=Paper=
{{Paper
|id=Vol-1814/paper-06
|storemode=property
|title=Dielectric Permittivity and Permeability Measurement System
|pdfUrl=https://ceur-ws.org/Vol-1814/paper-06.pdf
|volume=Vol-1814
|authors=Nikolay S. Knyazev,Alexander I. Malkin
}}
==Dielectric Permittivity and Permeability Measurement System==
https://ceur-ws.org/Vol-1814/paper-06.pdf
Dielectric Permittivity and Permeability
Measurement System
Nikolay S. Knyazev, Alexander I. Malkin
Ural Federal University, Yekaterinburg, Russia,
alexander.malkin@urfu.ru
Abstract. The article describes a measurement system, which is used
for determining the dielectric permittivity and permeability. The applied
methods and algorithms of recalculation allow one to measure the pa-
rameters of materials in wide frequency bandwidth with high accuracy.
Calibration during the measurements and the practical results are also
presented in the article. Choice of the Through - Reflect - Load (TRL)
calibration method is explained and the standards that were used during
the calibration procedure are described. The theory of material parame-
ters measurement and recalculation methods are described and the main
advantage and disadvantage of considered methods are explained. A sam-
ple of teflon (PTFE) was measured and errors, which had influenced the
measurement results, were discussed. The methods of increasing accu-
racy of material parameters measurement are presented in the article as
well.
Keywords: Permittivity, permeability, measurement system
1 Introduction
Nowadays we use a huge number of different radio devices. Commonly, various
types of dielectrics are used in design of these devices, for example, in printed
circuit board (PCB). It is very important to know the real parameters of the
used material at a stage of the devices elements development; otherwise, we
should make additional steps to determine correct size of the designed element.
The capacitance (parallel plate) method is used very often for the permittivity
determination. But this method has a lot of restrictions, especially, in frequency
above some hundred megahertz. Another method, which we can use for deter-
mination of permittivity, is a measurement with an open coaxial probe. But
this method is suitable to measure liquid not solid materials because we cannot
consider the air gap between probe and sample; and it adds additional errors in
our measurement result, which is unwanted. Another frequently applied method
is to use resonator for measurement. This method allows one to determine per-
mittivity of dielectric materials with the lowest possible errors. This happens
because we use a resonance effect for determining the parameters of materials.
We can measure only thin and low loss sample, because in other case if we use
thick or losses material, it will be impossible to find and measure the parameters
46
of resonance. In addition, this method has a restriction in frequency resolution
because we have a discrete frequency grid and a frequency step will be defined
by the parameters of resonator. The most suitable method, which allows one to
measure permittivity of various material, is a transmission line method.
2 Transmission line method
This method allows one to measure permittivity and permeability of various
materials using transmission lines (waveguide, airline, free space). In Figure 1, a
sample is placed in a waveguide or an airline. Parameters of a scattering matrix
of a measured sample, which we need to know to calculate parameters of material
sample, are found during analysis of distribution of the electromagnetic field in
using transmission line. During calculation, we need to take into account the
boundary conditions. We devided space into three areas and parameters were
measured separately in different areas.
Fig. 1. Measurement sample in the transmission line.
If we assume that the electric field in I, II, and III areas takes the value
accordingly EI , EII and EIII , we can write a distribution of the electric field as
follows:
EI = e(−y0 ·x) + C1 · e(y0 ·x) , (1)
(−y·x) (y·x)
EII = C2 · e + C3 · e , (2)
EIII = C4 · e(−y0 ·x) + C5 · e(y0 ·x) . (3)
The propagation constant in the used transmission line with measured sample
and without it is described:
s
ω 2 µr εr 2π 2
y=j· − ( ) , (4)
c2vac λc
47
s
ω 2 2π 2
y=j· ( 2 ) −( ) . (5)
clab λc
Here, cvac is the speed of light in vacuum, clab is the speed of light in the
transmission line, ω is the angular frequency, λc is a cutoff wavelength of using
waveguide, µr and εr are complex permeability and permittivity. The main ad-
vantages of this method are the following: possibility to measure a sample with
arbitrary form and different aggregate state, possibility to measure losses mate-
rials, possibility to make measurements in wide frequency bandwidth and with
arbitrary frequency step size. The method is based on measuring of the samples
S-parameters by using a vector network analyzer (VNA) [1]. Then, measured
parameters are recalculated in value of permittivity and permeability. Accuracy
of the permeability and permittivity measurement will depend on many different
factors such as:
– the error of an amplitude and phase measurement of S-parameters;
– the air gap between sample and sample holder;
– the error of sample length measurement;
– high order waves excitation;
– calibration errors.
There exist several methods of recalculating S-parameters of the sample into
permittivity [2]. A short overview of some of them is shown in Table 1. We
choose the Nicholson-Ross-Weir (NRW) method as the main one for the reason
that it is the most widely used. We calculate complex values of permittivity
and permeability from propagation constant using (4) and (5). According to the
NRW method, the formulas for calculating permittivity and permeability will
be the following ones [3]:
1+Γ
µr = q , (6)
Λ(1 − Γ ) λ12 − λ12
0 c
and
λ20 1 1 1 2
εr = ( 2 −[ ln( )] ). (7)
µr λc 2πL T
For a new non-iterative method, formula for calculating permittivity will be:
λ20 λ2 1
εr = (1 − 2
)εef f + 02 . (8)
λc λc µef f
There are several methods of recalculating S-parameters of the sample into
permittivity. A short overview of some of them is shown in Table 1
48
Table 1. Overview of recalculating methods.
Sample Calc. method Speed Accuracy
Thin losses non-magnetic materials NRW fast medium
Thin losses magnetic materials NRW fast medium
Thick low losses non-magnetic materials NIST Iterative slow good
Thick low losses non-magnetic materials New non-iterative fast good
3 Measuring system description
3.1 Hardware and Software
In our measurement system shown in Figure.2, we used the transmission line
method described above as well as two algorithms of recalculation - the NRW
and New Non-Iterative (NNI) were applied. NNI allows one to measure with
high speed and good accuracy, while the NRW method helps us to calculate
permeability.
For S-parameters measurement, we used the Rohde and Schwarz ZVA vector
network analyzer because it provides good accuracy. For calculating permittivity
from measured S-parameters, we decided to use external software because it
allowed us to make remote control of the equipment and to change parameters
of calculations method easily. Given in fact that the ZVA had already got the
LabVIEW driver for the remote control for programming, we just used it. The
graphical user interface for the LabVIEW program is shown in Figure.3.
Fig. 2. General view of the measurement system.
49
Fig. 3. View of the user interface.
3.2 Calibration and placement
For calibration of the ZVA with waveguides, the TRL method was used. Ad-
vantages of the TRL method are: possibility of using sample holder as the line
standard and possibility of using reflection standard with unknown S-parameters
[1]. Developed measurement system allows one to verify the state of calibration
of VNA and to set the main parameters (frequency bandwidth, number of mea-
surement points, and power of signal). It is possible to make measurements in
a single mode as well as in a continuous one and to choose different calculation
method (NRW or NNI).
During calibration, we have to provide the same reflection coefficients for
both measuring ports (for steps of calibration with reflection standard). If co-
efficients of reflection differ, we will see a ringing on trace of permittivity. The
right placement of the reference plane in our measurement system is also has
a great im-portance because samples and sample holders are not equal by size
(especially concerning thickness) so, there mismatches may become a cause of
the wrong value of phase. For the moving reference plane, we use offset feature
of VNA; and our program has possibilities of setting an offset. Taking into ac-
count an air gap between a sample and a sample holder, we use the capacitance
method in our program [2].
4 Measurement example
To make the real measurements, we decided to use the PTFE sample with thick-
ness 2 mm. The parameters of that sample were measured in 813 GHz frequency
band with using the WR90-type waveguide. We used the TRL method to do the
calibration. We have got a mismatch between the sample and the sample holder
of approximately 0.1 mm. The real and imaginary measured parts of complex
50
permittivity are shown in Figure4 and 5 respectively (the straight line is with-
out the gap correction, dash line with the gap correction). We can see that the
gap correction allows one to improve the measurement accuracy because these
results are much closer to the reference value of the PTFE permittivity (value
is about 2.1).
On the graphics we can also see the ringing in the high frequency area and
the cause of it is a nonequal reflection conditions on both measuring ports during
the TRL calibration.
Fig. 4. Real part of complex permittivity versus frequency.
Fig. 5. Imaginary part of complex permittivity versus frequency.
51
5 Conclusions
We can summarize that presented system is very flexible and has a great oppor-
tunity to measure the various types of dielectrics. Also it is a high-speed system
with a wide frequency bandwidth, which is limited only by the frequency range
used by the VNA and the measurement transmission line. It is possible to in-
crease the measurement accuracy by using special experimental processing data
algorithms that allow one to take take into account the air gap between the sam-
ple and the sam-ple holder into account. This helps to reduce the requirements
for precision of manufacturing the measured samples, which are important for
the practical application of the system.
References
1. Heibel, M.: Fundamentals of Vector Network Analysis. Rohde-Schwarz, Germany
(2008)
2. Kuek, C.: Measurement of Dielectric Material Properties: application note. Rohde-
Schwarz, Germany (2012)
3. Barker-Jarvis, J.: Improved technique for determining complex permittivity with
the transmission/reflection method. Trans Microwave Theory Tech, vol. 38(8), pp.
1096-1103. IEEE (1990)
4. Nicolson, A. M.: Measurement of the Intrinsic Properties of Materials by Time-
Domain Techniques, Transactions on instrumentation and measurement, vol. 19(4),
pp. 377-382. IEEE (1970)