RF sources and LLRF system

In the case of the radio frequency RF
acceleration as shown in Fig. 2. The electric field

1. Abstract

has reversed polarities in consecutive gaps.

RF sources are widely used for the beam
acceleration.

High

power

radio

frequency (HPRF) devices such as klystron willRFbe summarized. Recently, digital low-level
radio-frequency
popular(LLRF)(especiallyfor

controltheelectrodes

becomes

controlofsuperconducting cavities). System configuration

E

E

E
L

and RF performance with this digital LLRF will

Fig. 2: Radio frequency acceleration

be also presented.

If the synchronism condition

2. Introduction of RF system
LIn an accelerator, RF system will provide the

vTRF
2

(2-1)

accelerating energy for the charged beam

is fulfilled, where v is the velocity of the particle,

current. It is a system intended to transfer

L is the distance between consecutive gaps, andTRF the RF period, then for the given voltage
VRF, all the gaps will accelerate the particles

energy to beam of charged particles byinteraction with electric field oscillating at RF
frequency [1][2].
2.1.

and provide energy [1].

Why RF ?

2.2.

First of all, we rise a question spontaneously.
Why we does not use the simplest method forbeam acceleration? For instance, applying anelectrostatic field as shown in Fig. 1 toaccelerate a charged beam. In order to produce
higher energy beam current, the value of the DC

Vc, becomes higher and higher;
however, if the high voltage Vc exceed somevoltage,threshold, the electrical breakdown happens; as

As mentioned above, the RF system willtransfer the energy to the charged beam
current, but where is this initial energy derived
from at the very beginning and how does theenergy (or power) finally transfer to the charged
beam current? Fig. 3 illustrates the energy
transfer process in an RF system. Generally, theenergy (or power) is transferred to beam by
three steps [2].

a result, the energy gain of this electrostatic
field structure is limited to few MeV [1].
Vc

V1

V2

Components of RF system

x The transformation of the alternating
current (AC) power from transmission
network (50~60 Hz, 100 V~240 V) to direct

V3

current (DC) power (high voltage, e.g. 100

Charged particlekV) that take place in a power converter

E

E

x The transformation of the DC power into
electrodes

GND

radio frequency power (high power, andhigh frequency, e.g. 1 MW and 1.3 GHz).

GND

Fig. 1: Electrostatic field acceleration㸶㸫 

Master Oscillator
Low level RF
systemAC to DC
50-60 HzRF
SourceFeedback

HV Power
ConverterDCAC

DC to RFRF

Pick-upTransmission line
(E.g. Wave guide)

RF to Beam Energy
CouplerRF
CavityHigh energy beam

Low energy beam
VacuumSystemCryogenic
SystemWater
Cooling

Fig. 3: Block diagram of an RF system in accelerator
This transformation takes place in RF

transmission line to the RF cavity. In addition,

sources.

if the cavity is a super-conducting cavity, we

x The transformation from the RF power to acharged particle beams that occurs in theneed some auxiliary system, such as vacuum,
water cooling, and cryogenic system [2].
The main features of the components in an RF

gap of an accelerating cavity. The beam will
gain (or lose) energy from the RF field in

system is shown in Table 1. In this lecture, wewill mainly focus on the RF sources and LLRF

the cavity.
These three steps of the energy transmission
covers the three main components of the RF

feedback control systems.

3. RF sources

system which are, the HV power converter (orHV power supply), the RF source (or RF

As discussed above, the RF source will

amplifier), and the RF cavity. Furthermore, we

provide the RF power for the cavity byneed a control devices (LLRF) to regulate the RF

extracting the energy from the high voltage

cavity and RF sources. We also need apower converter (DC power). There are varioustransmission line (waveguide) to transfer thetypes of RF sources with different principle,

RF power from RF source side to the RF cavity

efficiency and applicability. The two mainside with minimum loss and zero reflection. We

categories are solid state equipment like solid

need a RF coupler to inject the power from thestate amplifier (SSA) and vacuum tubes such as㸶㸫 Table 1 Components of RF system
Elements

Main function

FeaturesPower
Convertor

AC power to DC power

RF source

DC power to RF power

RF cavity

RF power to beam Energy

Rectifier + HV transformer + energy storage
Pulsed power convertor is also named
Modulator.
The conversion takes place by means of anelectron beam accelerated by the DC voltage
and density modulated at the RF frequency
by a grid (vacuum tube), by a cavity(klystron), or directly by an applied voltage(transistor). The modulated RF power isthen extracted from a resonant cavity
excited by the electron beam.
Concentrate the RF energy under the formof electric field on a gap, with minimum
power loss.

LLRF

Stabilize the RF field

Stabilizing the cavity voltage against
disturbances coming from RF source, RFconvertor, the RF cavity, or the charged
beam current, and minimizing the cavity
input power with some tuning system. The
LLRF system is usually a set of electron
devices, with the development of digitaltechnique, digital LLRF system become
main stream.

Transmission
line

Transport the RF power to the RF
cavityTransport the power from RF source to theaccelerating cavity without reflection andloss (E.g. usually waveguide and coaxial).

Coupler

Inject the power from transmission
line to the RF cavity

Coupling the transmission line to the field
distribution in the cavity.

tetrode, klystron, and induced output tube (IOT)

power combiner. The schematic of SSA is

In the cERL at KEK, we have applied klystron,

illustrated in Fig. 4 [2-4]. Clearly, the RF power

SSA, and IOT as the RF sources. In the followed

is obtained by summing power output of

paper, we will mainly focus on these three RF

multiplesources [4-8].

combiners. The total output power depends eachdevicesbypower

splitterandamplifier’s power and the number of the
3.1.

Solid state amplifier

amplifiers. For instance, if we have total of 8

A solid state amplifier (SSA) mainly consistsof an power splitter, amplifier modules andamplifiers of 315 w, then we can obtainapproximately 2.5 kW output power.

㸶㸫 The SSA is has advantages in cost, stability,

power for the main linac cavity is not so highreliability and effectivity. It is very suitable forbecause of the energy recovery technique.

applications with lower power level. For

Therefore, we have installed two SSAs for theexample, in the cERL at KEK, the required

main linac cavities..

Amplifier × 8

Directional
couplerDriveramplifier

8-way splitter

8-way combiner

Fig. 4: Block diagram of an solid state amplifier
3.2.

The method to form the bunched electrons is

Klystron

named velocity modulation as shown in the Fig.
Klystron is another popular RF sources which
can be illustrated in Fig. 5 [5][6]. The electron
gun emits the electrons which will be focused on

6 and Fig. 7. The key-point of this method is togenerate a bunched electrons by velocity
modulation.

by a low positive voltage on the control grid,
thus the electron beams are formed. The beamis then accelerated by a very high DC potential
in the accelerator grid and buncher grid. A
resonance cavity with a RF input is connected tothe buncher grid. The cavity then produce anoscillating electron field that inside buncher
cavity. As shown in Fig. 7, the electrons will be
accelerated and decelerated because of the effectof the RF field. The butchered electrons is then

The function of the catcher grid is to extractthe energy from the electron beam. It will beplaced at the point that the bunched electron is
fully

formed.

Theelectronbuncheswill

introduce an RF voltage in the grid gap of thecatcher cavity. If the placement is appropriate,
the catcher cavity will decelerate the bunchedbeams, since the bunched beam contains the
majority of the electrons, the energy will betransferred from the beam to the catcher cavity.

formed in the drift space when the accelerated
electrons overtake the decelerator electrons.

㸶㸫 RF output

RF input

Buncher
CavityElectron
Gun

Catcher
CavityDrift space

Cathode

Ctrl.
Grid

Acc.
Grid

BunchedElectrons

Buncher
Grid

Collector
Anode

Catcher
Grid

Fig. 5 Schematic of a two cavity klystron

Buncher
CavityBuncher
CavityBuncher
CavityBuncher
CavityBuncher
CavityBunchedelectrons

a

Start

Moment t2

Moment t1

end

Moment t3
Buncher
Grid

Buncher
Grid0

Deacc.

BuncherGrid0

Buncher
Grid

Buncher
Grid

Acc.

0

t3
Start

t2
t1

Fig. 6 Buncher cavity action, the formation of the bunched electrons

㸶㸫 

end

Bunched
electrons

Positiontube except the positive half cycle of the RF
input. The electron bunches are then formed
and accelerated by the potential between theanode and control grid. In the next step, similar
to klystron, the bunched beam will pass througha catcher cavity. This cavity will be excited by

ωRF t
90

the electromagnetic energy if the beam is thenextracted.

180 270 360

The main difference between the klystron and
Fig. 7: Diagram showing formation of bunches in a

IOT is that the method to generate the bunchedvelocity-modulated electron beam.

electrons. In a klystron, this process occurs in

3.3.

the buncher cavity and drift space. The velocity

IOT

modulation is imposed on the beam current. In

Inductive output tube (IOT) is another RF

the case of the IOT, the bunched electrons issource which is a combination of coaxial gridded

formed within gun religion itself because of thetubes (like tetrode) and klystron, therefore, it isDC bias of the control grid [5].

also named Klystrode [7][8]. A schematic of IOT
is given in Fig.8. Similar with a tetrode, the IOT
also consist of a cathode with a biased control
grid, therefore, there is no beam current in the
RF output

RF input
Catcher
CavityBunchedElectrons

CathodeScreen
Grid

Ctrl.
Grid

Catcher
Grid

Grid Bias

Fig.8 Schematic of IOT

㸶㸫 

Collector
Anodeboth of the injector 2 and the injector 3, this is

4. RF sources in cERL

so called vector-sum control [9].

A compact energy recovery linac (cERL),

Table 2 Parameters of RF systems at cERL

which is a test machine for the next generation
Cav.

QL

RF power[kW]

RF source

Bun.

1.1×104

3

8 kW SSA

superconducting (SC) two-cell cavities were

Inj. 1

1.2×106

0.53

25 kW Kly.

installed for the injector, and two nine-cell SC

Inj. 2

5.8×105

cavities were installed for the main linac (ML).

Inj. 3

4.8×105

2.4

300 kW
Kly.

The RF sources for each cavity is given in Fig. 9ML1

1.3×107

1.6

16 kW SSA

ML2

1.0×1072

8 kW SSA

synchrotron light source 3-GeV ERL, wasconstructed at KEK. In the cERL, a normal
conducting (NC) buncher cavity and three

and Table 2. It should be mentioned that, weonly use one klystron to drive the cavities in

8 kW SSA

25 kW Kly.
300
kWSSA
Kly.
8 kW
8 kW SSA 16 kW SSA

Vector-sum
Controlling

Dump
Two-cell SC

Main linac 2 Main linac 1~ 20 MeVSC

SC
Nine-cell SC~3 MV/m for Injector Cavities~8.5 MV/m for main linac Cavities

Fig.9 Lay out of RF sources and cavities in cERL at KEK
5.1.

5. Tutorial of control theory

Components of control system

The LLRF system take charges of stabilizing

A control system is a device, or set of devices,

the RF filed inside the RF cavity. Before wethat manages, commands, directs or regulates

introduce the LLRF system in detail, we would

the behavior of other devices or systems

like to discuss the basic issues in a general[10]. Industrial control system are used in

feedback system. A tutorial including basic

industrial production for controlling equipment

definitions and principles in control theory willor machines. As shown in Fig. 10. A control

be presented at first.

system mainly include a plant, a sensor (or㸶㸫 detector), and a controller. The plant is a system

FF
Controller

or devices that need to be controlled. The sensor

Plant(or detector) is a measuring tool that measured
the response of the plant. The controller is a

Sensordevice to regulate or control the behavior of the“plant”. The main function of a control system is

Reference

to maintain some characteristic of the “plant” by

FB
Controller

Plant

applying appropriate sensor and controller.

SensorController

Plant
Fig. 11: Open loop vs. closed loop
5.1.2. Transfer function
A transfer function is a ratio of the output ofa system to the input of a system. Mathematicalrepresentation of a transfer function is given as

SensorFig. 10: Components of a control system

H s

5.1.1. Open loop and closed loop

Y s
, Y s
X s

H s X s .

(5-1)

Control system and control theory can bewhere the H(s), Y(s) and X(s) represent thedivided two major categories: open loop control

Laplace-transform of the system, output signal

and closed loop control.

and input signal, respectively.

In an open loop system, the controller (usually

The transfer function H(s) includes every

feedforward controller) directly drives the plant

information of the system (usually can be seen

without any feedback. In a closed-loop system,

as a representation of a system model) i.e. if wethe current output is taken into consideration

know the transfer function H(s) of a specified

and corrections are made based on feedback

system, we can calculate the output Y(s) by any[10]. A closed loop system is also called a

input X(s).

feedback (FB) control system. Fig. 11 has shown

Takes the cavity model as an instance. The

the difference between the open loop and closed

superconducting cavity can be seen as a parallel

loop

resonance circuits of resistor, capacitor, andinductor which can be shown in Fig.12.

Fig. 12: Cavity equivalent circuits

㸶㸫 The frequency response of a superconducting

The impedance (or conductance) of thecavity can be obtained by replace the Laplaceparallel resonance circuit is given by1Z

j
Z s s jZ

s
C
1
1
2
s 
s
RC
LC

Z s

notation “s” to Fourier notation “Mǚ” likeLs  RLCs 2  R
and
RLs

1
1
 sC 
R
Ls

(5-2)

and

Q

2

2
0

ZR

Z  Z  j

j

Z0
Q

Z

Z0
Q

R

(5-5)

Z2
Z
Z  0  j 0
Z
Q

It is clear to see that, if ǚ=ǚ0, then we havewhere the R, L, and C represent the resistance,
capacitanceZ0

inductance,

respectively.

Usually, we use quality factor, Q, and resonanceradian frequency, ǚ0 to replace the R, L and C.

Z(Mǚ)=R, that is to say, the cavity is onresonance, therefore, the parameter, ǚ0, is
named resonance radian frequency.
5.1.4. Bode plot

Therefore, the transfer function of the cavity
Bode plots is a diagram that describe themodel is given by

amplitude-frequency and/or phase-frequency of
Z s

s
C
1
2
s 
s  Z02
RC

RZ0
s
Q
s2 

Z0
Q

a system. It is actually a plot of the frequency(5-3)

s  Z02

response H(Mǚ). The bode plot of the cavity bodeplot is shown in Fig.13. The quality factor, Q,
and resonance frequency, ǚ0 are selected to bewhere we have Q

C
R
, Z0
L

1
.
LC

1.3×106 and 1.3×109 Hz.

-3 dB

5.1.3. Frequency response
Frequency

response

is

f1

a

measure

f2

BW

of

magnitude and place of the output as a functionof frequency. We can directly transform thetransfer function to frequency response bychanging the Laplace notation “s” to Fourier
Fig. 13: Bode plots of cavity.

notation “Mǚ”. This process can be expressed by

H s s jZ

H jZ

H jZ ej H jZ(5-4)

In a Bode plots of the cavity as shown in Fig.
13, we can also define the half power point and

The significant feature of frequency response

3dB bandwidth. The half power point in a bodeis that, we can directly obtain the amplitude andplots is that frequency at where the output

phase response of a specified sinusoidal input by

power has dropped its mid-band value, that is ausing the frequency response of a system. Sincelevel of -3 dB. There are two half power point f1

every input signal can be decomposed to a set ofand f2 in Fig.13. The 3 dB bandwidth is thensinusoidal signal by Fourier-transform, we candefined by the difference between f1 and f2. For

then obtain the corresponding output signal bysuperconducting

the frequency response.

between Q value and 3dB bandwidth is also
given by㸶㸫 

cavity,therelationshipBW3dB

f0
, f0
Q

Z0
2S

(5-6)

control system, we would like to set up thesystem model of a LLRF system as illustrated inFig. 15.

5.1.5. Stability Criterial and Gain margin

ReferenceK(s)Stable is the most important issue in a
feedback system. We cannot operate a system if

P(s)

Loop

it is unstable. There are a lot of stability
criterial for a feedback system, such as, rootF(s)locus method, characteristic equation, routhhurwitz method and bode plots. In this speech,

Fig.15: Models of LLRF system

we only discuss the Bode plots method because

Here K(s), P(s) and F(s) represent the transfer
function of controller, plant, and sensor(detector) in baseband, respectively. We would
like to discuss each of this models in detail.
The controller P(s) is usually a PI controller
in LLRF system. The schematic of aconventional PI controller is given in Fig.16
which holds a transfer function as

it is the most popular and simple criterial. The
Bode plot method compares the amplitudefrequency and phase-frequency plots of thesystem in its open loop as shown in Fig. 14. The
stability criterial based on Bode plots can be
described as follows.
x Find the frequency where the phase

K sbecomes -180 degrees.
x Find the gain, G (in dB) at the same

KI
 KP
s

frequency.

¦

KP

x Calculate the gain margin which is defined(5-7)

by 0-G (in dB).
x If the gain margin is larger than 0 dB, theKI³system is stable, or, system is unstable.
Fig. 16: Structure of PI controller.
The RF cavity is a first order low pass filter inbase-band (assume it is operated on-resonance).
A cavity with half bandwidth ǚ0.5 can be
expressed by

P s

Z0.5
s  Z0.5(5-8)

Fig. 14: Gain margin in a Bode plots.
5.2.

The sensor (detector) is also a low pass with alarger bandwidth ǚF which is given by

Analytical study of LLRF system

F s

The analytical study is useful, significant, andessential for a control experts. System model(transfer function) is required in analytical
study. Since the LLRF system is actually a FB

ZF
s  ZF(5-9)

In practice, the dead time exists in thesystem. The dead time is a time delay that thetime after each event during which the system㸶㸫 

is not able to record another event (see Fig. 17).
The transfer function of a time delay is given by

Step-inIn

ParameterValue(5-10)

ǚ0.5

93 kHzResponse

KI

0

KP

2

Td

1 µs

ǚF

500 kHzML2

1.0×107eTd sT sT(s)Table 3 Parameters in analytical study

Out

Step-in
Response

Fig. 17 Dead time in a system.
The overall models of a LLRF system is
illustrated in Fig. 18.

KI
 KP
s

The Bode plots is then given by Fig. 19. We
can then predict the system stability of the
LLRF system of the buncher cavity by its Bodeplots.

Z0.5
s  Z0.5

Closed loop
ZF
s  ZFeTd sFig. 18: Overall models of LLRF system includingtime delay.
The overall open loop diagram is then given
byFig. 19: Bode plots of LLRF system for buncher
cavity.
Furthermore, we would like to present the
influence of some critical parameters such asdead time, Td, and P gains, KP.

H OL s§ K I  K P s · § Z0.5 · Td s § ZF · (5-11)¸e ¨¸¨¸¨s©
¹ © s  Z0.5 ¹© s  ZF ¹

Take the buncher cavity as an example, wewill analyze its LLRF system based on Fig. 18
and Eq. (5-11). The parameters for the study are
given in Table 3

Fig. 20 compared the cases in which the deadtime are 1 µs (indicated by blue color) and 2.5 µs(indicated by red color), respectively. It is clear
to see from Bode plot that the amplitudefrequency response is same but the phasefrequency response has some delays in thelarger Td (2.5 µs) case. This phase delay will
result of unstable in the larger Td (2.5 µs) case.

㸶㸫 digital devices such as FPGA or/and DSP. In
cERL, FPGA-based LLRF system has beendeveloped as well.

CavityController

Plant

Fig. 20: Effects of dead time in the LLRF system
Fig. 21 compared the cases in which the P
gain are 2 (indicated by blue color) and 10(indicated by red color), respectively. This time
the amplitude-frequency response has somedifference in the Bode plots. After calculating
the gain margin, it is easy to find out that thesystem will be unstable in the larger KP case.

FPGA

SensorFig. 22: Components of digital LLRF system.
The FPGA is an integrated circuit that can be
programmed in the field after manufacture.
Application of FPGA becomes more and more
popular in the LLRF field. Since the FPGA isactually a digital devices, however, signals fromthe RF cavity or RF sources are analog,
therefore, the conversion from the analog(digital) to digital (analog) are required. These
requirements are fulfilled by analog to digital

Fig. 21: Effects of PI gains in the LLRF system.

converter (ADC) and digital to analog converter

6. LLRF(DAC). Fig. 23 has illustrated the digital LLRF

As mentioned above, the requirement of the
LLRF system is to stabilize the RF field insideplatform including FPGA, ADC and DAC, this
digital platform is applied in the cERL.

the RF cavity with some given tolerance. E.g.,

ADC: LTC 2208

Digital I/O

for cERL LLRF system, the RF field fluctuation
should be maintained at less than 0.1% for theamplitude and 0.1 degree for the phase. For
future 3 GeV ERL project, this requirement iseven tighter (0.01% for the amplitude and 0.01

Xillinx Virtex5 FPGA

degree for the phase) [12-15]. Like the generalcontrol system, LLRF system also include threebasic components: a controller, a plant, and a
detector (see Fig. 22). The plant need to control
in an LLRF system is usually a cavity (or RF

uTCA Digital Board
ADC & DAC Interface

source). For the controller and detector, since
the advantages of the digital technologies, newgeneration LLRF system usually apply the㸶㸫 Fig. 23: FPGA in cERL LLRF systems.

6.1.

­ I A  cos I0.
®
¯Q A  sin I0

Schematic of LLRF system

A simplified block diagram of the cERL LLRF
system is shown in Fig. 25. The 1.3 GHz RF­° A
I 2  Q2.
®
°̄I0 arctan Q I

signal (from cavity probe) is down-converted toa 10 MHz intermediate frequency (IF) signal.

(6-2)

The IF signal is sampled in the next stage at 80

Which means that the amplitude and phase of

MHz by a 16-bit analog to digital converter

the RF filed can be represented by the I and Q(ADC,

directly. Fig. 24 has illustrated the mapping

LTC2208)

and

fed

into

a

field-

programmable gate array (FPGA).

between IQ and amplitude and phase [11].

The base-band in phase and quadrature (I/Q)
components are extracted from the digitalized
IF signal by a digital I/Q detection model. The
notation “I/Q" derives from fact that any
sinusoidal signal can be represented by either
polar(amplitude/phase)orbyCartesiancoordinates. A sinusoidal signal y(t) withamplitude A, radian frequency, ǚ, and an initial
phase ߖ0, can be decomposed into its sin and cos
components by basic trigonometric functions.
Fig. 24: I/Q vs. amplitude and phase

A sin Zt  I0y t

A cos I0 sin Zt  A sin I0 cos Zt
I

The I/Q signals are then fed into a 2×2(6-1)

rotation matrix to correct the loop phase. AfterQ

being filtered by infinite impulse response (IIR)

I sin Zt  Q cos Zt

low-pass

filters, the I/Q components are

The amplitude of the sin component and thecompared to their set values and the IQ errors

cos component is then defined as in-phaseare calculated. Then, the I/Q errors arecomponent

quadrature-phaseregulated by a PI controller. The processed I/Q

component (Q). It is clear to see the relationshipsignals are added to their corresponding FF

between the I/Q and amplitude and phase ismodels. The combinational signals are fed into

given bythe I/Q modulator by a 16-bit digital to analog

(I)

and

the

(DAC) converter (AD9783) to modulate the 1.3GHz RF signal from the oscillator. Finally, the
LLRF feedback loop is closed by driving a highpower source, which drives the cavities [12-15].

㸶㸫 

1300 MHzLO §1310 MHz
Down
Convertor

Pre. Amp.

RF = 1300 MHz

SW1

FPGA
Clk §80 MHz
LTC2208
ADC
ADC

I_Set

IQ Mod.

Kly. / SSA

Analog filter

DIO (RF SW)
I_FF

Vector sum Fil.
I
IIR
§ cosT sinT ·

PI

DAC

IIR

PI

DAC

¨
¸
©sinT cosT ¹

Calib.

Q

Q_Set

IF § 10 MHz
ADC

I
Q

AD9783

Q_FF
Power PCLinuxEPICS IOCADC

AMC Card

Waveform

CommandFig. 25: LLRF system diagram in the cERL at KEK

Some basics features in the LLRF system need
to be discussed deeply.
6.2.

Sampling method shown in the lower figureof Fig. 26 is also named non-IQ sampling [16].

IQ detection

The I and Q signal was extracted from the IF
signals. If the value of the sampling frequency,

fS is four times of the IF frequency (fS=4fIF, aslo
named IQ sampling), as shown in upper figure/ YͲ/in the Fig. 26. The sequences I, Q, -I, and –Q
directly yield. On the other hand as shown inthe below figure of Fig. 26, if the relation
between fS and fIF is expressed by [11, 16]
fs

N
f IF
M

(6-3)

In this case, I and Q signal can be calculated byI

2 N 1M·§ ¦ yi  cos ¨ 2S k  ¸
N k 0
N¹
©

Q

2 N 1M·§ ¦ yi  sin ¨ 2S k  ¸
N k 0
N¹
©

(6-4)
Fig. 26: IQ detection

㸶㸫 

ͲY

6.3.

PI control and gain-scanning

,PD[

%DG

The digital PI controller, as shown as Fig. 27
is applied in the cERL LLRF system. The

2SWLPL]HG*DLQV

,*DLQtransfer function of the PI controller is given by[12-15]H ( z)KP KI
1  z 1

(6-5)

To determine the optimal PI gains, a gain

2

*RRG

3*DLQ

scanning experiment was carried out in thecERL LLRF system [12-15]. The system

Fig. 28: Gain-scanning experiment.

performance was measured and evaluated via
different proportional gain KP and integral gain

6.4.

KI. The measuring procedure comprise theSuperconducting cavities is subjected tofollowing steps:
x Keep the parameter KI at a constant value

disturbances like microphonics, or Lorentz

and gradually vary the parameter KP fromalways worked on resonance, as a result, more

0 to critical gain.

RF power is required for a detuned cavity. This

x

x

x

MeasureandrecordtheTuner control

detuning, that means, the SC cavity do not

systemproblem is resolved by applying for tuner control.

performance (the field stabilities with a

The schematic of tuner control is shown inclosed loop) based on a specified (KI , KP )Fig.29. The phase of the cavity probe signal andpair.

cavity incident signal are detected, and theUpdate the parameter KI to a new value

phase difference between them is calculated inafter all KP values are scanned and repeat

the next stage. This difference signal is

the procedure 1&2.

regulated by PI controller. The regulated signal

Evaluate the optimal gains according tois then send to the DAC for the piezo control andthe measured system performance after

to the digital input/output for the mechanicalall of the KP and KI are scanned.

tuner control. Similar with the LLRF field
control, the tuner control is also carried out byanother FPGA board.

¦

KP

6.5.

Stabilities of LLRF

The typical LLRF system performance andKI¦

operationalparameters

duringbeam

commissioning are listed in Table 4. Thez

1

feedback gains were determined by the gainscanning

Fig. 27: Digital PI controller.

experiments,

asstatedabove.

Disturbing signals such as microphonics andOne of the example of that gain-scanning

power supply ripples were suppressed well by

experiment is given in Fig. 28, the optimum

thegains are indicated by the white point.

stabilities of the amplitude and phase, for each㸶㸫 

high-gain

feedback.

The

typicalRF

MicroTCA

Pf
ADC1

ADC2

Pick up

I/Q I/Q
IIR
dem.



hold

Fil

DAC

Piezo

KI

ǻș
detectorCW

I/Q I/Q
IIR
dem.

Digital
I/O

sign
KP

CCW

Mechanical
Tuner

Fig. 29: Schematic of Tuner control.
cavity in the main linac and injector were given

7. Stability of beam current

in Fig. 30 and Table 4 [12-15]. As stated above,
our requirement for the cERL LLRF systems

The beam energy stability is measured by theare 0.1% for amplitude and 0.1 degree for phase.

screen monitor which is installed downstream ofResults in Fig. 30 and Table 4 indicate thatthe bending magnet with a 2.2 m dispersion andthese requirement is satisfied by the FPGA-

62.6

based LLRF system in compact ERL.

momentum jitter is calculated based on theĳb

Vc

resolution[13]. Thebeam

peak point of the beam projection in the screen

Table 4 Stabilities of LLRF system
Cavityµm/pixel

monitor. The calibrated beam momentum jitter

RF stability (rms)

is about 0.006% rms as shown in Fig. 31 This

į$/$        įș

value is in consistence with the measured RF

0.07%

0.04°

stability in the LLRF system.

0.006%

0.009 °

0.007%

0.025°

Buncher-90°

Inj. 10°

0.7 MV

Inj. 20°0.65 MV

Inj. 30°0.65 MVML1

0°8.56 MV

0.003%

0.010°

ML2

0°8.56 MV

0.003%

0.007°

Fig. 31: Beam energy stability in the cERL.

8. Summary
In this speech, we have introduced the RF
system at first, we present the main components
of an RF system. Furthermore, we havediscussed several main RF sources in the cERL.
In addition, we have presented the basic issueof the control theory and LLRF system, finally
we gives the performance of the RF system incERL.
Fig. 30 Stabilities of LLRF system.

㸶㸫 Reference[1] CERN accelerator school on RF engineering,Seeheim, Germany, 8-16 May 2000.
[2] CERN Accelerator School on RF for accelerators,
Ebeltoft, Denmark, 8-17 June 2010.
[3] A. Jain, et al, Compact solid state radio frequency
amplifiers in kW regime for particle accelerator
subsystems. Sadhana Vol. 38, Part 4, August 2013,
pp. 667–678.

[4] Jorn Jacob, RF Solid State Amplifiers, CASCERN Acclerator School, Baden, 7-14 May 2014(https://cas.web.cern.ch/cas/Switzerland2014/Lectures/Jacob.pdf)[5] R. Heppinstall, et. al, The inductive output tube.
The latest generation of amplifier for digitalterrestrial television transmission.
[6] Microwave
components
andcircuits.
(http://www.navymars.org/national/training/nmo_co
urses/nmo1/module11/14183_ch2.pdf)[7] Rebecca Seviour, et. al, Comparative Overview ofInductive Output Tubes, June 2011.
[8] H. Bohlen, et. al, IOT RF Power Sources for Pulsedand CW Linacs, LINAC 2004.
[9] F. Qiu, et. al, A disturbance-observer-based controller
for LLRF systems, proceedings of IPAC2015,
Richmond, USA, 2015[10] https://en.wikipedia.org/wiki/Control_system[11] T. Schilcher, Digital signal processing in RF

applications, CERN accelerator school on digital
signal processing, Sigtuna, Sweden, May 2007.
[12] F. Qiu, et al., Evaluation of the superconducting
LLRF system at cERL in KEK, IPAC2013,
Shanghai, May 2013.
[13] F. Qiu, et al., Digital filters used for digital
feedback system at cERL, LINAC14, Geneva,
Switzerland, 2014[14] F. Qiu, Performance of CW Superconducting
Cavity at ERL test facility, LLRF2013 workshop,
Lake Tahoe, California, US, 2013[15] F. Qiu, et al., Performance of the Digital LLRF
System at the cERL, IPAC’14, Dresden, June,
2014[16] S. simrock, Z. Geng, Cavity field control, RF signal
detection and actuation, 8th International

Accelerator School for Linear Colliders(https://agenda.linearcollider.org/event/6258/contrib
ution/27/material/slides/3.pdf)

㸶㸫 