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1、书书书 第 16 卷 第 2 期强激光与粒子束Vol. 16， No. 2 2004 年 2 月HIGH POWER LASER AND PARTICLE BEAMSFeb. ， 2004 Article ID： 1001-4322 （2004） 2-0227-04Log-ratio circuit and low frequency feedback system*LIU Jian-hong， WANG Jun-hua， ZHENG Kai， GONG Ding，YANG Yong-liang， SUN Bao-gen（National Synchrotron Radiation Labor
2、atory，University of Science and Technology of China，P. O. Box 6022，Hefei 230029，China） Abstract： During the past year，several measures have been tried to improve the stability of injected beam atHLS（Hefei Light Source） ，which has newly upgraded its injection system. To overcome the evident residual
3、betatronoscillation，one specific betatron-oscillation suppressor circuitry is accomplished to take it under control. Means to ex-cite and damp beam motions has been suggested，as well as a PLL circuit in plan to track the variation of tune undervarious machine states. In addition，works as improving t
4、he performance of early version of turn-by-turn system and re-building the software kit to make it a reliable instrumentation for beam nonlinear dynamics study and machine state mo-nitoring. Key words： Log-ratio circuit； Turn-by-turn system； Circuitry simulation； Resonant depressor CLC number： TL594
5、 Document code： A1 Log-ratio BPM and turn-by-turn investigation Because of the inherent log-ratio property for beam position monitoring，as well as the wide dynamic range，highbandwidth and good conformance of modern logarithmic amplifier，log-ratio BPM is an attractive and effective candi-Fig. 1 Log-r
6、atio equivalent electronics circuitrydate2， 3. The common signal processing circuitry is fairly sim-ple，instead of complicated down-converting transformation，the BPM RF pickup signal is directly detected and log-ampli-fied，as shown in Fig. 14. Take the BPM signal into consid-eration， the analysis st
7、arts from the capacitive button PU whichprovides ample signal in applications with bunched beams，aswell as properties as relatively broadband and mechanicallysimple5. For the long bunch，the beam signal is very nearly the derivative of the longitudinal bunch distribution. Suppose the bunch charge dis
8、tribution is Gaussian，for single bunch revolution operation mode，we have signalyielded at BPM pickup likeu （t）=+n = -ub（t - nT0） cos （2nvx + 0）（1）ub（t）=ddt（Q02e-t2/22）（2） The corresponding representative of equation（1）in frequency domain is like the following，here we use periodicsignal Fourier trans
9、formation principles and delta signal properties，the spectrum is shown in Fig. 2.U （）=12Ub（） 0ej0n （ - n 0- vx0）+ e-j0n （ - n 0+ vx0） （3）Ub（）= jQ0 e- （）2/2（4） Because of the periodic revolution of bunched beam，its spectrum is discrete，and as amplitude modulation，onesingle spectrum line is divided in
10、to two lines，which occur at both sides of the original one. Then the pickup signal is filtered by a bandpass filter，which has parameters set as center frequency 90f0，and*Received date： 2003-05-07； Revised date： 2003-08-05Foundation item： Supported by National Natural Science Project（10175063）Biograp
11、hy： LIU Jian-hong （1975） ，male，doctor，mainly studies beam diagnostication of accelerator；E-mail： allen mail. ustc. edu. cn。Fig. 2 Spectrum of pickup signal for single bunch beampass band 2f0. In our case，tune value of x direction，vxisbetween 0. 5 and 0. 6. So the bandpass filter output signal hasonl
12、y 4 spectrum elements， （90 - vx） ， （89 + vx） ，（91 - vx） ，（90 + vx） . Analytic representatives of 4 terms are-202（90 + vx） e （90+vx） 02/2sin （90 + vx） 0t + 0（5）-202（91 - vx） e （91-vx） 02/2sin （90 - vx） 0t - 0（6）-202（89 + vx） e （89+vx） 02/2sin （89 + vx） 0t - 0（7）-202（90 - vx） e （90-vx） 02/2sin （90 - v
13、x） 0t + 0（8） As for the wide band“log amplifier” ，it actually incorporates a detector cascaded with an intermediate frequencylog amplifier. Detection or demodulation of AM signal is equivalent to frequency mixing，that is，shifting spectrum el-ements to left or right by carrier frequency fc. Result of
14、 detection is202 （90 - vx） e- （90-vx） 02/2-（90 + vx） e- （90+vx） 02/2 sin （vx0t + 0）（9）202 （89 + vx） e- （89+vx） 02/2-（91 - vx） e- （91-vx） 02/2 sin （1 - vx） 0t + 0（10）By evaluating the two expressions，we can simplify it as the following equation，which is a standard beat amplitudemodulationFig. 5 Turn
15、by turn sampled record graph vx=0. 51sin （vx0t + 0）+ sin （1 - vx） 0t - 0= 2sin （vx20t） cos （2vx- 120t + 0）（11） The waveform of the final output may best illustrate the analyticprediction. In Fig. 4，the parallel vertical lines in upper half are plotted atturn to turn interval，the intersection points
16、of vertical lines and thedetection output is namely the turn by turn record points，which isshown at Fig. 5. As a matter of fact，the delay time of turn-by-turn starting point relative to one certain bunch（e. g.the base time point）only determines the magnitude of oscillation amplitude. From equation（9
17、， 10） ，we can assure FFT of the turn by turn records has only one frequency element，vx（for vx0. 5） . The similar rules of signal processing apply to multi bunch operation mode，are listed belowum（t）=n44i =0ub（t - nT0- iT045） cos （2nvx + 0+ i245）（12）822HIGH POWER LASER AND PARTICLE BEAMSVol. 16Um（）=02
18、e-jiT045ej （0+i245）n （ - n 0- vx0）+ e-j （0+i245）n （ - n0+ vx0）（13）Final output consists of the following elements-202（90 + vx） e- （90+vx） 02/244i =0sin vx0t + 0- i245（89 + vx） （14）-202（91 - vx） e- （91-vx） 02/244i =0sin （1 - vx） 0t - 0- i245（92 - vx） （15）202（89 + vx） e- （89+vx） 02/244i =0sin （1 - vx）
19、 0t - 0+ i245（88 + vx） （16）202（90 - vx） e- （90-vx） 02/244i =0sin vx0t + 0+ i245（88 + vx） （17）And the corresponding waveform are shown below The continuous waveform in Fig. 6 may be complicated depending on specific beam parameters. While the turnby turn result of multi-bunch resembles the one of sin
20、gle bunch mode，both are combinations of vxand（1 - vx）fre-quency elements.2 Damped betatron oscillation and observation For real world single bunch mode betatron oscillationu （t）=+n = ub（t - nT0） cos （nvx+ 0） e-t/ （9）Fig. 8 Damped oscillation of single bunch mode We have similar oscillation only with
21、 amplitude exponentialdamping at log-ratio ampilifier output as shown below. The same analysis can be applied to multi bunch mode andthe results remain the similar，so in our case，we can adopt Ber-goz instrument log-ratio BPM modules5for machine study，forboth single mode and multibunch mode. The log-
22、ratio BPM mod-ules we ordered are designed to work at 408MHz （90f0）with 10MHz bandpass and excellent -50 to 10dBm dy-namic range. Sampling the log-ratio output waveform with an ADC or digitizer with external clock as timing formsnamely the turn-by-turn system6.3 Application of log-ratio and turn-by-
23、turn system At HLS we have injection system newly upgraded， while commission and testing， the log-ratio module can be em-ployed to evaluate conformance of the local orbit bump and the integral field strength of individual pulse kicker for in-jection. Bad equipoise of four-pulse kickers may cause une
24、xpected orbit distortion beyond the injection region and del-922No. 2Liu Jian-hong，et al：Log-ratio circuit and low frequency feedback systemeterious betatron oscillation，known as“leaked bump” ，as shown in Fig. 91. From Fig. 9 we can see that injection pulse kicker may arouse remnant and deleterious
25、betatron oscillation besidesorbit distortion. Because our fast and wide bandwidth transverse feedback system is still in construction，we employ aquite easy means to overcome the remnant oscillation. First a bandpass filter pick up the tune frequency element， thenthe signal is phase shifted by 180 an
26、d applied to stripline kicker from the down stream end. After precise calculationof delay and shift of signal-processing chain circuitry and fine tune of phase shifter，the instrumentation can success-fully depress deleterious betatron oscillation as shown in Fig. 11. A plan in future is to replace t
27、he BPF with a PLL totrack tune variation better.Fig. 11 Effect of betatron oscillation depressor In commission of injection system，we found beamdegradation caused by inconformity of pulse kickers，iontrap etc. And tune shift caused by DC bump is also aproblem，with turn by turn system we can easily tr
28、ack thevariation7，investigation of its dependence on orbitshows that a parasitic octupole moment is driving the tuneshift8. All these factors may make contributions to accumulated current limit of HLS and need further study.References：1 Wang J H，Li W M，Liu Z P，et al. Experiment result of the turn-by
29、-turn system and its application in injection commission of HLS J . High PowerLaser and Particle Beams， 2004， 16 （1） ： 101104.2 Roberto G. Log-ratio technique for beam position monitor systems C . Proc of AIP conferonce C . 1993. 301.3 Medvedko E. The logarithmic beam position monitor R . SLAC-PUB-8
30、445.4 Hu K H，Chen J，Kuo C H， et al. Turn-by-turn BPM electronics based on 500MHz log-ratio amplifier A . Proc of PAC 99 C . New York： 1999.5 Bergoz Instrument. Log-ratio beam position monitor users manual M .6 Wang J H，Li W M， Sun B G， et al. Design and development of turn-by-turn system based logar
31、ithmic ratio J . High Power Laser and Particle Beams，2002， 14 （4） ： 485488.7 Hsu K T，Jenny，Kuo C H， et al. Experimental study of tune variation at the storage ring of SRRC A . Proc of EPAC 2000 C ，Vienna： 2002.8 Terebilo A，Pellegrini C， Cornacchia M， et al. Experimental non linear beam dynamics stud
32、ies at SPEAR A . Proc of PAC97 C . Vancouver： 1998.1457.对数比电路原理与低频工作点反馈系统刘建宏， 王筠华， 郑 凯， 贡 顶， 杨永良， 孙葆根（中国科学技术大学 国家同步辐射实验室， 安徽 合肥 230029） 摘 要： 在合肥光源注入系统升级改造后， 尝试了几种方法来改进机器注入束流稳定性。研制了用于抑制注入过程残余 振荡的水平和垂直方向的工作点振荡抑制模块， 尝试了包括逐圈测量和锁相环原理来激励和稳定束流等方法来跟踪工作点变化。详细分析了基于对数比原理的逐圈测量系统， 包括单束团和多束团模式， 证明在多束团模式下逐圈测量的可行性和意义， 更新了数据采集和可远程控制的软件集成环境。 关键词： 对数比电路； 逐圈测量系统； 电路仿真； 共振抑制法032HIGH POWER LASER AND PARTICLE BEAMSVol. 16
