calculation of parasitic shunt capacitance between the plate and
ground plane gives 0.5 pF for the perforation ratio of 56%, that is,
around 20% of the main capacitance. The capacitor with a con-
ventional blanket ground has an SRF of 6.83 GHz, f
Q30
of 6.1
GHz, and C
eff
of about 3 pF at 3 GHz. Also, the Q factor was
around 85 in the 3-GHz range, while the parasitic shunt capaci-
tance was 0.97 pF. The 56% perforation results in a 40% reduction
of shunt capacitance, which improves the SRF by 0.8 GHz, f
Q30
by 1.1 GHz, and Q factor by 224% without change of effective
capacitance. Even though there was a slight further improvement
of isolation with 44% perforation, the RF performance listed above
was seriously degraded, as compared to the 56% case. From the
analysis we can conclude that the capacitor cell shielded with 56%
perforation ground (600-m square edge and 200-m conductor
width) reveals the optimized isolation and RF performance for 3D
RF circuit integration.
5. CONCLUSION
This work reports the design of an isolated capacitor cell of high
values of Q factor and SRF for LTCC 3D RF circuit application.
The optimized capacitor cell with perforated ground of 600-m
square edge and 800-m pitch revealed good isolation of -20 dB
transmission up to 15 GHz from a vertical interferer (located
114-m above) and a lateral interferer (located 300-m away).
The fabricated 2.8-pF capacitor revealed an SRF of 7.6 GHz and
Q factor of over 190 up to 3 GHz, which is an improvement of
SRF by 0.8 GHz and Q factor by 224%, as compared to the
conventionally grounded capacitor.
ACKNOWLEDGMENTS
This work was financially supported in part by the Ministry of
Science and Technology of Korea and the Korea Institute of
Science and Technology Evaluation and Planning (KISTEP).
REFERENCES
1. A. Sutono, D.H. Heo, Y.J. Chen, and J. Laskar, High-Q LTCC-based
passive library for wireless system-on-package (SOP) module develop-
ment, IEEE MTT-S Int Microwave Symp Dig 49 (2001), 1715–1724.
2. M. Rytivaara, Buried passive elements manufactured in LTCC, IEE
Seminar, 2000, pp 6.1– 6.5.
3. G.E. Ponchak, D.H. Chun, J.G. Yook, and L.P.B. Katehi, The use of
metal filled via holes for improving isolation in LTCC RF and wireless
multichip packages, IEEE Trans Adv Packaging 23 (2000), 88 –99.
© 2003 Wiley Periodicals, Inc.
DOUBLE VOLTERRA SERIES
APPROACH TO FET MIXERS
Carlos Crespo-Cadenas and Javier Reina-Tosina
Radiocommunications Systems Group
Area of Signal Theory and Communications
Department of Electronics Engineering
University of Sevilla
Camino de los Descubrimientos, s/n, 41092-Sevilla, Spain
Received 18 February 2003
ABSTRACT: A double Volterra series approach to analyze nonlinear
microwave circuits is presented, with special emphasis on FET mixers.
Considering a FET as a circuit with two input ports, a procedure to
obtain closed-form expressions for nonlinear transfer functions is pre-
sented. Based on this approach, the known time-varying Volterra series
technique can be demonstrated. Calculated conversion loss and two-tone
IMD for a FET-resistive mixer are successfully compared with already
published data. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol
Lett 38: 486 – 488, 2003; Published online in Wiley InterScience (www.
interscience.wiley.com). DOI 10.1002/mop.11097
Key words: FET mixer; nonlinear analysis; double Volterra series
1. INTRODUCTION
A widespread method to analyze intermodulation distortion in
microwave mixers is an extension of the large-signal/small-signal
theory, combining any method to obtain the LO signal without
limitations with a time-varying Volterra series for the RF signal
[1]. This technique has been used repeatedly in FET microwave
mixers by several authors [2– 4].
A different approach had been presented by Rice [5] in a
previous paper, in which the output of a system with two input
ports is expressed as a double Volterra series. Although it seems to
be a powerful tool, to the author’s knowledge no attempt has been
made to analyze nonlinear distortion in FET microwave mixers
with double Volterra series.
Based on recursion formulas to determine nonlinear currents of
order n + m presented in [6], a procedure to obtain the corre-
sponding nonlinear transfer functions is reported in this paper. The
approach also serves to present a formal demonstration of Maas
technique [1]. The theoretical results are used to evaluate the
conversion loss and two-tone IMD response of a FET-resistive
mixer and they are compared with previously reported measure-
ments.
2. VOLTERRA SERIES IN TWO INPUT PORTS SYSTEMS
We consider a circuit with two independent inputs v( t ) and u( t ),
comprising a linear network and a controlled current source i ( u, v)
in parallel with input node u. The integrodifferential equations
relating node voltages and the current excitations i
v
( t ) and i
u
( t )
are given symbolically by
L
v
v, u = i
v
, L'
u
v, u + i
NL
v, u = i
u
, (1)
where i ( u, v) = g
10
v + g
01
u + i
NL
[ v, u] and
i
NL
v, u =
k=2
g
k0
v
k
+
l=2
g
0l
u
l
+
k,l=1
g
kl
v
k
u
l
. (2)
When inputs change to x ( t ) = i
v
( t ), z ( t ) = i
u
( t ), node
voltages change to y and w and their corresponding responses of
order n + m are related by
Figure 4 Measured and simulated Q factor, C
eff
, and SRF as functions
of frequency
486 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 38, No. 6, September 20 2003