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TRANSVERSE MULTI-BUNCH FEEDBACK DETECTOR ELECTRONICS
USING DIRECT SAMPLING ANALOG-TO-DIGITAL CONVERTERS FOR
THE SYNCHROTRON RADIATION SOURCE PETRA IV
S. Jablonski∗ , H.-T. Duhme, U. Mavrič, S. Pfeiffer, H. Schlarb
Deutsches Elektronen-Synchrotron, Hamburg, Germany
Abstract
PETRA IV, a new fourth generation synchrotron radiation
source planned at DESY, will require a transverse multibunch feedback (T-MBFB) system to damp transverse instabilities and keep the beam emittance low. The critical part of
the T-MBFB is a detector that must measure bunch-by-bunch,i.e. every 2 ns, position variations with the resolution not
worse than 1 µm for the beam dynamic range of ±1 mm. In
this paper, we present the conceptual design of the T-MBFB
detector from the beam position pickups to the direct sampling ADCs. We analyze noise sources limiting the detector
resolution and present measurement results based on theevaluation modules.

INTRODUCTIONPETRA IV will operate in two modes, i.e. the brightness
and timing mode. The requirements for the T-MBFB aresummarized in Table 1. Due to short bunch spacing of 2 ns
and low bunch charge of 0.4 nC in the brightness mode,
it is more challenging to fulfill the resolution requirementof 1 µm in this mode than in the timing mode. Therefore,
all performance calculations in this paper are done for thebrightness mode. It is expected that in the timing mode theresults are similar or better.

Table 1: PETRA IV design parameters in the brightness (B)and timing (T) mode and the requirements for the T-MBFB.
Design Parameter

Value

Energy 𝐸
Revolution freq. 𝑓rev
Emittance 𝜖 𝑥 /𝜖 𝑦

6 GeV
130.12 kHz< 20/4 pm rad (B)< 50/10 pm rad (T)200 mA (B), 80 mA (T)max. 3840 (B), 80 (T)∼0.4 nC (B), ∼7.7 nC (T)2 or 4 ns (B), 96 ns (T)∼45 ps (B), ∼64 ps (T)23.4 kHz, 35.2 kHz
750 − 1250 MHz±1 mm (from vacuum
chamber center)±1 mm

Total current 𝐼
Number of bunches
Bunch charge 𝑞 𝑏
Bunch spacing 𝑇rep
Bunch length 𝜎𝑡
Betatron freq. 𝑓 𝑥 / 𝑓 𝑦
T-MBFB det. bandwidth
Max. bunch offset 𝑟 dc
Max. betatron osc.
amplitude 𝑟 𝑎𝑐
T-MBFB det. resolution
T-MBFB damping time

< 1 µm (SNR> 60 dB)< 40 turns(for 𝑟 ac < 200 µm)

MODEL OF THE PICKUPS AND ANALOG
ELECTRONICS

T-MBFB DETECTOR SCHEME

Electron Bunch in the Vacuum Chamber Center

Figure 1 presents a simplified block diagram of the vertical T-MBFB detector electronics. The horizontal detector
differs only in the connection of the stripline electrodes tothe combiners in such a way that the detector is sensitive tohorizontal bunch variations. Hence, it will not be discuss
further in the text.
The stripline BPM is composed of four electrodes equallydistributed around the beam pipe, i.e. every 90°, with acharacteristic impedance 𝑍 𝑜 of 50 W. For the vertical beam
position measurement, electrical pulses from the upper andlower pick-ups are combined together, creating signals 𝑉AB
and 𝑉CD , respectively. The signals are doubled in the pulse
multiplier, and further, they are subtracted from each other inthe bunch offset compensation. The difference signal Δ𝑉 is
fed to the front-end electronics (DRTM-MBFB-FE) and thedigitizer (DAMC-DS5014RT), which are implemented in
the MicroTCA.4 form factor. The above mentioned hardware
is described in more detail in the following sections.

The frequency-domain transfer impedance of a stripline
cylindrical electrode can be modelled as [1]:





𝛼
𝐿
sin(𝜔Δ𝑡)𝐿
𝑍 (𝜔) = 𝑗 𝑍 𝑜 exp − 𝑗𝜔
+ Δ𝑡
sin 𝜔
,
2𝜋
𝑐0
𝜔Δ𝑡
𝑐0
(1)
where 𝑐 0 is the speed of light in vacuum, 𝐿 is the length ofthe electrode, 𝑅 is the radius of the vacuum chamber, 𝛼 isthe electrode width in rad (geometric coverage factor), Δ𝑡 isa time delay given by Δ𝑡 = 𝑅𝛼/𝑐 0 . Assuming the electron
bunch traveling in the middle of the vacuum chamber is apoint charge in the transverse direction and has a Gaussian
shape in the longitudinal direction with the rms bunch lengthof 𝜎𝑡 , the stripline coupler output voltage is−(𝜔𝜎𝑡 ) 2
𝑉 (𝜔) = 𝑍 (𝜔)𝑞 𝑏 exp,(2)2∗ szymon.jablonski@desy.de

where 𝑞 𝑏 is the bunch charge.
Figure 2 presents amplitude spectrum at the stripline coupler output for the brightness mode (3840 bunches, rep. rate

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Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

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Figure 1: Simplified block diagram of the vertical T-MBFB detector electronics.
of 2 ns, 𝑞 𝑏 =0.4 nC, 𝜎𝑡 =45 ps) and for different electrodelengths 𝐿 of 150 mm and 75 mm. The electrode length determines the optimal operating frequency of the receiver,which is around 500 MHz and 1 GHz, respectively. Thesefrequencies correspond to the first and second harmonicof the multi-bunch spectrum with the bunch repetition rateof 2 ns. The vacuum chamber radius 𝑅 is 17 mm and theelectrode width 𝛼 is 0.6 rad. The transfer function roll-off
for the 150 mm-electrode is steeper and the magnitude decrease equals about 3 dB for the fastest multi-bunch mode
at ±250 MHz. Hence, we decided to use the shorter 75 mmelectrode, for which the magnitude decrease is only 1 dB.

Figure 2: Amplitude spectrum at the stripline coupler output
for the brightness mode (3840 bunches, rep. rate of 2 ns,
𝑞 𝑏 =0.4 nC, 𝜎𝑡 =45 ps) and for different electrode lengths 𝐿of 150 mm and 75 mm.
Instead of cylindrical electrodes, flat electrodes were selected as they are easier to be manufactured. However, thegeometrical coverage factor is slightly different for both designs. Electromagnetic simulations [2] shown that the flat
electrodes have lower sensitivity by a coefficient 𝛽 of about
0.89, which will be further used to scale the signal amplitude.

Bunch Offset from the Vacuum Chamber CenterWith different machine configurations, the electron bunch
can be shifted by 𝑟 from the centre of the vacuum chamberand rotated with respect to the electrode axis by an angle of 𝛾
(see Fig. 1). The output voltage 𝑉 (𝜔) for different bunch
positions is scaled by a coefficient 𝑠(𝑟, 𝛾) given by [3]∞𝑠(𝑟, 𝛾) = 1 + 𝑛𝛼 
4 ∑︁ 1  𝑟  𝑛cos(𝑛𝛾) sin.
𝛼 𝑛=1 𝑛 𝑅
2

(3)

Finally, the output voltage at each electrode is𝑉𝑥 (𝜔, 𝑟, 𝛾 𝑥 ) = 𝛽𝑉 (𝜔)𝑠(𝑟, 𝛾),(4)where the subscript 𝑥 defines the electrode A, B, C or D.
The electrode angles equal 𝛾 𝐴 = 𝛾 − 𝜋/4, 𝛾 𝐵 = 𝛾 − 3𝜋/4,𝛾𝐶 = 𝛾 − 5𝜋/4, 𝛾 𝐷 = 𝛾 − 7𝜋/4. To make the detector
sensitive only to vertical bunch oscillations, the upper andthe lower electrode outputs must be combined together. The
summed signals, using only the first order component of
Eq. (3) (this simplification makes an estimation failure lower
than 6 % for small 𝑟 ≤ 1 mm), are given by
𝑉AB (𝜔, 𝑟) = 𝑉 𝐴 (𝜔, 𝑟, 𝛾 𝐴) + 𝑉𝐵 (𝜔, 𝑟, 𝛾 𝐵 )
"
#
√
𝛼
4 2 𝑟 sin,= 𝛽𝑉 (𝜔) 2 +
𝛼 𝑅
2

(5)

𝑉CD (𝜔, 𝑟) = 𝑉𝐶 (𝜔, 𝑟, 𝛾𝐶 ) + 𝑉𝐷 (𝜔, 𝑟, 𝛾 𝐷 )
"
#
√
𝛼
4 2 𝑟 = 𝛽𝑉 (𝜔) 2 −
sin
𝛼 𝑅
2

(6)

for 𝛾 in the range of [0, 𝜋]. Bunch offset from the vacuum
chamber center 𝑟 includes information about the verticalconstant orbit shift 𝑟 𝑑𝑐 and the vertical betatron oscillation
amplitude 𝑟 𝑎𝑐 , i.e. 𝑟 = 𝑟 𝑑𝑐 + 𝑟 𝑎𝑐 .

Bunch Offset Compensation
For high detector resolution, the full-scale input range ofan ADC should be used to sample only the betatron oscillation signal (amplitude modulation), which is about 22 dB
weaker as the "carrier" signal. The carrier is suppressed bymore than 30 dB by subtracting both signals 𝑉AB and 𝑉CD
using an RF hybrid as shown in Fig. 1. Before subtraction,
both signals are conditioned using variable attenuators 𝑔1
and 𝑔2 to get the same carrier amplitude. They are alsofiltered with a 6-pole, lowpass, 2 GHz bandwidth, Bessel
filter having a transfer function 𝐹 (𝜔). Due to linear phase
response of the filter, it does not produce any ringing overlapping the next bunch. Assuming all electrical components
are lossless, the vertical betatron oscillation voltage at theoutput of the bunch offset compensation equals
Δ𝑉 (𝜔) = 𝑔1𝑉AB (𝜔, 𝑟) − 𝑔2𝑉CD (𝜔, 𝑟)
#
" √
𝛼
4 2  𝑟 ac 
= (𝑔1 + 𝑔2 ) 𝛽𝑉 (𝜔)𝐹 (𝜔)
sin
.
𝛼
𝑅
2
(7)

MOP039116

08 Feedback Systems and Beam Stability

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SNR of the Analog Electronics
Integrating Δ𝑉 (𝜔) within the MBFB detection range from750 MHz to 1250 MHz for the maximum betatron oscillation amplitude of 𝑟 ac = 1 mm gives rms voltage of 0.25 V.
Referring this voltage to thermal noise of 50 Ω load resistor
gives SNR of 85 dB. However, the electrical components
and 25-m long coaxial cables connecting the pickups and thedetector electronics introduce insertion loss that degrades
the SNR. The estimated loss is about 15 dB that reduces the
SNR of the analog electronics to 70 dB, which is still 10 dB
more than required for the T-MBFB. However, the resolution
limiting component is the digitizer, which is discussed in
the following section.

DIRECT SAMPLING DIGITIZER
Direct Sampling vs. Down-Conversion
MBFB systems are mainly based on two detection
schemes, i.e. the direct sampling scheme as shown in Fig. 1or the down-conversion scheme, which additionally involves
an analog mixer in front of a digitizer to shift the detection
band to baseband. In the past, the down-conversion scheme
was preferred as ADCs did not have enough bandwidth fordirect sampling of wideband RF pulses. In recent years, theADC technology has moved forward - not only the input
bandwidth and sampling rate have increased, but also ADC
front-ends became better in terms of noise.
Noise floor of the down-conversion scheme is usually
3 dB lower than the direct sampling scheme (if using thesame ADC for both cases). However, the direct sampling
has a few advantages over the down-conversion:• The down-conversion requires a more complex hardware including the local oscillator (LO).
• The baseband detectors are more susceptible to electromagnetic interference (EMI), e.g. due to switchedmode power supplies.
• Up-conversion of 1/f noise of the ADC front-end isreduced in the direct sampling suppressed carrier detector [4] (carrier suppression is implemented in thebunch offset compensation module). In contrary, thebaseband detector resolution degrades due to 1/f noiseof the ADC.
• Designing of the front-end electronics with flat magnitude and linear phase is more difficult for the
baseband detector ([23.4 kHz, 250 MHz] spans over4.03 decades) than for the direct sampling detector([750 MHz, 1250 MHz] spans only over 0.22 decades).
Moreover, the DC coupling of the baseband detector
requires additional electronics for the common-mode
voltage adjustment.

that allows for flexible data processing like I/Q digital downconversion, calculation of the bunch-by-bunch oscillation
amplitudes and the transverse MBFB implementation.

Digitizer Noise and Interleaving Spurs
The betatron oscillation signal converted to digital can be
written as [5]Δ𝑉𝑘 = [𝑛 𝑘 + Δ𝑉 (𝑘𝑇𝑠 − 𝑥 𝑘 )] (1 − 𝑟 𝑘 ) + 𝑛𝑞 ,(8)where 𝑘 is the sample number, 𝑇𝑠 is the sampling period,𝑛 𝑘 is the additive noise of the ADC input stage, 𝑥 𝑘 is the
combined timing jitter caused by aperture jitter (time fluctuations in the ADC sample and hold) and by clock timing
jitter, 𝑟 𝑘 is the voltage reference noise, 𝑛𝑞 is the quantizationnoise (white, uniformly distributed with zero-mean). Noisesources 𝑛 𝑘 , 𝑥 𝑘 , 𝑟 𝑘 and 𝑛𝑞 are independent random processes.
Timing jitter 𝑥 𝑘 has a negligible impact for the amplitude
measurements. Quantization noise PSD can be estimated by
𝑆 𝑛𝑞 ( 𝑓 ) = −20 log(2𝑚 ) − 10 log( 𝑓𝑠/2) ≈ −178[ dBFS/Hz], (9)where 𝑚 is the number of bits (14) and of 𝑓𝑠 is the sampling rate (5 GSPS), which is also a negligibly small number.
The voltage reference noise 𝑟 𝑘 is usually considerably lower
than the input stage additive amplitude noise [5], which
was measured to be −155 dBc/Hz at 1 GHz. The integrated
amplitude noise within the detector range gives the SNRof 67 dB. However, the single pulse, corresponding to one
bunch, occupies about a half of the possible measurement
2-ns time window that reduces the SNR by about 3 dB down
to 64 dB — this is shown in more detail in the next section.
Each of the ADCs in the Zynq UltraScale+ RFSoC is built
on multiple sub-ADCs in an interleaving architecture. Theinterleaving process requires that a calibration algorithm to
be carried out, described in detail in Ref. [6]. Because of
the suppressed-carrier operation of the T-MBFB, the ADCs
can only be calibrated in the machine start-up. Later thecalibration coefficients are frozen. The long-term behaviourof the ADCs needs be studied in detail, but we do not expect
any detrimental effects, because the system is located in atemperature stabilized environment.
Even if the calibration procedure is carrier out, there aresome residual interleaving spurs. Since the gain and time
skew spurs depend on the input signal level, they are very low
for no-carrier operation. The DC offset spurs at 𝑛 𝑓𝑠 /8 (𝑛 =1 . . . 8) are below 80 dB and the sampling frequency 𝑓𝑠 is so
selected that the spurs do not overlap with the coupled-bunch
oscillation modes.

Zynq UltraScale+ RFSoC

SNR Improvement - ADC Parallelization and Pulse
Multiplication

Taking into account the pros and cons of both detector
schemes, the direct sampling has been selected using the
Zynq UltraScale+ RFSoC ADC. It has 14-bit resolution,
sampling rate of 5 GSPS and an input bandwidth of 6 GHz.
This module includes also FPGA and processing system

The basic detector structure provides the detector SNR of
64 dB, which is a 4-dB safety margin to the requirements.
However, the SNR can be further improved by two hardware
extensions, i.e. ADC parallelization and pulse multiplication.

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Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

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ISSN: 2 6 7 3 - 5 3 5 0
d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - M O P 0 3 9The single RFSoC module includes eight ADCs. Four
ADCs can be used for the T-MBFB detector and the rest areplanned to be used for different diagnostics like the measurement of bunch-by-bunch phase or absolute bunch position in
the vacuum chamber. The noise floor improvement factor isa square root of the number of parallel ADC channels, whichis 6 dB for four ADCs. The parallelization not only improves
the detector resolution, but it also provides redundancy incase of hardware failures.
The pulse multiplier improves the resolution by 3 dB,
which was presented in our previous publication [7].

by SNR, was analyzed separately for the analog electronics
and the digitizer. The analog electronics was analyticallymodelled to have SNR better than 70 dB. The digitizer was
experimentally tested both in the laboratory conditions andat PETRA III. The analysis shows that the dominant noise
source is the digitizer front-end noise, which limits the detector resolution to 63 dB for the PETRA IV system. This

DIGITIZER PERFORMANCEEVALUATION AT PETRA III
The digitizer performance was evaluated at PETRA III
using the sum signal from four stripline electrodes. The sum
signal amplitude depends only on the bunch charge, it does
not change with the transverse bunch oscillations. Since,
the bunch charge is relatively stable (life time is about 1.5 h,
the short-term pulse amplitude variations are dominated byresidual amplitude noise of the ADC. Figure 3 presents thepulse signal converted to digital with the sampling clockof about 5 GSPS generated by the RFSoC internal PLL andsynchronized to the machine main oscillator. In the digitaldomain, the RF pulse is IQ down-converted to baseband,
lowpass filtered and decimated by 10. Using IQ values, thebunch-by-bunch and turn-by-turn amplitudes are calculated.
In the next step, the SNR is computed for each bunch in thebunch train based on 132 revolutions, the SNR values arepresented in Fig. 4. The averaged SNR equals 66 dB, which
is only 1 dB worse than was estimated for 2-ns long pulse
using the laboratory setup. In the future PETRA IV, thesingle pulse will be twice shorter (as written in the previous
sections), therefore the SNR will decrease down to 63 dB.

Figure 4: SNR of the RFSoC based T-MBFB detector evaluated at PETRA III in the timing mode with 40 bunches.
fulfills the project requirements, however, if needed in the
future, the SNR can be improved by the ADC parallelizationand pulse multiplication to more than 70 dB.

REFERENCES[1] M. Wendt, “BPM Systems: A brief Introduction to Beam
Position Monitoring”, 2020.
doi:10.48550/arXiv.2005.14081[2] S. Strokov, “Stripline monitor simulation. S-parameters, Signal
strength and quality”, Internal Report, Aug. 2022.
[3] R. E. Shafer, “Beam position monitoring”, in AIP Conf. Proc.,vol. 212, pp. 26–58, 1990. doi:10.1063/1.39710[4] E. Rubiola and V. Giordano, “Advanced interferometric phaseand amplitude noise measurements”, in Rev. Sci. Instrum.,vol. 73, no. 6, pp. 2445–2457, Jun. 2002. doi:10.1063/1.
1480458[5] A. C. Cárdenas-Olaya, E. Rubiola, et al., “Noise characterization of analog to digital converters for amplitude and phasenoise measurements”, in Rev. Sci. Instrum., vol. 88, no. 6,
pp. 065108, Jun. 2017. doi:10.1063/1.4984948

Figure 3: Digitized bunch pulse at PETRA III with the sampling rate of 5 GSPS.

CONCLUSION
In this paper, we presented the structure of the T-MBFB
detector for PETRA IV. The detector resolution, specified[6] Zynq UltraScale+ RFSoC RF Data Converter
v2.6
Gen
1/2/3/DFE
LogiCORE
IP
Product
Guide(PG269),https://docs.xilinx.
com/r/en-US/pg269-rf-data-converter/
RF-ADC-Calibration-Mechanism[7] S. Jabłoński et al., “Conceptual Design of the Transverse
Multi-Bunch Feedback for the Synchrotron Radiation Source
PETRA IV”, in Proc. IBIC’22, Kraków, Poland, Sep. 2022,
pp. 488–491. doi:10.18429/JACoW-IBIC2022-WEP36

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08 Feedback Systems and Beam Stability