EVALUATION OF LLRF STABILITIES AT STF
T. Miura#, S. Michizono, T. Matsumoto, H. Katagiri, Y. Yano, S. Fukuda, KEK, Tsukuba, JapanY. Okada, NETS, Fuchu-shi,Japan

Klystron

Cavity 4
Cavity 3

IQ modulator

Cavity 2

M.O.

1300 MHz
Cavity 1

LPF(fc=0.4MHz)

L.O.(1310 MHz)I

FPGA
FF_I table P-Gain++

Digital delay

FEEDBACK INSTABILITY DUE TOPASSBAND OF TM010 MODE
The cavity is operated in the π mode, which has thehighest efficiency for beam acceleration. In the operationwith FB control, rf instability can occur due to the
passband of TM010 mode except for the π mode [3,4].
Table 1 shows the frequency difference between the πmode and the other modes measured at each cavity at theSTF. For a given mode, the frequency is different fordifferent cavities due to fabrication error.
Table 1: Frequency differences between π mode and theother mode for each cavity.
mode
8/9π
7/9π
6/9π
5/9π
4/9π
3/9π
2/9π
1/9π

Cavity 1fπ- f (MHz)
1.16753.6413
6.9246
11.8131
16.0743
20.8873
24.101326.4603

Cavity 2fπ- f (MHz)0.72233.53927.3201
11.690216.4536
20.7968
24.500327.2074___________________________________________#takako.miura@kek.jp

Cavity 3fπ- f (MHz)1.12253.47427.0056
11.611616.3576
20.9104
24.4863
26.6434

Cavity 4fπ- f (MHz)0.88593.39317.082211.500916.2954
20.6134
24.171726.6119++

Set_I table+I
Set_Q table

FF_Q table
Digital delay

ADC

10MHz
cPCI board

ADC

QADC

The Superconducting RF Test Facility (STF) is theR&D facility of the International Linear Collider (ILC).
In the STF phase-1, four nine-cell cavities [1] wereinstalled in a cryomodule and operated using the vectorsum feedback (FB) control[2]. They were driven by apulse with a width of 1.5 ms and a repetition rate of 5 Hz.
The rf stability of 0.07% in amplitude and 0.24° in phaseis required at the flat-top region for ILC.
In this paper, we report the measurement of rf
instability arising from other passband like a 8/9π mode,
FB operation in combination with feedforward (FF) table
improved overshoot at the leading-edge of the flat-topregion, and the test on the operation using an electricalquasi-beam.

ADCINTRODUCTIONDACIn STF phase-1, four-cavities are operated with vectorsum feedback (FB) control. The FB control instabilities
arising from passband of TM010 mode other than π mode
were measured. Further, a feedforward (FF) table wasused in combination with FB control, which improved
the flatness of the flat-top region. A method for reductionof overshoot in FB + FF operation is also proposed. Byelectrically developing a quasi-beam, the response for
quasi-beam injection was also measured, and thecorrection on beam-loading was performed.

Figure 1 shows the diagram of the LLRF control
system [5] at the STF.
The pick-up signal from each cavity is down-converted
to an intermediate frequency (IF) of 10 MHz. These IF
signals are sampled by 16-bit ADC at 40 MHz.
Separation of I/Q components, vector-sum and FB
calculations are performed on a field programmable gatearray (FPGA). The baseband I/Q signals are output froma 14-bit DAC. They are fed into the IQ modulator via a0.4-MHz low-pass filter (LPF) in order to reject thesignals corresponding to modes other than the π mode.
In this study, the LPF was removed to measure the raw
intensities of the signals of the other modes. A digitaldelay system with a clock of 40 MHz was implemented
in the FPGA to observe the relation between feedback
loop delay and the rf instability. The digital delay wasvaried between 1 and 120 clocks (3 μs).

DAC

Abstract

P-Gain+-QFigure 1: Schematic diagram of LLRF system. In theinstability measurement arising from the other mode πmode, low pass filter placed between DAC and IQ
modulator was removed.
The feedback became stable or unstable depending on
the digital delay. In the case of unstable, 8/9π, 7/9π and
6/9π modes are observed other than π modes in thefrequency spectra. The rms values of amplitude
indicating instability for additional loop delay is shownin Fig.2; the upper four graphs in the figure show theresult of the FB at each cavity, while the lowest graphshows the result of the vector-sum FB operation. In thecase of high gain, i.e., p=50, stable region is extremely
narrow in individual operation because of the large
excitation by the 8/9π and 7/9π modes; the position ofstable region is different for each cavity, sincefrequencies of the 8/9π and 7/9π modes are different foreach cavity. The result of vector-sum operation, therefore,became unstable over all regions of loop delay. In thecase of low gain, i.e., p=5, the stable region became
wider. In the vector-sum operation, since the intensitiesof the signals from each cavity become ~1/4, lessinstability is observed over almost the entire range ofadditional loop delay.

longer than the loop delay of the FB-circuit itself, whichis estimated to be approximately 3.26 μs (LPF: 1.476 μs+ Amp: 0.763 μs + klystron: 0.123 μs + FPGA: 0.4 μs +cable/waveguide: 0.5 μs). The FB delay depends not
only on QL but also on the FB gain. Under FB + FFSM
condition, the overshoot decreased to 0.1% and 0.1°.

Figure 3: Comparison of FFDAC with FFSM

Figure 2: Result of rms values of amplitude indicating
instability for additional loop delay. The upper four graphs
are results of FB operation of the individual cavity, thelowest graph is the result the vector-sum operation.

FEEDFORWARD TABLE
In this section, we discuss the FB operation with the useof a FF table. The amplitude and phase of the flat-top
region was measured under three operational conditions;
FB, FB + FFDAC, and FB + FFSM; the measurement
results are shown in Fig.4. The result under FB differs
slightly from the set value, and the amplitude and phaseare sensitive to the FB Gain. In contrast, in the case ofthe use of a FF table such as FFDAC or FFSM (see.
Fig.3) in combination with FB, the results are in goodagreement with the set value. The flatness observed at700~1600 μs corresponds to 0.02% rms and 0.016° rms
in the case of FB operation and 0.007% rms and 0.015°
rms in the case of FB operation with a FF table. Figure 3
shows a comparison between the FFDAC and FFSM.
FFDAC is the FF table whose output is the same as thatfrom DAC in the FB operation. DAC output is used asthe FF table to correct the nonlinearity of a klystron or
the RF amplifier. Under FB + FFDAC condition,
however, a large overshoot of 1% was observed at theleading-edge of the flat-top region. The overshoot isthought to be caused by the delay in the feedback. To
compensate the delay, FFDAC should be shifted
temporally forward the length of delay. FFSM is madeby applying the smoothing procedure from each channel
to the next X channel which is corresponding the twice
the amount of the delay. The amount of delay for FB gain
= 90 was approximately 20 μs for QL (loaded Q) = 3 ×
106 and ~8 μs for QL = 1.2 × 106. These delay length are

Figure 4: Comparison of amplitude and phase measured
at flat-top region. Under FB + FFDAC or FB + FFSM
condition, stability at 700~1600 μs is 0.007% rms and0.015° rms.

OPERATION WITH QUASI-BEAM
In STF phase-1, the beam is not available. Therefore,to measure the response of a beam, a quasi-beam waselectrically fabricated. For this, a square wave with anangle of −180° was introduced for klystron input, asshown in Fig.5. The DAC outputs of the FB operation
with and without the quasi-beam are shown in Fig.6. The
amplitude of quasi-beam was adjusted such that theresultant DAC outputs in FB operation had the same
amplitude between the filling time (100−600 μs) and thebeam injection time (812−1322 μs).

Figure 7 shows the comparison of the response of FB
operation with and without the quasi-beam at the flat-topregion. The quasi-beam showed a drop of 1.5% in
amplitude and offset of 0.2° in phase. Therefore, beamcorrection using FF(beam) table was achieved bysubtracting the DAC output obtained with the quasibeam from that without it, as shown in Fig.6.
Figure 8 shows the result of measurements around thequasi-beam injection in FB + FFSM + FF(beam)
operation. The timing of the FF(beam) is adjusted tominimize the overshoot or undershoot. The flatness at
beam region excluding the head and tail corresponds to
0.04% rms in amplitude and 0.02° rms in phase.

Figure 5: Block diagram of quasi-beam introduction.

Figure 8: Flat-top stability around quasi-beam injection inFB + FF table(including beam compensation) operation withtiming adjustment.

SUMMARY

Figure 6:DAC output in FB operation with and without
quasi-beam (DAC1 and DAC2, respectively) and that bysubtracting (DAC1 − DAC2) that is used for FF(beam).

The vector-sum operation for four cavities wasperformed at the STF. The instability arising from theother mode except for the π mode was measured. In high
FB gain, the vector-sum operation become unstable over
all regions of additional loop-delay. In contrast, in low
FB gain, the vector-sum operation is stable over almost
the entire range. In the operation of FB + FF table,0.007% rms and 0.015° rms was achieved. Finally, tests
were performed using a quasi-beam, and a FF(beam) wasdeveloped as a FF table to compensate the beam loading.
By adjusting the timing of the FF(beam), the stability at
beam region excluding the head and tail was achieved to
be within the range required by ILC.

REFERENCES

Figure 7: Difference between normal FB operation withand without quasi-beam at the flat-top. A drop of 1.5% in
amplitude and 0.2° in phase by the introduction of quasibeam was observed.

[1] E. Kako et al., “Cryomodule Tests of Four Tesla-likeCavities in the STF Phase-1.0 for ILC”,
PAC09,(2009), TU3RAI04, in these proceedings.
[2] S. Michizono et al., “Vector-Sum Control ofSuperconducting rf Cavities at STF”, PAC09, (2009)
WE5PFP083, in these proceedings.
[3] E. Vogel, “High gain proportional rf control stability
at TESLA cavities”, Phys. Rev. ST Accel. Beams 10,052001 (2007).
[4] T. Miura et al., “Measurements of Feedback
Instability due to 8/9π and 7/9π modes at KEKSTF”, Linac08, (2008), THP109.
[5] T. Matsumoto et al., “Low-Level RF System forSTF”, LINAC06, (2006), THP010.