The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Current Modulation in the Power Supply of Rapid Cycling Synchrotrons
Feng-qing ZHANG, Kuninori ENDO*The Graduate University for Advanced Studies, KEK*KEK, High Energy Accelerator Research organization
1-1 Oho, Tsukuba-shi Ibaraki-ken, 305 Japan

Abstract
In a 50 Hz pulse power supply for rapid cycling
synchrotrons, a current modulation which affects current
stability was observed. In this paper, the modulation
behavior is examined by experiment and analysis, and themethod of the modulation suppression is described.

modulation period is hf).j.
(3). The modulation amplitude decreases with the increaseof the order of the subharmonics.
In this paper, we make a further measurement toexamine the results above and give a demonstration tosuppress the current modulation.

2 Experimental Observation

1 Introduction

Firstly, we give a measurement result shown in Fig. 2
to examine the modulation frequency.

Energy-storage
DC Power

Capacitor&Source

Charging Circuit

Lf....
II)
t::II)

Pulse-discharging
Circuit~LpRf_..

___...
Ir:>+~u~uIZ!
Fig.1Ipfr

Crs::::0Rp

P-SCR:

Pulsed power supply and resonant network
for a rapid cycling synchrotron

In rapid cycling synchrotrons, a pulse power supply isusually used as the AC power source for the resonant
network as shown in Fig. 1[1]. The DC power source isprovided by an SCR converter, which produces bothcharacteristic and non-characteristic harmonics due to "unideal" converter operation. The non-characteristic
harmonics, also named subharmonics, are the components
with lower frequencies than the fundamental frequency ofthe converter. These subharmonics will be transmitted tothe resonant magnet-current I m and cause a current
modulation. This phenomenon has been reported andinvestigated by both computation and experiment[2].
Assuming that the line frequency is f 0 , the switching;{3.15§24!(second)

68Fig.2 Measured resonant current I m at difference fs ,(a) 49.35, (b) 49.75, (c) 50.13 and (d) 50.00 Hz.
The currents I m are sensed with a DCCT (1500N10V)

summarized as follows.

and sampled near the peaks. The component of 100Hz isdominant in the subharmonics of the source voltage.
Therefore, the modulations are arisen chiefly by the 2ndorder subharmonic in this measurement. As a result, themodulation periods are 2f).j approximately as shown in thefigure.
Secondly, a measurement (Fig. 3) is shown to confirm
the correlation between the sidebands and the order of thesubharmonics. We set the resonant frequency f -49.75
s(1). The current modulation appears when f).j :1- 0.

Hz and measured the spectrum of the. source voltage V and(2). Corresponding to a subharmonic of order h, themodulation appears as the sidebands with frequencies ofnfs ± hf).j around each harmonic of the resonant current

the sidebands around · f in the pulse current I . Inspfrequency(= the resonant frequency)
difference f).j =jJ

0 -fs

fs and the frequency

I,the modulation behavior can bes

with frequency of nfs, n=1,2,3, ... , accordingly, themeasurement (1),the sidebands f s ± 24[ are the mostprominent since the 2nd-order subharmonics of the source
voltage is the highest one. In contrast, in measurement (2)-41-The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

f s ± 24[ disappear when the 2nd-orderfactor of 781 .VI5.1 V is used for the measurement of Vs andsubharmonic is made absent intentionally by means of thefeedback control to be introduced in Sec. 3.
This proves that the 2nd-order subharmonic causes thesidebands fs ± 2Af. Extending of this result leads to thea DCCT with the coefficient of 1500A/10V for themeasurement of I ni • A numerical computation has been

the sidebands

general statement (2) made in Sec.l.

made to evaluate this transmission[3]. A comparison ismade between the measurement and computation ( seeTable 1).
Table 1 Evaluation of the sidebands in I m
Frequency

10.. '---'----'---''--"-----'--'----'
0

100
200
300
frequency(Hz)

48

400

r::

49
50 . 51
frequency(Hz)52rr11 rrrr!rrr ;!1!!!!111 111

10-5 ; .. ~ ... : ··::. (;.: ._.

fs + 211/ I fs + 311/ I fs + 411/ I
fs- 211/ fs- 311f fs- 44[Measured

1.03 I

0.469 I

0.2061( x1o-2 )

0.73

0.296

0.204

Computed

1.211

0.481

0.23 I( x1o-2 )

0.93

0.40

0.21

The errors between the measured values and thecomputed ones are due to the dynamic changes in source
voltage subharmonics and measurement uncertainty.
Taking into account these error factors, we regard themeasurement and computation are in fairly good agreement.
A further calculation gives the estimated modulation for
1% subharmonics as shown in Table 2.

·:1· ....

48

Fig. 3 Correlation between the sidebands andthe order of the subharmonics for I pFinally, let us evaluate the transmission from the source
voltage subharmonics to the resonant current.

Table 2 Estimated modulation for 1% subharmonics
at 11/ = 0.25Hz
Subharmonics in Vs

Modulation in Im

50Hz

1.12 X 10-3100Hz

2.8xl0-4

150Hz

1.19xl0-4

200Hz

5.6lxto-5

It is seen that the modulations, especially those withlower orders, affect the current stability noticeably.

3 Modulation Suppression
49

49.5

50

51

Frequency (Hz)Fig.4 Spectrum of the source voltage (a) andsidebands of the resonant current (b)To do this, we measured the spectrum of the source
voltage [Fig. 4(a)] and the sidebands of Im [Fig. 4(b)]aroundf s , then normalized the sidedbands with thecorresponding subharmonics. Note that a divider with theHaving explicated the behavior of the modulation andevaluated its affect, we proceed to introduce a scheme tosuppress this undesirable variation in the resonant current.
As the modulation is usually related to some
predominant subharmonics in the source voltage in practice,
we proposed a voltage feedback loop with one or two
passband amplifiers tuned to the frequencies interested. In
the model power supply under discussion, the mainsubharmonics are 50, 100 and 150Hz components among
which the 100 Hz is dominant while the 50 Hz is-42-The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

negligible. Therefore, we designed a feedback loop mainly
for the rejection of the 100 and 150 Hz components asshown in Fig. 5, where we have:the input-output parameters as
Vr =voltage reference
Vd =voltage output, the full voltage is VdO =781/5.2

V =perturbations including the subharmonics ;pthe regulation element as
H=5.21781 is the feedback coefficient
G = 1 I sr: i is an integration regulator

Fig. 6 Bode

Vd I VP ,IThe Bode plots of Vd I VP in Fig. 6 shows the rejection
characteristic of the loop. With this scheme, we obtain an
attenuation of over 20 dB at 100 and 150Hz.
Experimental result is presented in Fig. 7 where we
see that the experiment demonstrates an effective
suppression of the subharmonics interested.
(a)10''.-.-,~.,-,-,-,,~,~.,-,.,,,.,.,.,-,,,~,.,..,.,.~...

-- ................ ;:··----··········

kb1(1+~-)

27ifb11+ofr.: _0.01, ---0.005, ... 0.001

sGb 1(s) =plots

S+(~S-)2

Qb1 27ifb1

27ifb1andskb2(1+--)27ifb2Gb2(s)=ss+(--)2
2 7ifb2
Qb2 27ifb2
are two passband amplifiers with
fbi =100Hz ,fb 2 =150Hz,kbl = kb 2 = 0.25

1+

andQbi = QbZ = 50 for a design to achieve a gain above 20dB at the central frequencies

ft, 1 and fb 2 .
Fig. 7 Experimental results of the voltage feedback withthe passband amplifier(s):(a) none, (b) 100Hz,(c) 150Hz and (d) both 100 and 150Hz
Since the subharmonics are reduced effectively, theresonant current reaches a high stability of ±1.56 x 10-4,
I-I
where the stability is defined as: + m,peak(max) m,peak(min)I m,peak(max) + I m,peak(min)H

4 Conclusion

Fig. 5 Feedback loop with passband amplifiers

We have described the phenomenon of the current
modulation in the 50 Hz power supply. The behavior ofmodulation has been explained· and confirmed. By
diminishing the subharmonics in the source voltage, themodulation is suppressed effectively.

References
frequency (Hz)[1]j150 .

"'~100r-:~·~=10'
frequency (Hz)J.A. Fox, "Resonant Magnet Network and Power
Supply for the 4GeV Electron Synchrotron Nina,"
Proc. lEE, 112 (1965) 1107 ..
[2] F.Q. Zhang, T. Adachi, K. Endo, ''Effect of Source
Voltage
Subharmonics on a Rapid Cycling
Synchrotron Power Supply," Proc. 1997 Part. Accel.
Conf., Vancouver, B.C., Canada (1997).
[3] F.Q. Zhang, "Study on Power Supply for 50 Hz-43-