Proceedings of IBIC2012, Tsukuba, Japan

TUPA12AN DBPM CALIBRATION METHOD IMPLEMENTED ON FPGA *X.D. Sun#, Y.B. Leng†, SINAP, CAS,Shanghai, CHINA
Abstract
An calibration method on the four channels of DBPM
is discussed. Using interpolation, the method isimplemented on FPGA, which can handle the data on-line.
The calibration algorithm is mono-channel dependent andis intended to solve the beam current dependence problem
and increase resolution. Orientations of the method arepresented. Basic design diagrams of the pipelined FPGA
modules are listed and comparisons are made before andafter the calibration.

INTRODUCTION

200position / Pm

0-200-400

Figure 2: The four channel gain inconsistency of DBPM.
Different calibration methods have been proposed andimplemented as a solution on respective instrument[2][4][5]. Libera EBPM use a Quasi-crossbar switch torandomly connect inputs to different channels thus inaverage remedy the inconsistency [2][3]. The SNS use thewave reflection to do calibration on the s plane analysis[5].

-600-8000510152025
signal amplitude / mV303540

Figure 1: The beam current position dependence problemof the DBPM .
When Beam stays at the same position with increasing
intensity, the same demodulated position output isexpected but in practice not. The demodulated position
output tend to be stable as beam current intensity
increases as show in figure1. This is resulted from the factthat the channel give different gain to signal with thesame frequency band but varying intensity, which we callsignal channel nonlinearity and another aspect that fourchannels give different gain to the same signal.
The across channel inconsistency is caused byhardware inconsistency on the front end, which meansthat the four channel outputs differ with the same inputs,
as shown in figure 2. whilst the mono channel
nonlinearity refers to the fact that the gain of a channel toinputs with different intensity and deviates from a linear
gain. The two aspects are shown together in figure3.

Figure 3: Across channel gain inconsistency of DBPM.
We have put forward a new approach based on DDC
algorithm and attest its validity using Matlab on PC
offline [4]. In this article, the calibration method using
piece-wise linear interpolation is realized it on our selfdeveloped DBPM using FPGA, thus the calibration isimplemented on line directly after TBT data.
The advantage of our tactic is that it can remedy theinconsistency across different channels and the monochannel inconsistency together.
The basic idea of our method is that it try to align thefour channel inconsistency to a single reference.

_________________________________________*Work supported by National Nature Science Fundation of China11075198, #sunxudong@sinap.ac.cn, † leng@sinap.ac.cn

ISBN 978-3-95450-119-9
Beam Position Monitor System

1c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Due to the gain inconsistency across different channelsof DBPM and the gain nonlinearity of the mono channel ,problems of beam current dependence occur, which blurs
beam position measurement.

TUPA12

Proceedings of IBIC2012, Tsukuba, Japan

The position calculation is carried out using formula1,
while the processing gain of channel a and channel b willmake the calculated position drift from the ideal one asshown in formula 2.

uncalibrated  positiona G ( A)  bG ( B )aG ( A)  bG ( B )(2)

The question then moves to how to use the 5*Nparameters to construct the map from the TBT amplitude
back to the signal source amplitude as shown in formula
3 ,where and is the map function.

calibrated  position

Figure 4: The calibration dataflow diagram.

Here we use piecewise interpolation to thread thediscrete input-response pair to approximate the amplitude
response curve of DBPM in figure 3, thus giving the mapfunction andc 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○OVERVIEWThe overall diagram is shown in figure 4, calibration isdone to the TBT data after DDC process. A generaldescription to our calibration strategy is as below: using
standard signal source, inputs with constant frequency but
varying power are fed to the four channels of the DBPM
through a power splitter, response data after theprocessing of the 4 channels is acquired using an Ethernet
interface and the energy at the critical frequency areconstructed using harmonic analysis, thus a table isestablished that maps the processed data back to theoriginal data. Gain experiments of the DBPM show thatthe nonlinearity of the gain of each channel can be wellapproximated by linear interpolation on small intervals.
Herein, the dynamic range of the input is divided into N-1
sections, thus 5*N parameters are acquired after doing thecalibration, as show in table 1.
Table 1: Calibration parameters
Input

CH1
response

CH2
response

I1

R11I2

CH3
response

CH3
responseR12R13R14R21R22R23R24

ĂĂ

ĂĂ

ĂĂ

ĂĂ

ĂĂ

IN

Rn1

RN2

RN3

RN4

The DDC process moves the frequency band inquestion down to the base band. Thus the amplitude
variance reflects the energy of the critical frequency after
the processing of the channel, a map back to the preprocessing state thus correct the four channel
inconsistency and mono channel nonlinearity together.

position

A-BABa c [a G ( A)]  b c [bG ( B)](3)a c [aG ( A)]  b c [bG ( B)]gpA general
expressionof interpolation is(4)Where (xi,fi) is the control point sampled. Lj(x) is theblending function or base function used to interpolate.
When reduced to linear segmented interpolation, theblending function becomes linear, and the formulap
simplifies
to(5)Figure 5 and Figure6 shows the blending function.
Therefore, a core module in the FPGA would be arealization of formula 2 with inputs x, which is theuncalibrated DDC data, xn, xp, the lower and upperbound of x

Figure 5: The global plot of blending function.

(1)

ISBN 978-3-95450-119-92Beam Position Monitor SystemProceedings of IBIC2012, Tsukuba, Japan

TUPA12position / Pm

5000-500
before calibration
after calibration-10000TECHNICAL DETAIL
General Layout
The algorithm is implemented on FPGA which ismounted on the digital board of the DBPM. A work flowof the calibration process looks like this:First the data after the DDC( TBT data ) are put into asegmentation module to judge which interval the current
data belong to. The two ends of the TBT interval xn, xp
and the corresponding signal source amplitude interval
yn,yp are decided. Thus in this interval, all the parameters
are determined in order to calculate the calibrated value
using formula 5.

10152025
signal amplitude / mV

303540Figure 8: The beam current dependence comparison.

Disscussion
The discussed method try to align the 4 channel
processing to a common reference which closely rely on
the relative accuracy of the signal source. The signal
source should be stable as time varies insuring an relative
accurate power ratio between different input level during
the calibration parameter acquire process.
Finite word length of the FPGA without floating pointoperation might impair the precision of the calibration but
can be ameliorated by increasing the word length.
Refinements to our solution will soon be carried out. In
the coming future, the whole calibration process will becontrolled by the on board ARM and can be accessed
remotely in an automatic way. Communication of FPGA
and ARM is being brought out.

ACKNOWLEDGMENT
The author gets a lot of helps from lab members andacademic advisor professor Leng, and would like toexpress sincere thanks to them.

REFERENCES
Figure 7: The working flow inside the FPGA LOGIC.
The 5*N calibration parameters in table 1 are stored on
the FPGA IP CORE ram and can be dynamically altered.
The whole FPGA logic is divided into several modules
that are decoupled, ready for future update.

Results
Experiments are conducted which verified thefeasibility of our approach. The beam current dependence
problem is well suppressed as show in figure 8.

[1] YI Xing, Leng Yongbin, other, RF front end for digital
beam position monitor signal processorˈNuclear Scienceand Techniques22(2011)[2] Multiplexed Beam Position Monitor, www.Bergoz.com.
[3] Libera Electron User Mannual 1.20, Instrumentation
Technologies, 2006
[4] Yi Xing, Leng Yongbin, other, A calibration method for
the RF front-end asymmetry of the DBPM Processor,
Proceeding of DIPAC2011,Hamburg, Germany[5] J.Power,L.Day,M. Plum,M.Stettler, Beam position monitor
systems for the SNS LINAC,PAC2003

ISBN 978-3-95450-119-9
Beam Position Monitor System

3c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Figure 6: The local plot of blending function.

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