6(b ).
• It can be seen that the wideband detection algorithm has larger bandwidth without notches at the IF frequency and double of the IF frequency.

2.3 RF Detection Regardless of Trigger

• The phase of the first sample after the trigger is defined as the reference phase of the demodulation and the phase variations of the later samples are detected by removing the expected phase lags compared to the reference phase.
• If the rising edges of the trigger and clock signals are very closely aligned in time, the trigger may fall randomly into two adjacent clock cycles and select different ADC samples.
• Fig. 8 . Reference IF signal derived quadrature signal with synchronous sampling at SwissFEL.
• Because the RF detection strategy in Fig. 7 always compares the RF phase and the MO phase regardless to the trigger, the phase jumps caused by the racing between trigger and clock can be avoided.
• The low-frequency noises, which are the drifts in the amplitudes and phases of the reference and RF signals, are mostly correlated while the high-frequency noises are mostly uncorrelated.

2.4 RF Detection with Asynchronous LO or Clock

• Instead, it might be easier to get separate oscillators to provide the LO and clock signals, which are not synchronized with the RF signal to be detected.
• The major differences are the implementations of the 0º/90º splitter and the LPF due to asynchronous sampling.
• With asynchronous sampling, the IF phase lag   between two adjacent ADC samples is unknown so the authors cannot use the simple algorithm in (12) to calculate the quadrature signal of the reference signal.
• Practically the authors can use an FIR filter to approximately implement the Hilbert transform.
• Fig. 13 shows the frequency response of a 16-tap Hilbert transform FIR filter designed with the "Filter Designer" of Matlab.

4 Conclusions and Outlook

• The digital RF amplitude and phase detector is one of the key components in LLRF systems.
• Based on the same hardware, different digital demodulation algorithms should be implemented to address different requirements on the RF detection.
• This paper describes several RF detection algorithms to satisfy different requirements that the author has met when working on different LLRF systems, which can be used in other machines with similar conditions.
• New algorithms will be developed for newly emerging requirements on the performance, reliability and robustness of RF detectors.
• If the requirements (e.g. bandwidth requirements) exceed the limits of the existing hardware, a modification of the RF detector hardware could be also needed together with the demodulation development.

Figures

Fig. 4. Synchronous sampling of IF signal.

Fig. 5. Results of wideband detection algorithm and non-IQ demodulation algorithm for the same data in Fig. 2. (a). amplitude waveform; (b). amplitude zoom-in at rising edge; (c). phase waveform; (d). phase zoom-in at rising edge.

Fig. 6. (a). Spectrums of the baseband RF pulse; (b). Frequency responses of non-IQ demodulation and wideband detection algorithms.

Fig. 11. RF detection with asynchronous LO or clock signals.

Fig. 12. Implementation of 0º/90º splitter with Hilbert transform.

Fig. 1. General architecture of an RF detector.

Fig. 7. Strategy of RF detection regardless of trigger.

Fig. 10. Generation of the reference quadrature signal with amplitude noise reduction.

Fig. 15. Results of asynchronous detection algorithm and non-IQ demodulation algorithm for the same data in Fig. 2. (a). amplitude waveform; (b). amplitude zoom-in at rising edge; (c). phase waveform; (d). phase zoom-in at rising edge and the phase difference between two cases.

Fig. 2. Transient detection with non-IQ demodulation algorithm with an IF frequency 41.65 MHz and clock frequency 249.9 MHz. (a). amplitude waveform; (b). amplitude zoom-in at rising edge; (c). phase waveform; (d). phase zoom-in at rising edge.

Fig. 14. Generation of in-phase and quadrature signals of the reference IF signal with FIR-based Hilbert transform and the calibration of imbalances.

Fig. 8. Reference IF signal and derived quadrature signal with synchronous sampling at SwissFEL. The LPFs in the I and Q output paths in Fig. 7 can also be implemented as simple moving-average FIR filters for synchronous sampling. As discussed in section 2.1, a moving-average FIR filter with n taps, where n is the minimum number of samples to cover full IF periods, will provide notches at different harmonics of the IF frequency.

Fig. 3. (a). Spectrums of the baseband RF pulse; (b). Frequency responses of 3-tap and 6-tap movingaverage FIR filters and the cascaded filter with non-IQ demodulation + 3-tap moving-average filter.

Fig. 13. Frequency response of an FIR filter for Hilbert transform. The clock frequency is 249.9 MHz. The phase lag caused by group delay has been removed from the phase response.

Fig. 9. Results of trigger independent detection algorithm and non-IQ demodulation algorithm for the same data in Fig. 2. (a). amplitude waveform; (b). amplitude zoom-in at rising edge; (c). phase waveform; (d). phase zoom-in at rising edge and the phase difference between two cases.

Frequently asked questions

Q1. What have the authors contributed in "Advanced topics on rf amplitude and phase detection for low-level rf systems" ?

Low-Level RF ( LLRF ) systems stabilize the electromagnetic field in the RF cavities for beam acceleration in particle accelerators. Different sampling strategies and demodulation algorithms have been developed and will be introduced in this paper. This article will focus on some advanced topics for RF detection like the accurate RF transient measurement, wideband RF detection and the RF detection with asynchronous trigger, Local Oscillator ( LO ) or clock. The analysis will be based on the measurement from SwissFEL but the introduced algorithms are general for the RF signal detection in particle accelerators. 

Q2. How can the authors generate the quadrature signal from the time series of the reference IF signal?

In order to generate the quadrature signal from the time series of the reference IF signal, the last two ADC samples denoted as xref,k-1 and xref,k can be used. 

Q3. What is the importance of a RF detector in a feedback loop?

The latency of the RF detector is critical when using in an RF feedback loop for which the overall loop delay will limit the closed-loop bandwidth that the feedback loop can achieve [15],[16]. 

Q4. What is the purpose of the LPFs in the The authorand Q output paths?

The LPFs in the The authorand Q output paths are used to remove the leakage of the IF frequency and the higher-order (especially the second-order) harmonics of the IF frequency. 

Q5. What is the cost of keeping the unwanted frequency components in the RF detector?

The wideband detection algorithm can detect faster transients in the RF pulse with a cost of keepingall unwanted frequency components introduced in the down-conversion mixing and ADC sampling processes, such as the DC offset in ADC samples, leakage of IF frequency in demodulation and all higher-order harmonics of the IF frequency due to the non-linearity in the RF detector. 

Q6. What is the phase of the first sample after the trigger?

4. The phase of the first sample after the trigger is defined as the reference phase of the demodulation and the phase variations of the later samples are detected by removing the expected phase lags compared to the reference phase. 

Q7. Why is the phase lag between two samples unknown?

Due to the asynchronous sampling, the phase lag ̂ between two samplesis unknown, but it can be estimated with the phase slope of the complex signal in equation (18)calculated with linear fitting of the phases of each sample. 

Q8. What is the main requirement of a RF detector?

A precise RF detector will be able to detect small changes in the RF field or in other words, with high resolution in RF measurements. 

Q9. What is the phase lag between two adjacent ADC samples?

With asynchronous sampling, the IF phase lag ̂ between two adjacent ADC samples isunknown so the authors cannot use the simple algorithm in (12) to calculate the quadrature signal of the reference signal. 

Q10. What is the simplest way to detect RF signals?

2.1 RF Transient Detection with non-IQThe non-IQ algorithm is a popular demodulation algorithm for RF detection based on synchronoussampling of IF signal. 

Q11. What is the role of the RF detector in LLRF systems?

In LLRF systems, the RF detector is one of the key devices to diagnose and control the RF fields in cavities used for beam acceleration. 

Q12. Why is the moving average FIR filter not suitable for the firmware?

Due to the asynchronous sampling, the moving-average FIR filter is no longer suitable toimplement the LPFs at the firmware or software side in Fig. 11. 

Q13. What is the simplest way to calculate the IF signal?

Counting from the first sample after the trigger, the kth and (k+1)th sample of an ideal IF signal (single-tone without amplitude or phase noises) can be written as 0 01 0 0sin 1sinkkx A kx A k . 

Q14. What is the RF detection algorithm for asynchronous LO?

4) RF detection with asynchronous LO or clock: in some applications, the phase locked LO andclock generator are not available, and this demodulation algorithm should allow using asynchronous LO or clock sources to perform RF amplitude and phase measurement. 

Q15. How many samples are needed to get the The authorand Q components?

The The authorand Q components of the IF samples in Fig. 4 are represented by the amplitude A0 and initialphase φ0 of the IF signal:0 0 0 0cos , sinI A Q A . (7)In order to get the The authorand Q components, at least two samples are needed, resulting in the possible maximum RF detection bandwidth. 

Q16. What is the problem with asynchronous sampling?

To overcome this problem, someLLRF systems use asynchronous trigger, LO and clock signals generated by separate oscillators, resulting in the asynchronous sampling scheme. 

Q17. What is the phase-lag between two ADC samples?

(12) Similar as the discussion for equation (9), the phase-lag Δφ between two ADC samples shouldn’t be close to integer times of π. 

Q18. What is the way to detect a pulsed RF signal?

2.3 RF Detection Regardless of TriggerFor RF systems working in pulsed mode, the measurement of an RF pulse is usually started with atrigger as shown in Fig. 

Q19. What is the main requirement for an RF detector?

With an accurate measurement of the RF amplitude and phase, the authors will be able to capture the exact changes in the RF field really felt by the beam.