SIGNAL TRANSMISSION CHARACTERISTICS IN STRIPLINE-TYPE
BEAM POSITION MONITOR
T. Suwada∗ , KEK, Tsukuba, Ibaraki 305-0801, Japan
Abstract
A new stripline-type beam position monitor (BPM) system is under development at the KEK electron/positron injector linac in order to measure transverse beam positions
with a high precision less than 10 µm towards the SuperKEKB-factory (SKEKB) [1] at KEK. The new striplinetype BPMs with a large aperture compared with previously
designed BPMs have been designed for the installation in
the positron capture section. In this report, the basic designfor the fabrication of the prototype BPM, the theoreticalanalysis, and the experimental investigation on the signaltransmission characteristics and its performance are in detail described on the base of a coupled-mode analysis in
uniform transmission lines.

INTRODUCTION
A stripline-type BPM is a well-known beam diagnostics
device to measure transverse beam positions in a plane perpendicular to the beam axis. There are many excellent review articles on this subject (see, for example, [2, 3]). In
general, a stripline-type BPM has four stripline electrodes
which are mounted on the inner surface of a circular pipewith π/2 rotational symmetry. The upstream port of the
stripline electrode is a signal pickup and the downstream
port may be short- (or 50-Ω-) terminated to the pipe groundor left open.
When a charged-particle beam passes through the BPM,
a characteristic signal with bipolar shape is induced on
all the stripline electrodes due to electromagnetic coupling
between the electrodes and the beam. The induced signals are fed into a detection electronics through vacuumfeedthrough pickups, and the signal intensities are measured by the detection electronics. The transverse beam
positions can be obtained by calculating a weighted average of the four signal intensities based on algebraic calculations. This is a basic principle on measuring transverse
beam positions with a stripline-type BPM.
The signal intensity induced on each stripline electrodecan be generally analyzed based on a so-called wall-current
model [2], in which the wall current is a mirror current induced on the stripline electrode. Based on this model, thesignal intensity may be proportional to the intensity of thewall current, that is, the beam charges, and also proportional to the angular width of the stripline electrode. Suchthe analysis may be fundamentally based on an electrostatic
model taking into account only electrostatic coupling between the stripline electrodes and the beam.
In conventional stripline-type BPMs, there are some va∗ tsuyoshi.suwada@kek.jp

rieties in spatial configuration and mechanical structure of
the stripline electrodes which are mounted on the inner surface of the BPM. The stripline electrode with a finite angular width viewed from the beam may be mounted with acertain gap between the electrode and the inner surface ofthe pipe. In such a mechanical configuration, not electrostatic coupling but electromagnetic coupling may dynamically arise between the electrodes and also between theelectrodes and the beam, and thus, the signal intensities
may change to some extent from the wall-current model.
From another point of view on a signal-gain calibration
in a stripline-type BPM, it is important to analyze the electromagnetic coupling strengths between the stripline electrodes. An excellent calibration procedure has been implemented to stripline-type BPMs by Medvedko et al. of
SLAC [4]. In this calibration procedure, an on-board calibrator embedded in the detection electronics sends its calibration signal to one of the electrodes. When the calibration signal is fed into the electrode, similar bipolar signals
are induced on the other electrodes due to electromagnetic
coupling. The induced signal goes back to the corresponding channel in the detection electronics in which the signal
intensity is precisely measured. Thus, in such a calibration procedure, not only the signal gains in the detection
electronics but also the transmission losses in entire transmission lines including the stripline electrodes themselves
can be calibrated with high precision. Thus, this new calibration procedure make use of electromagnetic coupling
between the stripline electrodes of the BPM.
Although electromagnetic coupling between the striplineelectrodes is an important physical phenomena in the
stripline-type BPM, only a few analyses have been performed to investigate the signal transmission characteristics
taking into account electromagnetic coupling between theelectrodes. A new analysis on the signal transmission characteristics with electromagnetic coupling between the electrodes are presented in this article. The new analysis exploits a similar method developed in microstripline circuitswith electromagnetic coupling. Based on the new analysis,
the signal transmission characteristics in the stripline-type
BPM is systematically investigated in frequency domainalong with experimental verification.

STRIPLINE-TYPE BEAM POSITIONMONITORA new stripline-type BPM with a large aperture is shownin Fig. 1. This BPM is under development for the newpositron beam line so as to reduce the beam losses in thepositron transmission as small as possible. The mechanical structure of the BPM is a conventional stripline-type

(a)

(b)

83
34
28.6
20.4

205
132.5

42.5
2 5 7.5

30

Ø6

Ø 63
Ø 66

(20.4)

83

Ø 66
Ø 63

1.5

Ø63

4.2

Hyperbola curve ofquadrupole bore radius

8

36°
54°

30

Figure 1: Mechanical drawings of the prototype new stripline-type BPM, (a) in front view and (b) in side view.
BPM with π/2 rotational symmetry. The development of
the present stripline-type BPM previously designed was reported elsewhere [5]. The requirements for the new BPM isthat (i) firstly, the aperture diameter must be as large as possible and the diameter is required to be larger than 60 mm,
and (ii) secondly, the outer diameter of the BPM must be
68 mm so that the BPM body can be precisely mounted
inside a bore of a quadrupole magnet.
Based on these requirements, in order to enlarge theaperture diameter of the BPM, the four electrodes havebeen symmetrically mounted to the inner surface of thepipe with a same diameter, while the electrodes of thepresent BPM were designed to be protruded away fromthe inner surface of the pipe with a different diameter [5].
The electrode length is 132.5 mm and the angular widthof the electrode is 36o . The characteristic impedance ofthe stripline electrode has been designed to be ∼50 Ω
so as to match a characteristic impedance of the signaltransmission line. The upstream end of the electrode is asignal-pickup port comprised a 50-Ω SMA-type vacuumfeedthrough while the downstream port is short-terminatedto the pipe ground. The main mechanical design parameters are summarized in Table 1.

Table 1: Main Mechanical Design Parameters of the Prototype BPM
Design parameter[Electrode]
Inner diameter
Thickness
Angular width
Gap length[Body]
Inner diameter
Outer diameter

unit
63 mm
1.5 mmo
36
4.2 mm
63
68

mm
mm

SIGNAL TRANSMISSION
CHARACTERISTICSElectromagnetic Coupling Between the Stripline
Electrodes
A principal picture in electromagnetic coupling between
the stripline electrodes is shown in Fig. 2. For example,
#2

Vc

#3

#1

V3

V1

#4 V4

Figure 2: Principal picture of electromagnetic coupling between the stripline electrodes of the BPM in the front view.
when a calibration signal (Vc ) is directly sent to a specificelectrode (#2) from a detection electronics through a coax
cable, bipolar signals are induced in the other electrodes #1(V1 ), #3 (V3 ) and #4 (V4 ) due to electromagnetic coupling.
Here, only the induced signals of the nearest-neighbor electrodes (#1 and #3) to the input channel (#2) are taken into
account. The strength of electromagnetic coupling can beobtained by measuring the intensity ratio of the induced
signal to the input calibration signal. If this procedure aresimilarly carried out for other electrodes, whole the calibration procedure can be easily performed to the BPM.
For simplicity, taking into account two transmission
lines as the stripline electrodes to analyze the electromagnetic coupling between the electrodes, an equivalent model
may be conceivable as shown in Fig. 3.
Here, taking into account proper symmetry, two calibrators in both the first and second transmission lines, VG1 and
VG2 , respectively, are shown in Fig. 3, and the corresponding output impedances of the calibrators are ZG1 and ZG2 ,standing waves are excited along the stripline electrodes inspite of any type of the terminators at the downstream port.

ab

THEORETICAL ANALYSIS
abl

Figure 3: Equivalent model in the signal transmission linesof the BPM.
respectively. The characteristic impedances of the corresponding stripline electrodes are Z1 and Z2 , respectively.
The resistive terminated impedances of the correspondingtransmission lines are ZL1 and ZL2 , respectively. The
length of the transmission line is l. The normalized amplitudes of forward and backward waves transmitting along
the stripline electrodes are indicated by ai and bi (i = 1, 2),
respectively, and on these waves, detailed discussions are
given in later section.

Equivalent Circuit
An equivalent circuit related to the equivalent modelon the stripline-type BPM may be shown in Fig. 4. Thisequivalent-circuit model is based on a distributed-constantcircuit model with distributed capacitances and inductances.

Figure 4: Equivalent circuit on two transmission lines withelectromagnetic coupling.
Here, Ci and Li (i = 1, 2) are a self-capacitance and aself-inductance per unit length in terms of the i-th striplineelectrode without any electromagnetic coupling. CM andLM are a mutual-capacitance and a mutual-inductance perunit length between the two stripline electrodes. In such theequivalent circuit, quasi-TEM waves can propagate along
the transmission lines with electromagnetic coupling [6].
In a case that resistive terminators matched to the characteristic impedance of the stripline electrode are applied at thedownstream port of the electrodes, the forward waves areabsorbed by the terminators, and however, the backward
waves are generated at the downstream port due to electromagnetic coupling. On the other hand, in a case that thedownstream port is short-terminated (or open) to the pipe
ground, the forward waves are reflected and the backward
waves propagate in the direction of the calibrator. Thus,

The quasi-TEM wave propagating along the striplineelectrodes with electromagnetic coupling can be describedwith well-known telegraphic equations as follows [6]:
∂V1
∂z
∂I1
∂z
∂V2
∂z
∂I2
∂z

∂I1
∂I2
− LM
,
∂t
∂t
∂V1
∂V2
= −C1
+ CM
,
∂t
∂t
∂I2
∂I1
= −L2
− LM
,
∂t
∂t
∂V2
∂V1
= −C2
+ CM
.
∂t
∂t
= −L1

(1)
(2)
(3)
(4)

Here, Vi and Ii (i = 1, 2) are the voltage and current amplitudes in the i-th electrode at the position z and time t,
respectively. When CM = 0 and LM = 0, the telegraphic
equations are ascribed to simple equations related to the
independent two stripline electrodes without any electromagnetic coupling. The theoretical analysis discussed hereis briefly summarized, since a detailed analysis is available
elsewhere [7].
The voltage and current amplitudes of the standing wave,
Vi (z) and Ii (z)(i = 1, 2), are represented by using therelations, Vi = Vi (z)ejωt and Ii = Ii (z)ejωt , respectively.
Using the corresponding characteristic impedance Zi for
the i-th stripline electrode, the normalized amplitudes ai (z)and bi (z) of the forward and backward waves are given byai (z)=bi (z)=Vi (z) + Zi Ii (z)
√
,
2 2Zi
Vi (z) − Zi Ii (z)
√
.
2 2Zi

(5)
(6)

Solving Eqs. (5) and (6) inversely, the voltage and current
amplitudes of the standing wave are represented by
Vi (z)=Ii (z)=√
2Zi (ai (z) + bi (z)),√
2(ai (z) − bi (z)).
Zi

(7)
(8)

Here, taking into account only one calibrator, that is,
VG1 6= 0 and VG2 = 0, the boundary conditions at theend ports, z = 0 and z = l, are given by
V1 (0) + ZG1 I1 (0) = VG1 ,(9)

V1 (l) = ZL1 I1 (l),V2 (0) + ZG2 I2 (0) = 0,

(10)
(11)

V2 (l) = ZL2 I2 (l).

(12)

Thus, taking into accout these boundary conditions,the telegraphic equations with electromagnetic coupling,
Eqs. (1)−(4), can be directly solved. The results for the[first transmission line are given by

V2 (l) =V1 (0)=

1 + ΓL1 ζ1−2V,
1 − ΓG1 ΓL1 ζ1−2

(13)

V1 (l)=

ζ1−1 (1 + ΓL1 )V,
1 − ΓG1 ΓL1 ζ1−2

(14)

and the results for the second transmission line are givenby[κ(ζ1−1 − ζ2−1 )(ΓL1 ζ1−1 + ΓL2 ζ2−1 )V2 (0) =(1 − ΓG1 ΓL1 ζ1−2 )(1 − ΓG2 ΓL2 ζ2−2 )](15)
χ(1 − ζ1−1 ζ2−1 )(1 + ΓL1 ΓL2 ζ1−1 ζ2−1 )+V20 ,(1 − ΓG1 ΓL1 ζ1−2 )(1 − ΓG2 ΓL2 ζ2−2 )[V2 (l) =κ(ζ1−1 − ζ2−1 )(1 + ΓL1 ΓG2 ζ1−1 ζ2−1 )(1 − ΓG1 ΓL1 ζ1−2 )(1 − ΓG2 ΓL2 ζ2−2 )](16)
χ(1 − ζ1−1 ζ2−1 )(ΓL1 ζ1−1 + ΓG2 ζ2−1 )+V2l .
(1 − ΓG1 ΓL1 ζ1−2 )(1 − ΓG2 ΓL2 ζ2−2 )Here, the parameters (i = 1, 2) are defined by
ΓLi

≡

V

≡

V20

≡

κ ≡
kL

≡

ZGi − Zi
ZLi − Zi
, ΓGi ≡,ZLi + Zi
ZGi + Zi
(1 − ΓG1 )
VG1 , ζi ≡ ejβi l ,2(1 + ΓG2 )V, V2l ≡ (1 + ΓL2 )V,
√
Z2
κ
1√
, κ≡
β1 β2 (kL − kC ) ,Z1 β1 − β22CL√ M , kC ≡ √ M ,
L1 L2
C1 C2

where βi is the uncoupled wave number in the i-th
stripline electrode. It should be noted that kL and kC are
the important parameters which represent the magneticand electric-coupling parameters between the striplineelectrodes, respectively. Thus, Eqs. (13)−(16) give the analytical formula in the voltage amplitudes at the end portsof the stripline electrodes with any output impedances of
the calibrators (ZG1 , ZG2 ), any characteristics impedancesof the transmission lines (Z1 , Z2 ), and any resistive terminated impedances (ZL1 , ZL2 ).
Here, taking into account symmetrical structure for the
stripline electrodes short-terminated to the pipe ground,
let’s impose following restrictive conditions for the parameters, (i) ZG1 = ZG2 = 50 Ω, (ii) ZL1 = ZL2 = 0 Ω, (iii)Z1 = Z2 = Z0 , and β1 = β2 = β ≡ ω/v0 where ω andv0 are the angular frequency and velocity of the propagating wave. Under these restrictive conditions, the voltage
amplitudes at the downstream ports are modified according
to[jωKf (ΓL1 + ΓL2 )ζ −2
V2 (0) =(1 − ΓG1 ΓL1 ζ −2 )(1 − ΓG2 ΓL2 ζ −2 )] (17)
Kb (1 − ζ −2 )(1 + ΓL1 ΓL2 ζ −2 )+V20 ,(1 − ΓG1 ΓL1 ζ −2 )(1 − ΓG2 ΓL2 ζ −2 )jωKf (1 + ΓL1 ΓL2 ζ −2 )ζ −1(1 − ΓG1 ΓL1 ζ −2 )(1 − ΓG2 ΓL2 ζ −2 )](18)
Kb (1 − ζ −2 )(ΓL1 + ΓG2 )ζ −1+
V2l .
(1 − ΓG1 ΓL1 ζ −2 )(1 − ΓG2 ΓL2 ζ −2 )Here, the parameters are defined by
Kf
χ

κl
χ
, ζ1 = ζ2 = ζ ≡ ejβl ,≡ − , Kb ≡
ω
2β
√
Z2 χ
1
, χ ≡ β (kL + kC ) .
≡
Z1 2β
2

Under these restrictive conditions, assuming that the velocity of the propagating wave is equal to the velocity oflight (v0 = c), the parameters kL , kC , l and Z0 are thefree ones to be experimentally determined. These free parameters can be quantitatively obtained on the base of aleast-squares fitting procedure using the analytical formulae Eq. (17). The experimental tests can be systematically
performed with an rf network analyzer which can measure
S-parameters. The electromagnetic coupling strength Cs is
directly related to the parameter S21 as follows:Cs
S21

V2 (0),
VG1= 20 log10 Cs .

=

(19)
(20)

EXPERIMENTAL TESTS
Characteristic Measurements
Using an rf network analyzer, the coupling strength between the stripline electrodes #2 (input port) and #1 (or#3) (output port) was obtained by measuring the parameter S21 in frequency domain (see Fig. 2) in which the frequency region is from 10 MHz to 1.2 GHz. The results areshown in Fig. 5. Figures 5(a) and 5(b) show the measurement results of the amplitude and the phase in the parameter S21 between the stripline electrodes #2 and #1, respectively, where the experimental data are indicated with crosspoints. The solid lines represent fittings of the experimental data using the analytical formulae (Eq. (17)) based ona least-squares fitting procedure, and the broken lines indicate calculations with the different parameters on kL while
the other fitted parameters are fixed. The similar results
were obtained for those between the stripline electrodes #2
and #3.
In Fig. 5(a) we can see a well-known resonant structure
in frequency domain in the amplitude of the parameter S21
measurement due to the excitation of a standing wave on
the stripline electrodes. The dip frequency fd at the central
region is 538.2 MHz. The frequency fm giving the maximal sensitivity (or the maximal coupling strength) and theamplitude of the parameter S21 are 315.8 (837.1) MHz and−39.7 (−36.4) dB in the first (second) lobe, respectively.
The coupling strength is Cs ∼ 1% while fm in the first lobe
is very close to the frequency (f = 300 MHz) of the onboard calibrator under development for the new detection
electronics.

(a)

(b)

Figure 5: Measurement results of the parameter S21 , (a)the amplitude and (b) the phase. It should be noted that thephase is defined in the region within ±180 o .
The coupling strength obtained for the new BPM is about
one-eighth smaller than that for the present BPM [5]. The
results may come from (i) the elongation of the length between the stripline electrodes due to the increase of the
BPM aperture, (ii) the reduction of the angular width of theelectrode, and (iii) the coupling strength is reduced due tothe different mechanical structure of the stripline electrodecompared with that of the present BPM. The third item isin detail discussed in later section.

Characteristic Analysis and Discussions
The characteristic analysis was performed for the freeparameters based on a least-squares fitting procedure withthe analytical formula. The results are obtained to be kL =0.011, kC = 0.013, Z0 = 42.5 Ω, and l = 128.1 mm.
In Figs. 5(a) and 5(b), the calculated lines are obtained depending on the magnetic-coupling parameter kL while theother fitted parameters are fixed. The experimental results
are in good agreement with calculations. The characteristic
impedances of the stripline electrodes were directly measured to be Z0 = 41 ± 2 Ω with a time-domain reflectometer (TDR). The measurement result is also in good agree-

ment with this characteristic analysis. It should be notedthat the measurement results with a TDR give the characteristic impedance under a condition with electromagnetic
coupling between the four stripline electrodes, while thecharacteristic analysis gives the characteristic impedance
Z0 as a free parameter under a condition without any electromagnetic coupling. However, the difference is quantitatively small within experimental errors. Thus, the characteristic analysis is satisfactory enough with the experimental results.
On the length of the stripline electrode, the mechanicallength of the transmission line for the stripline electrode isl = 132.5 mm, is slightly different from the electric lengthof l = 128.1 mm obtained by the characteristic analysis.
This may come from slight electromagnetic distortion of
the propagating quasi-TEM wave at the end ports because
the characteristic analysis is simply based on an analysis in
one dimension, and thus, it should be carried out by taking
into account more rigorous electromagnetic distortions at
the end ports in three dimensions.
The results also show that the magnetic-coupling parameter kL is smaller than the electric one kC by ∼15%. It canbe understood that because the inner radius of the striplineelectrode is the same as the pipe radius without any mechanical steps away from the inner surface of the pipe, themagnetic-coupling strength may be reduced in comparison
with the electric one.
Again, in Fig. 5(a) we can clearly see a slight asymmetry
in the resonant structure in terms of the dip frequency, andalso see an asymmetric structure even in each lobe. These
results have not been observed at all in the present BPM forwhich kL ' kC . The results in the phase of the parameter
S21 measurement are shown in Fig. 5(b). The experimental
results are also in good agreement with calculations.

CONCLUSIONS
We have successfully tested a new stripline-type BPM
with a large aperture for analyzing electromagnetic coupling between the stripline electrodes. The couplingstrength was measured to be ∼1%. With the analyticalmodel based on a coupled-mode theory in transmission
lines with electromagnetic coupling, the experimental results are in good agreement with calculations.

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[3] S.R. Smith, AIP Conf. Proc. 390, 50 (1997).
[4] E. Medvedko et al., Procs. the 2008 Beam Instrumentation
Workshop (BIW08), Lake Tahoe, California, 2008, p. 190.
[5] T. Suwada et al., Nucl. Instr. and Meth. A 440 (2000) 307.
[6] B.M. Oliver, Procs. the I.R.E., Vol. 42, Nov. (1954) 1686.
[7] S.J. Orfanidis, Electromagnetic Waves and Antennas,
p. 456 (2010) (see http://www.ece.rutgers.edu/∼orfanidis/ewa).