Two port cavity Q measurement using scattering parameters
Dae‐Hyun Han, Young‐Soo Kim, and M. Kwon
Citation: Review of Scientific Instruments 67, 2179 (1996); doi: 10.1063/1.1147034
View online: http://dx.doi.org/10.1063/1.1147034
View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/67/6?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Two electric-field components measurement using a 2-port pigtailed electro-optic sensor
Appl. Phys. Lett. 99, 141102 (2011); 10.1063/1.3646103
Technique for measuring the two-port scattering matrix of a plasma current drive antenna during high power
operation
Rev. Sci. Instrum. 68, 1168 (1997); 10.1063/1.1147879
New approach of measuring the Q factor of a microwave cavity using the cavity perturbation technique
Rev. Sci. Instrum. 65, 453 (1994); 10.1063/1.1145156
Three‐port two‐microphone cavity for acoustical calibrations
J. Acoust. Soc. Am. 71, 1276 (1982); 10.1121/1.387734
Horn and horn driver two‐port measurements
J. Acoust. Soc. Am. 65, S3 (1979); 10.1121/1.2017235
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
141.223.201.61 On: Tue, 02 Jun 2015 04:27:50
Two port cavity Q measurement using scattering parameters
Dae-Hyun Han and Young-Soo Kim
Department of Electronic and Electrical Engineering, Pohang University of Science and Technology, San
31, Hyoja Dong, Pohang, Kyungbuk 790-784, Korea
M. Kwon
Pohang Accelerator Laboratory, POSTECH, San 31, Hyoja Dong, Pohang, Kyungbuk 790-784, Korea
~Received 30 October 1995; accepted for publication 23 January 1996!
A method of measuring Q of a two port cavity by scattering parameters is described. The scattering
parameters of a two port cavity resonator are derived by a lumped equivalent circuit model as a
function of cavity parameters, including the cavity Q. These can be also obtained by direct
measurement with a modern network analyzer. The results agree well with those from other
well-known methods. This two port measurement can provide additional information such as the
coupled power ratio, which is one of the important parameters for the beam-accelerating cavities.
© 1996 American Institute of Physics. @S0034-6748~96!00405-1#
I. INTRODUCTION
II. SCATTERING PARAMETERS OF EQUIVALENT
CIRCUIT
The cavity resonator has sharp resonances at distinct frequencies. In the vicinity of each resonance, the behavior of
the cavity may be represented by an equivalent lumped
circuit.1 The cavity parameters such as resonance frequency,
coupling factor, and unloaded quality factor can be obtained
by analyzing the equivalent lumped circuit.
Several books have described cavity measurement procedures in a classical way.1–3 For example, Khanna and Garault have described measurement on a dielectric resonator
coupled to a microstrip line which therefore has the same
input and output coupling factors.4 McKinstry and Patton
described a loaded Q measurement method using a scalar
network analyzer.5 The classical method for determining the
unloaded Q of a two port cavity involves independent measurements of the loaded Q and of the coupling factors. Khanna’s method is limited to a cavity with the same input and
output factors. McKinstry’s method is not applicable for unloaded Q measurements.
This article describes a method for measuring the circuit
parameters of a two port cavity with arbitrary input and output coupling factors using scattering parameters measured
with a modern network analyzer. The measured scattering
parameters then yield a number of cavity parameters including the unloaded Q. This method reduces the number of measurement steps compared to the classical method and gives
additional information, such as the coupled power ratio defined as
S D
P out
,
C ~ dB ! 510 log
Pc
~1!
where P c is the cavity wall loss and P out is the coupled
output power at a separate monitor port normally used to
monitor the electric field inside the cavity. The coupled
power ratio is one of the important factors for beam accelerating cavities.
The scattering parameters are defined as6
F GF
V2
1
5
V2
2
GF G
S 11 S 12 V 1
1
S 21 S 22 V 1
2
~2!
,
2
where V 1
n and V n are the amplitude of the voltage wave
incident on and reflected from port n. The specific scattering
parameter can be determined as
V2
i
Si j5
V1
j
uV
1
k 50
~3!
for kÞ j.
When the cavity is magnetically coupled to the input and
the output as shown in Fig. 1~a!, the equivalent circuit becomes that in Figs. 1~b! and 1~c!.2 Scattering parameters of
this equivalent circuit at the detuned open position 1-1’ and
2-2’ can be expressed as
@S#5
1
11 b 1 1 b 2 1 j2Q u d
3
F
12 b 1 1 b 2 1 j2Q u d
Ab 1 b 2
Ab 1 b 2
11 b 1 2 b 2 1 j2Q u d
G
,
~4!
where d , b 1 , and b 2 are detuning factor, input, and output
coupling factors, respectively. The detuning factor is defined
as
d5
v2v0
,
v0
~5!
where the subscript 0 designates value at resonance. The
coupling factors b 1 , b 2 are defined as the ratio of the external resistance R e1 , R e2 to the cavity resonator resistance R at
resonance frequency or
b 15
R e1 n 21 Z 1
5
,
R
R
~6!
Rev. Sci. Instrum. 67 (6), June 1996
0034-6748/96/67(6)/2179/3/$10.00
© 1996 American Institute of Physics
2179
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
141.223.201.61 On: Tue, 02 Jun 2015 04:27:50
In Eq. ~9!, the half power points 2Q l d 561 are easily obtained by finding the frequencies f 1 , f 2 that satisfy
U
U
1
S 21~ v !
5
S 210
A2
~10!
from which the loaded Q is obtained:
Q l5
f0
.
f 22 f 1
~11!
If the scattering parameters at resonance are
@ S0#5
F
S 110
S 120
S 210
S 220
G
~12!
,
then
11 b 1 1 b 2 5
2
S 110 1S 220
~13!
and the unloaded Q is
Q u 5 ~ 11 b 1 1 b 2 ! Q l 5
2
Q .
S 110 1S 220 l
~14!
Equation ~13! may be verified as taking the limit
b 2 →0, S 220 →1 for the case of a single port cavity. Then
Eq. ~13! becomes
b 15
FIG. 1. ~a! The measurement system, ~b! equivalent circuit of a loop
coupled cavity, ~c! equivalent circuit referred to the middle loop.
R e2 n 22 Z 2
5
.
b 25
R
R
~7!
These coupling factors relate the various quality factors as
Q u 5 ~ 11 b 1 1 b 2 ! Q l 5 b 1 Q e1 1 b 2 Q e2 ,
~8!
where Q u , Q l , Q e1 , and Q e2 are unloaded, loaded, input
external, and output external quality factors, respectively.
The method of finding the loaded Q is well described by
Ginzton,1 and only a brief description is presented here for
completeness. The relative transmission characteristic is
U
U
S 21~ v !
1
5
.
S 210
A114Q 2l d 2
~9!
12S 110
.
11S 110
~15!
For the overcoupled case, S 110 52 r . Then Eq. ~15! becomes
b 15
11 r
5SWR,
12 r
~16!
and for the undercoupled case, S 110 5 r , so that
b 15
12 r
1
.
5
11 r SWR
~17!
These results duplicate Ginzton’s description for the single
port cavity.1
The cavity wall loss P c may be written as
P c 5 P in2 P r 2 P out5 ~ 12 u S 110 u 2 2 u S 210 u 2 ! P in ,
~18!
where P r and P in are the reflected and the input power. Then
the coupled power ratio, given by Eq. ~1! is obtained as
C ~ dB ! 520 logu S 210 u 210 log~ 12 u S 110 u 2 2 u S 210 u 2 ! .
~19!
TABLE I. Measurement results with this method and Ginzton’s method.
Q0
Cylindrical
cavity
Reentrant
cavity
f0
b1
b2
S 110
S 220
Ql
Ginzton’s method
This method
3.858 GHz
0.504
0.314
0.449
0.649
2917
5302
5315
500.120 MHz
1.192
0.051
-0.102
0.993
17288
38766
38802
2180
Rev. Sci. Instrum., Vol. 67, No. 6, June 1996
Cavity Q measurements
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
141.223.201.61 On: Tue, 02 Jun 2015 04:27:50
III. MEASUREMENT EXAMPLE
A reentrant type cavity ~23.4 cm in radius, 42 cm in
height! and a cylindrical cavity ~2.56 cm in radius, 8.74 cm
height! were used for testing this method and the results
obtained from the scattering parameter measurements were
compared to those obtained from Ginzton’s method. The input and output were inductively coupled to excite and extract
the TM010 mode for the reentrant cavity and the TE111 mode
for the cylindrical cavity. Note that the reference plane is the
detuned open position for this method which is easily accomplished using the electrical delay function in modern network
analyzers. The measured parameters are listed in Table I
showing excellent agreement between the two methods. The
measured coupled power ratio is 243.4 dB for the reentrant
cavity, whereas the designed value is 244 dB.
IV. CONCLUSION
Two port cavity scattering parameters as a function of
the unloaded Q and the coupling parameters were derived
from an equivalent circuit. The validity of this expression for
the scattering parameters are confirmed by duplicating the
well-known formula for the case of a single port. The measured results agree well with other proven methods. This
method reduces the number of measurement steps compared
to other methods and also gives additional information, such
as the coupled power ratio.
ACKNOWLEDGMENTS
This work was supported by the Pohang Iron and Steel
Company and the Ministry of the Science and Technology of
Korea.
E. L. Ginzton, Microwave Measurement ~McGraw-Hill, New York, 1957!.
M. Sucher and J. Fox, Handbook of Microwave Measurement ~Wiley,
New York, 1963!.
3
C. G. Montgomery, Techniques of Microwave Measurement ~McGrawHill, New York, 1947!.
4
A. Khanna and Y. Garault, IEEE Trans. Microwave Theory Tech. 31, 261
~1983!.
5
K. D. McKinstry and C. E. Patton, Rev. Sci. Instrum. 60, 439 ~1989!.
6
D. M. Pozar, Microwave Engineering ~Addison-Wesley, New York,
1990!.
1
2
Rev. Sci. Instrum., Vol. 67, No. 6, June 1996
Cavity Q measurements
2181
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
141.223.201.61 On: Tue, 02 Jun 2015 04:27:50