A new IQ detection method for LLRF

Nuclear Instruments and Methods in Physics Research A 675 (2012) 139–143

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

A new IQ detection method for LLRF Feng Qiu a,b,n, Jie Gao a, Hai-ying Lin a, Rong Liu a, Xin-peng Ma a,b, Peng Sha a, Yi Sun a, Guang-wei Wang a, Qun-yao Wang a, Bo Xu a, Ri-hua Zeng c a

Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China Graduate School of Chinese Academy of Sciences, Beijing 100049, China c European Spallation Source ESS ABP.O Box 176, SE-221 00 Lund, Sweden b

a r t i c l e i n f o

abstract

Article history: Received 10 May 2011 Received in revised form 20 December 2011 Accepted 31 January 2012 Available online 8 February 2012

Digital LLRF technology has been widely used in new generation particle accelerators. IF quadrature sampling is a common method for amplitude and phase detection. Many strategies, which obey the same rule of f sample ¼ ðM=NÞf IF (M=N is a rational number), have been proposed to reduce the effects of spectrum aliasing. However, we found that M=N does not need to be a rational number according to Shannon’s theorem. Therefore, we propose a new IQ detection method in this paper. This method is based on a special IIR filter which is derived from an RLC circuit. The unique characteristic of the method is that the value of f IF is independent of the value of f sample . We have set up an experimental platform to verify our method. A 122.88 MHz sampling clock is used to sample a 3 MHz IF signal. The DDS and PI control techniques are used to realize the closed-loop control. Results show that the stability of the system is within 7 0.05% (peak to peak) for the amplitude, and with 70.031 (peak to peak) for the phase in 5 h. & 2012 Elsevier B.V. All rights reserved.

Keywords: LLRF IQ detection IIR filter RLC circuit DDS

1. Introduction The amplitude and phase stability of the RF field directly affects the quality of the beam in accelerators. With increasing requirements for higher quality beams, high precision feedback control is desperately demanded by LLRF systems. For example, International Linear Collider (ILC [1]) and X-Ray Free Electron Laser (XFEL [2]) require the RF amplitude stability of 0.07% and 0.01%, phase stability of 0.241 and 0.011, respectively. With the development of microelectronic technology, especially the high performance Field Programmable Gate Array (FPGA), many concepts and techniques have been introduced in the commercial and military fields. The 4G terminal and the software defined Radio are proposed in such a background. These two techniques and the digital LLRF have a similar structure, while the algorithm is the core function. An overview of a typical software defined Radio system is shown in Fig. 1. All these new techniques have set up a solid foundation for the development of high precision feedback control in RF control systems for modern accelerators. High accuracy IQ detection is the basic for the high precision RF control. At present, the IQ [3] and non-IQ [4] are the best rounded sampling method in the main labs such as DESY, KEK and

n Corresponding author at: Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China. Tel.: þ86 15810237902. E-mail address: [email protected] (F. Qiu).

0168-9002/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2012.01.068

Fermilab [5]. This paper presents a new IQ detection method. Compared with the traditional method, the proposed method is based on a narrow band IIR filter with advantages in short latency and high flexibility.

2. The new method for IQ detection A rotation vector algorithm has been used in this IQ detection method. The continuous-time IF signal f(t) can be represented by a discrete-time signal consisting of a sequence of samples f ðnÞ ¼ A cosðO0 T  n þ f0 ÞnuðnÞ, where O0 is the radian frequency of IF signal, T is the sampling period, and u(n) is the unit step sequence. The IQ components of f(n) are I0 ¼ A cos f0 ,

Q 0 ¼ A sin f0 :

ð1Þ

Fig. 2 show the IF signal and the IQ signal under the IQ coordination.1 The ðI0 ,Q 0 Þ pair is the IQ signal we need to demodulate. Supposing ðIn ,Q n Þ is already known, then ðI0 ,Q 0 Þ can be obtained by multiplying ðIn ,Q n Þ with a rotation factor ejo0 n , where o0 ¼ O0 T. Therefore, it is important to acquire ðIn ,Q n Þ at the first step. The RLC filter which is derived from the RLC resonant circuit 1 The sequences In and Qn are the real part and the imaginary part of Aejðf0 þ O0 TnÞ , respectively. i.e., In is the discrete-time IF signal and Qn is the quadrature signal of In.

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define hðnÞ ¼ eaTn þ joa n

ð4Þ

then this impulse response function in complex form has two outputs. In the following we try to demonstrate that the ðIn ,Q n Þ pair is just involved in the steady-state response of hðnÞ for a sinusoidal input signal. The z-transform of hðnÞ can be expressed as Fig. 1. Block diagram of software defined Radio system.

HðzÞ ¼

1 z ¼ : 1eaT þ joa  z1 zeaT þ joa

ð5Þ

The input sinusoidal signal is f ðnÞ ¼ A cosðon þ f0 ÞuðnÞ, the corresponding z-transform is FðzÞ ¼

Aejf z Aejf z   þ : j o 2 ze 2 zejo

ð6Þ

The output YðzÞ ¼ HðzÞFðzÞ is given by YðzÞ ¼

z zeaT þ joa

! Aejf z Aejf z   þ : 2 zejo 2 zejo

ð7Þ

There are two parts in Eq. (7), and the only difference of them is the sign of o and f. Supposing MðzÞ ¼ zðzeaT þ joa Þ1  zðzejo Þ1 , then MðzÞ has two poles: z1 ¼ ejo , which is on the unit circle, and z2 ¼ eaT þ joa , which is inside the unit circle. According to the residue theorem [7,8], the inverse transform of MðzÞ is mðnÞ ¼ P2 n1 z ¼ zk , which is k ¼ 1 Res½MðzÞz mðnÞ ¼ ½ðzz1 Þ  MðzÞzn1 z ¼ z1 þ ½ðzz2 Þ  MðzÞzn1 z ¼ z2 ¼

Fig. 2. IQ signal and IF signal in IQ coordinate.

ðexpaT þ joa Þn þ 1 þ : 1eaT þ jðoa oÞ eaT þ jðoa oÞ ejo ejon

ð8Þ

When n-1, the second part of Eq. (8) is zero, and the steady response of mðnÞ is ð1eaT þ jðoa oÞ Þ1 ejon . Considering the symmetry, the eventual steady response of hðnÞ is yðnÞ ¼

Aejf  ejon Aejf  ejon þ :  a T þ jð o  o Þ a 1e 1eaT þ jðoa þ oÞ

ð9Þ

When o ¼ o0 , considering that oa 6o0 , Eq. (9) can be simplified as yðnÞ ¼

Fig. 3. Series RLC circuit.

can be used to generate ðIn ,Q n Þ from IF signal. It will be introduced in the next section.

3. The basic principle of RLC filter The RLC filter is based on the RLC resonant circuit. The transfer function of a series RLC circuit (see Fig. 3) is [6] HðsÞ ¼

O0 U R ðsÞ Q s ¼ UðsÞ s2 þ OQ0  s þ O20

ð2Þ

where Q is the quality factor. The inverse laplace transform of Eq. (2) is the continuous-time impulse response   a hðtÞ ¼ 2a eat  cosðOa tÞ  sinðOa tÞ ð3Þ Oa qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where a ¼ O0 =2Q and Oa ¼ O20 ðO0 =2Q Þ2 . Usually a larger value of Q is used to obtain a better frequency-selective property. Ignoring the constant multiple factor and the second small value part in the square brackets, the discrete-time impulse response can be simplified as hðnÞ ¼ eaTn  Rðejoa n Þ, where oa ¼ Oa T. If we

Aejf  ejo0 n Aejf  ejo0 n þ : 1eaT 1eaT þ 2jo0

ð10Þ

For k-th order hk ðnÞ, which has a z-transform function Hk ðzÞ ¼ ð1eaT þ joa z1 Þk , the system has a multiple-order pole eaT þ joa . According to the residue theorem, the steady response of hk ðnÞ can be expressed by Refs. [7,8]2 " # k  k 1 1 2jðo0 nfÞ : ð11Þ yk ðnÞ ¼ Aejðf þ o0 nÞ þ e 1eaT eaT þ 2jo0 Eq. (11) includes the IQ components and the secondary harmonic components. Normally the Q value is large enough, then the value of aT is very small, thus, the IQ components become the dominant components. Therefore, the ðIn ,Q n Þ pair can be obtained in the outputs of this filter. Then the analysis of the frequency-selective properties of the RLC filter with Eq. (5) can be extended further. When z ¼ ejo , the system function HðzÞ becomes the frequency response Hðejo Þ. Defining the relative power spectral density function P 1 ðejo Þ ¼ 2 9Hðejo Þ=Hðejo0 Þ9 . Considering that oa 6o0 , then P1 ðejo Þ can be 3 simplified as P1 ðejo Þ ¼

1  o 2 : 0 1 þ o aT

ð12Þ

2 Some comparisons of several different kinds of high order infinities are involved in the derivation of Eq. (11). 3 Taylor series expansion is applied in this derivation.

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Fig. 4. Illustration of a 3rd order RLC filter group and the IQ detection method. From Eq. (4), we can easily get a ¼ eaT cosðoa Þ and b ¼ eaT sinðoa Þ. Some techniques are used to reduce the number of the multipliers (a and b). The parameter c ¼ cosðo0 nÞ and d ¼ sinðo0 n) are derived from the rotation factor ejo0 n , and they are pre-stored into look-up-tables in practise.

Table 1 Phase difference of the two channels in RLC filter. Order of RLC filter

1 2 3 4

Phase difference Q ¼ 10 f 0 ¼ 3 MHz

Q ¼ 100 f 0 ¼ 3 MHz

87.16729712 89.97479015 90.00156372 90.00002982

89.71587937 89.99977859 90.00000162 90.00000000

Fig. 5. Comparison of the power–frequency response curve among the single order to quadruple order RLC filter.

According to Eq. (12), the bandwidth of a single-order filter is given by B1 ¼ 2aT. The k-th order power spectral function is P k ðejo Þ ¼ Pk1 ðejo Þ, and the corresponding bandwidth is qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð13Þ Bk ¼ 21=k 1  B1 :

4. The simulation of RLC filter Fig. 4 illustrates the main structure of the RLC digital filter and the IQ detection method. Fig. 5 and Table 1 show the frequency response curve of the filter and the phase difference of the two channels, respectively. The bandwidth of the filter varies with the order according to Eq. (13), while the phase difference between the two channels gets closer to 901 with a higher order filter. (The deviation is even less than 0.000000011 in a Q¼100 fourth order filter.) The RLC filter can be regarded as a 901-phase splitting system. It can be applied in the Single Side Band (SSB) modulation and demodulation system and the image edge extraction technology, etc. Compared with the traditional Hilbert transform filter, this filter has simpler structure, less delay and higher precision.

Fig. 6. Spectrum of the input/output signals of an RLC filter. The SNR and SFDR are improved by 18 dB and 21 dB, respectively.

5. Experimental results and analysis A latest generation FPGA development board from Altera is used to demonstrate the performance of the filter and the IQ detection method. We intentionally choose an unrelated f IF =f sample rate: the 3 MHz IF frequency and the 122.88 MHz sample frequency.4

4 Theoretically, the f IF =f sample rate can be arbitrary, but you should pay attention to the storage capacity of the look-up-table in practice (c and d in

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F. Qiu et al. / Nuclear Instruments and Methods in Physics Research A 675 (2012) 139–143

Fig. 9. Amplitude control precision (5 h).

Fig. 7. Phase detecting precision (7 h).

Fig. 10. Phase control precision (5 h).

Table 2 Main specifications of the LLRF system. Fig. 8. Overview of the RF system for the 1.3 GHz nine cell cavity. The detail structure of RLC filter and rotation model can be found in Fig. 3.

A Q 625, order¼4 RLC filter group is selected after a tradeoff has been performed between the bandwidth and the precision. Fig. 6 depicts the comparison between the raw signal and the filtered signal. The results have showed that this filter can significantly improve the SNR and SFDR. The final measuring result of the phase is given in Fig. 7. We have established an RF system at room temperature with a retired KEK 1.3 GHz 9-cell cavity MHI-04 to verify our IQ detection method. This RF system consists of the cavity, a tuner, a LLRF system, a communication system and some RF equipments with a frame diagram is shown in Fig. 8. A precise RF signal generated by a Agilent signal source is sent to an IQ modulator. After being amplified by a 42 dB power amplifier, this signal is coupled into the cavity with a high power coupler 778D. The RF field of the cavity is disturbed by beadpulling. The disturbed signal is then picked up in the other end of the 9-cell cavity, then it will be fed into the digital LLRF cabinet. The cabinet down-convert the RF signal to IF signal at first. The

(footnote continued) Fig. 4). Anyway, this IQ detecting method can greatly relax the requirement of a strict f IF =f sample rate.

Parameter

Index

Amplitude stability Phase stability Settling time Latency Dynamic range

7 0.05% 7 0.031 70 ms 1 ms 20 dB

FPGA board which is the core component of the cabinet will process the IF signal, and the main functions of the board are IQ detection and PI feedback control. The control information is then sent to the IQ modulator and the tuner to control the amplitude, phase and frequency loops. The control precision is shown in Figs. 9 and 10. The stability of the system is within 70.05% (peak to peak) for the amplitude, and within 70.031 (peak to peak) for the phase in 5 h. The detail specifications are shown in Table 2.

6. Summary This paper presents a new IQ detection method. Theoretically, this method can realize high precision IQ detection with arbitrary f IF =f sample rate. In addition, it has advantages of short latency and simple structure. The 5 h results show that it achieves amplitude stability within 70.05% (peak to peak) and phase stability within 70.031 (peak to peak).

F. Qiu et al. / Nuclear Instruments and Methods in Physics Research A 675 (2012) 139–143

Acknowledgment We do appreciate Doctor Larry Doolitle from the Lawrence Berkeley Accelerator Lab for his valuable guidance and advice. References [1] ILC Reference Design Report (RDR), /http://www.linearcollider.org/cms/ ?pid=1000437S.

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[2] S. Simrock, Overview of XFEL RF specifications and comparison to ILC specs, in: ILC RF/Timing workshop, FNAL, January 2006. [3] H. Klingbeil, IEEE Transactions on Instrumentation and Measurement 54 (3) (2005) 1209. [4] L. Doolittle, Digital low-level RF control using non-IQ sampling, in: LINAC06, Knoxville, TN, USA, 2006. [5] U. Mavric, B. Chase, M. Vidmar, Nuclear Instruments and Methods in Physics Research Section A 594 (2008) 90. [6] /http://en.wikipedia.org/wiki/RLC_circuitS. [7] A.V. Oppenheim, R.W. Schafer, Digital Signal Processing[M], second ed., Prentice-Hall, New Jersey, 1989, pp. 113–115. [8] /http://ssli.ee.washington.edu/courses/ee518/notes/lec6.pdfS.