Two basic signal-processing techniques are presently in wide use for the processing of signals from beam position monitors (BPMs); difference-over-sum, and amplitude-modulation-to-phase-modulation (AM-PM) conversion. Difference-over-sum offers simplicity and low cost, but poor real-time normalized response and amplitude dynamic range. AM-PM offers fast real-time response and large dynamic range, but is costly and difficult to implement. Logarithmic-ratio processing, a technique using newly available inexpensive hybrid circuits, appears to offer the advantages of both, and the disadvantages of neither. This paper reviews the features techniques, and highlights the features of the log-ratio technique. Among the advantages of log-ratio is a beam-displacement response linearity that is superior to either difference-over-sum or AM-PM for circular-aperture BPMs

Shafer, Robert E.

UNT Digital Library

b“... . IA-UR-93-0043litb:Author(s):c+B14~~10ti OFTM DOf#)MEMT 18 UNLIMITELos AlamcwNATIONAL LABORATORY.OG-RATIO SIGNAL-Processing TECHNIQUE FOR BEAM)OSITK)N ~ONiTORS~~-~R--93-43D~93 007356lobett E. Shafer992 Beam Instrumentation Workshop.BL, Berkeiey, CA)ctober 26-29, 1992LOG-RATIO SIGNAL-PROCESSING TECHNIQUEFOR BEAM POSITION MONITORSR. E. ShaferLos Alamos National LaboratoryLOS Aknos, NM 87545INTRODUCTIONTwo basic signal-processing techniques are presently in wide use for theprocessing of signals from beam position monitors (BPMs); difference-over-sum, andamplitude-modulation-to phase-modulation (AM-PM) conversion. Diffcrence-over-sutn offers simplicity and low cost, but poor real-time normalized response andamplitude dynamic range. AM-PM offers fast real-time response and large dynamicrange, but is costly and difficult to implement. Logarithmic-ratio processing, atechnique using newly available inexpensive hybrid circuits, appears to offer theadvantages of both, and the disadvantages of neither. This parreviews the featuresof all three processing techniques, and highlights the features o the log-ratio technique.Among the advantages of log-ratio is a beam-displacement response linearity that issuperior to either difference-over-sum or AM-PM for circular-aperture BPMs.SIGNALS FROM BEAM POSITION MONITOR ELECTRODESSignals tlom most beam position monitors, including both buttons and directional-coupler or srnpline pickups, are not linear in the transverse beam displacement from theBPM axis. For a pencil-beam current lb at posuion r,f) in a circular-aperture BPM ofradius b and electrode-width @as shown in Fig. 1, the dectrode response is given by 1andThe beam position displacement response of a pair of electrodescharacterized by the d.11-ratioof the two electrode signals:sin(4iQ) ~ + hi~cr order tCr’mS(&) =20 Log,o(f) = &—LdB @b(1)(2)is best(3)where R and L represent the right and left electrode signal amplitude outputs, andx = r sin O, certain special geometry electrodes can provide a linear response tobeam displacement, but at the expense of sacrificing the high-frequency responsecharacteristics of the electrodes. A diagonally-cut electrode psir is a good example.L1,* b IFig. 1. Cross section of a circular-aperture beam position monitor.BPM SIGNAL PROCESSING CONSU3EWTIONSIn designing a signal processing system for use with BPM signals, a wide vtictyof features must be considered. Some of the more important considerations arc listedbelow.vs. .~~. A wide-band processingsystem generally processes BPM si nals in the tima domain, while a narrow-bandfs~stcm can process a single Fourier arnmrtic component of the rf-mochdatcd BPMsignal, thus allowing the ~rocessing to be carried out in the f~uency domain.There is more available sl$nal power in the wide:-band processing system, butbecause of signal attcnuatmn and dispersion in cables, some of the tcm~ralinfommtion (e.g., pulse shape) is distorted. In narrow-band processing, signaldispersion is not a concern, but there is lCSSavailable signal power (trod less kTBnoise). Some signal-processing methods arc best suited for frequency-domainprocessing, while others are equally suited for both time- and fkcqucncy-domaintnccssing. Frequency-domain processing can be used with individual isolatedL am bunches as well as cw modulated beams..“~ Gencndly, processing of frequency-domain signals atthe beam-bunching ficquency is the most straight forward. Signal power from theelectrodes is very frequency dependent, depending on both the particle bunchlength and clectrodc len th. For accelerators with high-bunching frequenciest(e.g., 425 MHz), signal own-conversion to an intermediate frequency must beconsidered, due to limitations of the electronics. AM-PM processing at anintermediate frequency is also required when the beam-bunching frequency varieswith time, such as in a low-energy proton synchrotrons. In this case, tlE localoscillator must track the rf frequency.~ The signal power output from the BPM electrodes variesquadratically with the beam current. Any signal-processing system that processesthe electrode signals directly must be able to hande this required dynamic range insignal power. Furthermore, any R - L (difference) signal of the two opposite Rand L (for right and left) electrodes generally also varies nonlinearly with the beamdisplacement, so the total electronics dynamic range must be quite large. Forexample, a system designed to handle a 100:1 range of beam current and achieveresolmion of about l&J of the aperture needs a linear dynamic range of nearly I@to 1. This dynamic range is not achievable for un-norrnalized signals withoutrange switching.4. No~ If the processed analog signals arc of the form R/L (i.e.,ratio) or (R - L)/(R + L) (difference-over-sum), then the signal amplitude isindependent of beam current, which reduces the electronics dynamic-rangerequirement. Both AM-PM and log-ratio processing provide normalized outputresponse,$ WUmuxmw- Some applications of BPM ~ignal processing systemsrquire fast real-time normalized response, If the electrode signals arc separatelydigitized, and the normalization is performed digitally, there is a long delay timebetween the signal acquisition and the available normalized beam position signal.Both AM-PM and log-ratio processing can provide the normalized real-tirnc signalwithout off-line processing.fd2iw@mamu9n~c l~nem.“ No BPM signal processing technique canprovide normalized signa~s from stripline or button electrodes that are completelylinear in beam displacement. The natural nonlinearity in some signal processingtechniques can compensate for this, however..~ Some signal ‘occssing techniques rquirc C1OSCphasematching of the signals from the indiwduai electrodes. Generally the AM-PMprocessing method requires phase matching to about M degrees of phase at theprocessing frequency. This is also true of difference-over-sum processing if thediffcrcncc and sum (R - L and R + L) signals are formed prior to the rf envelopedetection.IMWQWQL Absolute position accwacy is usudy limited to abouthalf-aperture, unless special techniques are used to monitor andcorrect the channel-to-channel gain disparity, This includes self-calibrationprocedures that measure both the cable attenuation and electronics drifts, BPMKsition resolution on the other hand can achieve MJO1% of the half-aperture orttcr, depending primarily on the signal-to-noise ratio, which is limited by thermalnoise and by the electronics noise figure,COMPARISON OF SIGNAL PROCESSING METHODSFor two opposing stnpline or button electrodes providing output electricalamplitudes R and L (representing IR and IL), the three signal processing techniquesprovide the following normalized (meaning independent of barn current) outputresponses: 1Difference-over-sum (R - L)/(R + L)AM-PM tan-l (R/L) - nj4 = tan-l[(R - L)/(R + L)]Log ratio 0.5* b (R/L)= tanh-~[(R - L)/@+ L)]Thus the linearity of AM–PM u.d log-ratio processing is essentially that of anonlinear difference-over-sum response. For a circular-aperture BPM with 45-degreeelectrode widths, the signal processing responses to a displaced beam are shown inFig. 2. It is appttrent that the log-ratio processing technique has the most linear overallre@onse to tiam displacement.2.s- 1 I 1 I IOUTPUTAWU?UDR Vus ots--~lomm0s . — -~of-—Qf~t0.00.0 0;1 0,8 0:s 0.4 O!c 0.0 o,~ 0.0 0.0 0Fig. 2. Signal w ut response to a displaced beam in a circular-apature BPMrwith 45dcgree wi c electrodes, for difference-over-sum, AM-PM, and log-ratioprocessing electronics. I.mg-ratio processing has t’!emost linear response.Of the three methods, difference-over-sum processing is the simplest and leastexpensive. Thu R and L signals can either be combined to cmatc the difference andsum signals prior to or afler rf signal envelope detection. The detected R tind L si nalscan even be digitized directly, and the sum and differences calculated digitally. & ereare two main shortcomings in the difference-over-sum processing method. First,processing the R, L, R -- L, or R + L signals separately requires a large amplitudedynamic range, especid!y of the R -L signal. Secondly, producing the ratio of R - Lto R + L necessary to nommlize the signals is difficult in real-time, in either analog ordigital processing. Digital processing methods necessarily introduce LSB (least-significant-bit) A-DCerrors that limit the ultimate resolution.Amplitude-to-phase conversion (AM-PM) processing uses the two in-phasesignals from the BPM electrodes in a circuit that converts the amplitude disparity to aphase disparity. The two resultant output signals have the dependence on the beamcl~rrcnt renxnuxi by means of a matched pair of hard limiters that preserve the phaseinformation. A double-balanced mixer (or an exclusive OR) is then used to develop asignal proportional to the phase disparity. .1 typical block diagram is shown in Fig. 3.R— FlllmINPUTS Smll-fcusa.L o — 1ss~ -Llnlmsb!!M-JFig. 3. Block diagram of an amplitude-modulation-to-phase-modulation (AM-PM)conversion signal processing system. Amplitude disparities are convened to phasedisparities, which are measured in the double-balanced mixer.The original log-ratio circuits were based on the exponential V-I relationship ofsemiconductor junctions. Specifically , for a forward-biased bipolar junction:I=I~[exp[f#]-1)or(4)(5)where 10 is a characteristic (the reverse-polarity saturation current) of the specificsemiconductor junction, and kT/e is about 25 mV at morn temperature. An operationalamplifier can usc a semiconductor junction in a feedback loop as shown in Fig. 4 andachieve a logarithmic response. Because of the dependence of kT/e on temperature,and the dependence of 10on the junctiorl characterisbcs, these amplifiers usually shouldbe used in pairs,Fig, 4. Simple amplifier cimuit with logarithmic response,A log-ratio amplifier uses a matched pair of forward-biased diode junctions tomatch the reverse saturation cuments. In this case, the output response is of the form(6)where G is the gain of the output stage (a difference amplifier). Even in this case, thetemperature dependence of kT/e must be compensated with a thermistor in the outputcircuit. Bwause real diodes have a poor ideal diode response, the best semiconductor-juncticm log-radio amplifiers are constructed using the baseanitter junctions of bipolartransistors as shown in Fig. 5.ccFig. 5. Log-ratio signal processing system using NPN transistors in a tram-diodeconfiguration. The input circuit is a 50-ohrn termination followed by a low-passfilter into the summing junctions, The thermistor is required to correct thetemperature dependence of the semiconductor junction dynamic resistance.Junction capacitance (about 5 pF) limits the bandwidth. This circuit can onlyprocess unipolar signals.There are two additional parameters that limit the usefulness of these log amps,however. One is that the circuits are unipolar, i.e., the input voltage or cument cannotbean w signal. The second limitation is the available bandwidth.We can define the dynamic impedance of a diode junction as the derivative of Eq.(5):(nThus at I = 1 mA, the dynamic resistance is dmut 25 Q, rising to about 25 Ml forI = 1 vA. Log amplifiers have the best logmithmic response when 1 is in the 1-p%rmgc. A junction capacitance of about 5 pfi thus limits the bandwidth to N 1 MHzRecent advances i.nhybrid circuit design have led to the availability of inexpensivequasi-logarithmic-response amplifiers such as the Analog Devices AD 640.s Theseamplifiers have bandwidths exceeding 100 MHz, and compress the detected rf-envelops signal in a series of nonlinear amplification stages, providing a quasi-Iogarithmic response. Thus the AD @O overcomes several of the limitations inherent inthe bipolar junction log-amps, including the temperature dependence, the unipohrsignal requirement, and the low attainable bandwidth. A log-ratio circuit using fourAnalog Devices AD 640 amplifiers is shown in Fig, 6.L06AnP4LOGAMPsoFig.6. Block diagram of a log-ratio circuit using four Analog Devices AD 640 log-amplifter hybrids.The response uniformity of a cimuit comprised of four Analog Devices AD 640s at60 Ml-@ is shown in Fig. 7. The 21 cutwes represent input disparities from -10 to+ iO dB in l-dB steps. Two amplifier chips are required on each input in order toachieve the large dynamic range, The observed response uniformity over a 60-dBdynamic range is about t 0.1 dB. The ripple structure observed for off-center beams inFig, 7 is due to the successive saturation of the various gain stages in the AD 640. Theeffect is minimized for centered beams, because the log-amplifiers on the two inputstrack one another.The expected resolution for beam position signal processing cim:its is given by therelation, using Eq, (1-3).(8)where &xis the resolution, b is the IIalf aperture, F is the electronics noise factor (notfigure), kTB is the thermal noise power in bandwidth B, and Pin is the signal powerper electrode. The measured noise figure for the AD 640 log-ratio circuit in a 220-kHzbandwidth at 60 MHz M about 15 dB4 (corresponding to a noise factor of 32), asshown in Fig. 8,Higher frequency log-ratio operation is possible with any of several Plessey hybridcircuits,s at considerably higher cost. Figure 9 shows the response uniformity of fourPlessey SL3522A chips at 425 MHz,6 Although the individual Plesscy chips have therequired dynamic range, the ripple effect is very large, requiring the amplifiers on eachinput to be paralleled with a small gain offset between them.1050-5-10-80 -70 -60 -50 40 -30 -20 -lo 0Pin[dEm]Fig. 7. Response uniformity for the circuit in Fig. 6 operating at 60 MHz. Thehorizontal axis is the signal input power in dBm. The vertical axis is the signaloutput voltage, The cluwes represent the amplitude disparity between inputs,ranging from -10 to +10 dB in l-dB steps. Data is from R. Aiello (see paper inthese Proceedings).,:p,\\= ~[\- -.\‘ ——\I(-F —.. ..~40 .70 -60 .50 -40 -30 42PinhiBrnlFig. 8, Plot of the expected resolution for a b = 33-mm half-aperture BPM vs.signal power for the AD 640 log-ratio amplifier circuit at 60 MHz with a 220-kHzbandwidth, and for an ideal circuit with only kTB noise. The amplifier noisefigure is estimated to be about 15dB. Data from R, Aiello (these Proceedings),4@20 0284?0 so 30 10Fig. 9. Response uniformity of a log-ratio cirwt using four Plessey SL3522Achips operating at 425 MHz. Data from F. D. Wells (LANL).suMMARYTIMfollowing Table summarizes some of the basic features of the three types ofBPM signal processing.w&&l?&l L5?&ra@Timdomain processing yes no noFrequency-domain processing yes yes yesCmicr frequency range >1 GHz <1 OOMHZ <XX)MHZCarrier frequency slewing yes no yesAcquisition bandwidth >1OOMHZ <1OMHZ <100 MHzAmplitude dynamic range low high highDisplacement response linearity intermediate poorest bestNormalized real-time response no yes yesCable phase-matching required depends yes noAmp]iller noise figLIre can be very low >20 dB typ 15 dB achievedcost lowest highest intmmdaleCircuit complexity lowest highest intermediateIn summary, the recent availability of hybrid logarithmic amplifiers have providedsystem designers a new option in BPM system design.REFEiZENCESR. Shafer, “Beam Position Monitoring,” in AIP Conf.proc. #212, page 26 (19~9).R. Shafer, S, Jachim, and R. Webber, “AM-PM Position Measurement Circuit forthe Tcvatron,” IEEE Trans. Nucl, Sci., Vol NS-28, Page 2323 (1981).Analog Devices Corp. Cambridge, MA 02139.R. Aicllo, these Proceedings,Plcsscy Corp,F. D, Wells, private communication ( 1992).

Log-ratio signal-processing technique for beam position monitors

Shafer, R. E.

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Log-ratio signal-processing technique for beam position monitors

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