PIERS Proceedings, Cambridge, USA, July 2–6, 2008
566
Measurement of the Dielectric Constant of Liquids Using a Hybrid
Cavity-ring Resonator
M. S. Kheir1 , H. F. Hammad1 , and A. S. Omar2
1
Faculty of Information Engineering and Technology
German University in Cairo, Cairo, Egypt
2
Microwave and Communication Engineering
University of Magdeburg, Magdeburg, Germany
Abstract— A simple and efficient solution for extracting the dielectric constant of liquids
utilizing microstrip ring resonators simultaneously with rectangular waveguide (RWG) cavities
is presented. Employing both techniques in a single structure is a confirmation procedure rather
than comparing the obtained results with any other standard method. The proposed structure
is intended to be mechanically suited for holding liquid samples without enclosing any air gaps
which enhances the measurement sensitivity. Since the structure is being totally enclosed, the
loaded quality factor will be consequently increased due to the absence of radiation losses. The
waveguide cavity acts as metallic enclosure for the ring circuit in order to maintain the design
procedures as well.
1. INTRODUCTION
Material characterization is an important field in microwave engineering since it is employed in
various systems and applications ranging from high-speed circuits to satellite and telemetry applications [1]. Several measurement techniques are already available nowadays and can be mainly
classified into transmission-reflection, free-space, and resonance techniques. The later technique is
of a great interest and wide range of application due to its higher accuracy and resolution. Among
the resonant methods used in material characterization are waveguide cavities and printed-line
resonators [3–11]. Rectangular and cylindrical waveguide cavities have been commonly used for a
long time in characterizing low-loss materials [4–6] as they offer a high quality factor. However,
performing material measurement with waveguides concurrently with another printed resonator
has not been investigated yet and will be the goal of this work It is intended to use both structures
simultaneously as a double-check procedure for measurement convenience and low fabrication cost.
Using both methods consequently will definitely reduce measurement ambiguity. The key feature
in this structure is that it is an ordinary microstrip ring resonator covered with a metallic enclosure
which acts as a RWG as illustrated in Section 3. Above all, a practical solution for characterizing
the electrical properties of liquids is strongly needed.
2. MEASUREMENT THEORY
Napoli and Hughes [10] introduced a simple and accurate technique for determining the dielectric
constant of integrated circuit substrates. It was assumed that the substrate material forms a
parallel-plate waveguide cavity if it is metallized on both sides. Using the formula below the
relative dielectric constant (εr ) can be easily obtained just by detecting the resonance frequency
(fmn ) of this waveguide.
r³ ´
c
m 2 ³ n ´2
+
(1)
fmn = √
εr
2w
2l
where
c is the speed of light,
m is the order of transverse resonance,
n is the order of longitudinal resonance,
w is the waveguide width,
and l is the waveguide length.
However, the resulting quality factor was not as high as expected. In a later work, Howell [7]
suggested a slight modification to this method which significantly increased the quality factor and
Progress In Electromagnetics Research Symposium, Cambridge, USA, July 2–6, 2008
567
offered a convenient way of measurement. In his work he short-circuited the ends of the parallelplate waveguide to eliminate the losses due to end-effect and fringe fields. The resulted resonator
was a simple RWG with the resonance equation
¶
µ 2
c2
q2
p
εr =
+ 2
(2)
4fpq a2
b
where p and q are the transverse and longitudinal resonance modes respectively while a and b
are the transmission line length and width. By observing the resonance frequency and applying
the above-mentioned formulas, the effective dielectric constant can be calculated. Nevertheless,
Robinson [5] also investigated the resonant modes that result from RWG cavities partially loaded
with a microstrip line. This approach still can be a good approach for representing the modes of
the metallic enclosure used in our proposed design. The guided wavelength (λg ) of this excited
mode is given by
λo
λg = v
(3)
µ ¶2
u
1
λo
u
¶−
µ ¶µ
u
t
h
1
2l
1−
1−
b
εr
where h represents the substrate thickness, b is the cavity height (including the substrate material),
and λo is the free space wavelength.
3. THE HYBRID CAVITY-RING STRUCTURE
The detailed structure of the proposed hybrid resonator is shown in Fig. 1(a) with a separate
illustration of the ring circuit structure in Fig. 1(b). It consists of three major parts; the microstrip
ring resonator, the metallic enclosure and the common ground plane. This structure is made of
Aluminum and is fed by an SMA coaxial-to-microstrip transition for measurement using the vector
network analyzer (VNA). The details of the hybrid resonator structure are declared next.
Metallic Enclosure
Ring Resonator
Ground Plane
(a)
(b)
Figure 1: Exploded view of the proposed hybrid resonator (a) and top view of the used ring resonator (b).
3.1. The Microstrip Ring Resonator
A gap-coupled microstrip ring resonator with an FR4-type substrate has a dielectric constant
(εr = 4.4), a loss tangent (tan δ = 0.02) and a thickness (h = 1.5 mm) is used. The operation of
the ring resonator is based on the well-known relation
nλg = 2πr
(4)
where r is the mean radius of the ring and n is the harmonic order of resonance. Then the effective
dielectric constant (εeff ) can be extracted from the above equation since
λo
λg = √
εeff
(5)
Meanwhile, the resonance frequency can by detected by observing the peaks of the magnitude
and the rapid phase variation of the insertion loss (S21 ) of the ring. Considering that the ring is
operating at its fundamental resonance.
PIERS Proceedings, Cambridge, USA, July 2–6, 2008
568
3.2. The Waveguide Enclosure
Another way for confirming the estimated εeff is to use the metallic enclosure which acts as a waveguide cavity with L-band standard dimensions [2] operating at its dominant mode TE10δ . When the
cavity is perturbed by the material under test (MUT) the resulting resonance frequency will be
deviated from its original resonance frequency. From this frequency shift the material properties
can be evaluated using the Cavity-Perturbation theory [4]. However, through the following section
the details of the dielectric constant extraction procedures will be illustrated.
4. MEASUREMENT AND EXTRACTION PROCEDURES
1
2.4
2.6
2.8
1. 2
1. 4
1. 6
2
2. 2
2.2
Cav ity Reso na tor
Ring Resonat or
2
1.8
1.6
Relative Dielectri c Co ns ta nt
1.4
1.2
22
20
18
16
14
12
10
8
6
4
2
Effective Dielectric Cons tant
In the simulation phase, several materials with different dielectric constants have been tested and
the resulting effective dielectric constant of the substrate has been extracted using a finite-elements
method simulator. The detected resonance frequency of the overall structure is used in Equations (2) and (4) to calculate the respective εeff of the cavity and ring resonators. Fig. 2(a) shows
the effective dielectric constants calculated in both cases while the results are in excellent agreement. In Fig. 2(b) the relative dielectric constant extracted at different resonance frequencies is
plotted where the simulation points precisely fit a fourth order polynomial function. This curve
can be efficiently used to extract the dielectric constant of any MUT using the proposed structure
only by measuring its resonance frequency.
50 45 40 35 Simulation
30 Cu rve Fitting 25 20 15 10 5 1
1.8
2.4
2.6
2.8
Frequency (GHz)
Fr equency (GHz)
(a)
(b)
Frequency (GHz)
(a)
0
-5 -10 -15 -20 -25 -30 -35 -40 -45 -50
0.5
1
1.5
2
2.5
3
Sij (dB)
Figure 2: The extracted εeff from both resonators (a) and the estimated εr against frequency (b).
(b)
Figure 3: The measured S11 and S21 (a) and a photograph (b) of the resonator.
As a measurement example the experimental prototypes have been filled with an unknown liquid.
As shown in the S-parameters curve in Fig. 3(a) that the first resonance peak appears at 1.25 GHz.
Such result typically corresponds to a liquid with εr = 40 according to the previously depicted
graph. The measurement was performed by the Rohde and Schwarzr ZVB-20 network analyzer.
Progress In Electromagnetics Research Symposium, Cambridge, USA, July 2–6, 2008
569
The photograph of this prototype is shown in Fig. 3(b) where the screw-hole in the middle of the
enclosure is intentionally introduced for transferring the liquid into the structure. The structure
was mechanically suitable for holding such liquids due to its sealed design. A screw is then used to
close this hole which completes the upper metal boundary of the waveguide.
5. CONCLUSIONS
A simple method for evaluating the dielectric constant of liquids has been proposed. It is based
on using ring and RWG cavity resonators simultaneously in a single structure. By observing the
resonance frequency of this hybrid resonator the effective dielectric constant can be extracted. An
excellent agreement between the results extracted from both cavity and ring resonator has been
achieved. Such technique can give a preliminary indication about the dielectric properties of the
tested material. It can also be suitable for characterizing biological liquids such as blood or urine
as a promising technique for medical diagnosis.
ACKNOWLEDGMENT
The authors are sincerely grateful to Prof. Hisham El-Sherif, the Head of Industrial Automation
Dept., German University in Cairo, for his helpful consultations and efforts in fabricating the
experimental prototypes.
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