PHASE DIFFERENCE MONITOR BETWEEN SUPERKEKB INJECTOR
LINAC AND RINGS USING DIRECT SAMPLING TECHNIQUE
N. Liu†,1, T. Miura1,2, T. Matsumoto1,2, F. Qiu1,2, S.Michizono1,2, D. Arakawa2, H. Katagiri2,
Y. Yano2, B.T. Du1, 1SOKENDAI, Kanagawa 240-0193, Japan, 2KEK, Ibaraki 305-0801, Japan
Abstract
In the SuperKEKB Phase2 operation, the beam injection
phase from the injector LINAC to rings drifts several degrees or more per day. The monitoring and compensation
system of the phase drift between the LINAC master oscillator (MO) and the ring MO is important for stable beam
injection. The frequency of LINAC MO and the ring MO
is 571.2 MHz and 508.9 MHz, respectively. Both MO signals are monitored by the direct sampling technique using
the same sampling frequency (clock). There are several
combinations of the clock generation. In this paper, thepossible three combinations will be compared including
the clock jitter performance and the short-term phase stability and the combination 1 is selected for the phase difference monitor system. The 1ms short-term phase stability
is 0.04 deg. (RMS) without digital filter and 0.005 deg.
(RMS) with 10 kHz bandwidth digital filter for both MO
signals in the laboratory. Finally, the long-term phase drift
between LINAC MO and ring MO is monitored at the injector LINAC.

INTRODUCTION
The luminosity of the SuperKEKB upgrade project is 40
times higher than KEKB. The lower-emittance and highercurrent beam is required. The beam injection phase stabilization between the injector LINAC to rings is very important for stable beam injection. Figure 1 shows the master oscillator (MO) system for LINAC, damping ring (DR)and main ring (MR). The MO of the LINAC and the rings
is 571.2 MHz and 508.9 MHz, respectively. They are synchronized by 10 MHz trigger but the phase drift between
them was found to be several degrees per day [1].
KEKB Control Room

LINAC Gallery

PLL
10 MHzPS
1/51
10 MHz

1/51
LINAC-MO
571.2 MHz

MR-MO
508.9 MHz

DR-MO
508.9 MHz

RF-Dist.
&PLL

PS

LER/HER PS
Reference Signal Generator

510 MHz MO

RF-Dist.
&PLL
PS

508.9 MHz
PLL

LINAC-Phase Monitor

e- gunInjector LINAC

508.9 MHzDR ControlRoomPS(Inj. Phase)

PSPS
LER

HERDR

Figure 1: Master oscillator system for LINAC, damping
ring and main ring.
___________________________________________† liuna@post.kek.jp

DIRECT SAMPLING AND NON-IQ DETECTION
The RF frequency can be measured with the sampling
rate lower than the Nyquist rate (twice the maximum frequency component in the signal), which called the undersampling or direct sampling technique [5]. In order to derive the phase of the RF signal, the sampling frequency
must be synchronized with the frequency of the measured
RF signal and selected based in the non-IQ algorithm [3,6]. The sampling frequency f s and the measured RF frequency f RF must satisfy

f RF, K  0,1, 2...
(1)
NK
M
where N is an integer and M is also an integer but greaterthan 3, N and M represent the phase difference ∆φ between
adjacent samplesN  2
(2)
M
The I and Q baseband component of the sampled RF signal can be calculated by the following equations
fs 

Ring-Phase Monitor

571.2 MHz 114.24 MHz 2856 MHz 508.9 MHz

571.2 MHzFor the radio frequency (RF) phase detection in accelerators, the analog down-conversion with digital IQ (Inphase and Quadrature component) detection and direct
sampling technique are widely used [2]. The direct sampling technique gets rid of the down-converter and makes
the RF measurement circuit much simpler and smaller, but
it is sensitive to the clock jitter [3]. In the direct samplingtechnique, all the frequency components within the ADC
bandwidth are converted into the first Nyquist zone. The
non-IQ algorithm can suppress the harmonics of the carrier
frequency and digitally reduce the clock jitter inducedmeasurement errors by averaging over multiply samples[4]. Therefore, the higher phase measurement accuracy canbe achieved. The frequency of the measured RF signal isdifferent so that the direct sampling technique is more suitable.
In this paper, we monitor the two MO signals with different frequency by the direct sampling technique using thesame sampling frequency. The possible combinations of
the clock generation for the phase monitor system will becompared including the clock jitter and short-term phasestability. The short-term phase stability is improved by applying the digital low pass filter (LPF). After the system
performance evaluation, the phase difference monitor system is implemented at injector LINAC gallery and thelong-term phase drift between two MOs is measured.

2 M 1N
x  n  sin   2  n 
M n 0
M

M 12
N

Q
 x  n cos  M  2  n M n 0I

(3)
(4)

where x  n  is the n th ADC sampled data. The phase (φ)
of the measured RF signal can be calculated by  tan 1  Q / I  . Hence, the phase of the RF signal is obtained.

SELECTION AND GENERATION OF THE
SAMPLING FREQUENCY
The numerical relationship between LINAC MO (571.2MHz) and ring MO (508.9 MHz) isf LINAC _ MO 571.2 MHz 55
f RING _ MO 508.9MHz 49
In order to sample two different frequency MO signals
by the same sampling frequency, the K, M and N coefficients must satisfy the following formula from Eq. (1)f LINAC _ MO
f RING _ MO, and M1  M 2  M
fs 
NNK1  1
K2  2
M1
M2
So K1M  N1  55 and K 2 M  N 2  49 .

The possible combinations (comb.) of sampling frequency for LINAC MO (571.2 MHz) is summarized in Table 1. The combination of M  10 and N1  5 can’t provide enough amplitude and phase information of the measured RF signal. So the other three combinations are considered.

SYSTEM PERFORMANCE EVALUATIONMeasurement setup
The configuration of the clock generation and the phasedifference monitor system by direct sampling technique isshown in Fig. 3. The 571.2 MHz MO signal is generatedby the signal generator (Keysight E8663D) and then split
in two. One is used to generate the 571.2 MHz (LINACMO frequency) signal and 508.9 MHz signal (ring MO frequency), the other is for the clock generation. The 571.2MHz signal and 508.9 MHz signal are sampled by ADC1and ADC2 (14-bit, 400 MSPS ADS5474), individually. According to the different RF frequency, different pairs of N1, M 1 and N 2 , M 2 are applied to non-IQ algorithm based on
the same sampling frequency and then the IQ components
are calculated inside field programmable gate array(FPGA) board. The phase of each RF signal is obtained andthe phase difference between 571.2 MHz signal and 508.9
MHz signal is monitored.

Figure 2: Block diagram of the clock generation for direct
sampling technique.
Table 1: Possible Combinations of Sampling Frequency
Combination

X

1×2

11115

3

5++

Filter[MHz]
623.13519.27685.44-456.96

Y
5511Clock[MHz]
124.63103.8562.31

121061141.54

4

𝑴

The block diagram of the clock generation for direct
sampling is shown in Fig. 2 [7]. The LINAC MO 571.2
MHz is used as MO for clock generation. The frequency of571.2 MHz MO signal (RF) is divided by X and then mix
with itself to obtain another frequency RF  1  1 X  .
Then this frequency is filtered by a band pass filter (BPF)
or LPF. Finally, the filtered signal is divided by Y with another frequency divider to generate the required sampling
frequency. The sampling frequency can be calculated by
the following equationf LINAC _ MO(5)fs XYX 1
Where X, Y are both integers. Therefore,K1M  N1  XY  55 and M  X  1 .

Figure 3: Configuration of the clock generation and thephase monitor system by direct sampling technique.

Jitter performance of the clock signal
In direct sampling technique, the measurement error issensitive to the clock jitter. The RMS jitter of the clock signals generated by three combinations (Comb.) are measured by the signal source analyzer from 10 Hz to 10 MHz.
Figure 4 shows the single side-band phase noise power
spectrum of three clock signals. Table 2 summarizes theresults of the clock jitter. The combination 1 has the best
jitter performance.
Table 2: RMS Jitter and Phase Noise for Clock Signals

Comb.1
Comb.2
Comb.3Freq.
[MHz]
124.6362.31
41.54

Power[dBm]
-2.58
-3.36
-1.88

Jitter[fs]
126.48222.23464.7

Phase Noise[mdeg.]
5.67
4.99
6.95

Figure 5: The 1ms short-term phase stability of the combination 1 for 571.2 MHz (left) and 508.9 MHz (right) MO
signals without IIR LPF (blue line) and with 10 kHz bandwidth (BW) (red line) IIR LPF.
Figure 4: Jitter performance of the clock signals.

Short-term stability
In order to compare the short-term stability in time domain, the phase stability of two different RF signals (571.2MHz and 508.9 MHz) sampled by three different sampling
frequencies is measured by the phase difference monitor
system as shown in Fig. 2. The coefficients ( N1 , N 2 , M )of the non-IQ algorithm for 571.2 MHz signal and 508.9
MHz signal are listed in Table 3, respectively.
Table 3: Coefficients of Non-IQ Algorithm
Combination
123

Clock [MHz]124.63
62.31
41.54

M
1264

𝑵𝟏713

SHORT-TERM AND LONG-TERM MEASUREMENT RESULT AT LINAC
Jitter performance
The phase noise is measured by the signal source analyser from 10 Hz to 10 MHz. Figure 6 shows the single
side-band phase noise power spectrum of MO signals andthe clock signal. The RMS jitter is 97.32 fs (LINAC MO),
104.78 fs (LINAC MO monitored signal), 172.48 fs (ringMO monitored signal) and 167.54 fs (clock signal).

𝑵𝟐
1
1
1

Table 4: 1ms Short-term Phase Stability in Deg. (RMS)
Combination
123571.2 MHz
0.038
0.058
0.081

508.9 MHz
0.035
0.054
0.086

Table 4 summarizes the 1ms short-term phase stabilityof three combinations without digital filter in degree(RMS). The combination 1 has the best performance inshort-term stability due to the low clock jitter and the averaging over many multiply samples. The phase stability of571.2 MHz and 508.9 MHz RF signals is 0.038 deg. RMS
and 0.035 deg. RMS, respectively. So the combination 1 isselected for the phase difference monitor system between
SuperKEKB injector LINAC MO and ring MO.
For the phase difference monitor system, the target is tomeasure the long-term phase drift between LINAC MOand ring MO. For higher accuracy, the IQ components ofthe RF signals are filtered by the digital infinite impulse
response (IIR) LPF to suppress the clock jitter and ADC
noise [8]. The 1ms short-term phase stability of the combination 1 without and with different bandwidth IIR LPF isshown in Fig. 5. The phase stability is up to 0.005 deg.
RMS with 10 kHz bandwidth IIR LPF.

Figure 6: Single side-band phase noise power spectrum
from 10 Hz to 10 MHz for MO signals and clock signal.

Long-term phase drift
The LINAC MO signal and ring MO signal are monitored by the phase difference monitor system by direct
sampling technique with the sampling frequency 124.62
MHz. Both IQ data is filtered by 10 kHz IIR LPF for higher
accuracy. Then the averaged raw data is used for the longterm phase drift measurement. All the monitor system is
inside the thermostat chamber to minimize the systemphase drift. The phase drift between LINAC MO and ring
MO is observed 2.3 deg. (peak to peak) for 2 days by thephase difference monitor at LINAC (blue line) in Fig. 7.
The phase difference is also monitored by the phase
monitor at rings. The results are matched very well asshown in Fig. 7. The phase drift compensation system isunder consideration for stable beam injection.

Proc. 12th Mixed Design of Integrated Circuits and Systems(MIXDES), Cracow, Poland, 2005, pp. 783–788.
[7] T. Matsumoto et al., “Simultaneous measurement of RF signal and LO signal using direct sampling detection technique”,
in Proc. 14th Annual Meeting of the Japanese Society of accelerator (PASJ’17), Hokkaido, Japan, Aug. 2017, paper
TUP063, pp. 493-495.
[8] F. Qiu, private communication, July 2018.

Figure 7: The long-term phase drift of the phase difference
between LINAC MO 571.2 MHz (ADC1) and ring MO
508.9 MHz (ADC2) with 10 kHz bandwidth IIR LPF. The
blue line is monitored by the phase monitor at LINAC andthe orange line is monitored by the phase monitor at rings.

CONCLUSION
In order to monitor the different frequency 571.2 MHz
and 508.9 MHz RF signals by the direct sampling technique using the same sampling frequency, the performanceof the three possible combinations of the clock generation
are evaluated in the laboratory including the clock jitter andshort-term phase stability. The combination 1 of the clock
generation is selected due to its good jitter performance andshort-term stability. The clock jitter of combination 1 is126.48 fs at 124.63 MHz and the 1ms short-term phase stability is 0.04 deg. (RMS) without digital filter. The shortterm phase stability is improved by applying the digital IIR
LPF for higher accuracy and the phase stability is up to0.005 deg. (RMS) with 10 kHz bandwidth IIR LPF for both
MO signals. Finally, the phase different monitor system isimplemented based on the combination 1 at injector
LINAC gallery. SuperKEKB LINAC MO signal (571.2MHz) and ring MO signal (508.9 MHz) are both monitored
at LINAC and rings and the results are well matched. The
long-term phase drift between two MOs is observed 2.3
deg. for 2 days. The phase drift compensation system isunder consideration for stable beam injection.

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