development of measurement and extraction technique of

This article has been accepted for publication in the Journal of Infrared, Millimeter and Terahertz Waves, December 2017, Volume 38, Issue 12, pp 1510–1520. The final publication is available at link.springer.com, DOI: 10.1007/s10762-017-0421-y

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Development of measurement and extraction technique of complex permittivity using

transmission parameter 𝑺𝟐𝟏 for millimeter-wave frequencies

Turgut Ozturk*a, Martin Hudličkab, İhsan Uluera

aDepartment of Electrical-Electronics Engineering, Karabuk University, Karabuk, Turkey

bCzech Metrology Institute, Okruzni 31, 63800 Brno, Czech Republic

Abstract

This study provides an overview of measured S-parameters and its processing to extract the

dielectric properties of materials such as Teflon, PMMA and PVC which are preferred for

material characterization process. In addition, a correction model is presented for transmission

parameter (𝑆21) to obtain the dielectric constant with high accuracy. A non-destructive and

non-contact Free Space Measurement method has been presented to measure S-parameters of

thin samples in the low THz frequency range. S-parameters are collected in free space by Vector

Network Analyzer which is supported with two frequency extenders. Additionally, the

parabolic mirrors are used to collimate the generated signal in wide frequency range.

Furthermore, a standard filter process is performed to remove the unwanted ripples in signal

using Singular Spectrum Analyzer before the implementation of extraction process. Newton-

Raphson extraction technique is used to extract the material complex permittivity as a function

of frequency in the Y-band (325-500 GHz).

Keywords: Complex permittivity, material characterization, Newton-Raphson technique,

quasi-optical free space measurement.

* Corresponding author: Turgut Ozturk ([email protected])

1. Introduction

The dielectric properties are measures of the material polarization based on the electric field in

a material. The permittivity, which is an internal property independent of the measurement

method, is considered as an important characterization parameter used in electrical engineering.

It varies according to the materials’ response to the electrical signal [1–4]. The material

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mailto:[email protected]


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properties of materials, such as permittivity, permeability, and refractive index are important in

many applications to understand interaction between the electromagnetic radiation and the

material. Therefore, the material characterization is an increasingly important issue in the mm-

wave and THz wave frequency range [2,5]. Engineers need material properties for

electromagnetic simulations, which is cheaper than the trial and error estimation methods.

Therefore, the material properties (휀, 𝜇, 𝑡𝑎𝑛𝛿) are very important in engineering applications.

The application areas cover, e.g., monitoring of moisture, food industry, medicine, military and

security [6–8].

There are different measurement methods for different phase (gas, liquid, and solid) of material

from microwave to THz wave frequency range. Generally, the measurement methods are

divided into two groups as down and up conversion frequency. We convert up the signal from

microwave frequencies using a frequency extender in order to measure at hundreds of GHz and

opposite we use down-conversion from optical or THz waves in order to measure at hundreds

of GHz using time-domain spectroscopy [2,9]. These can be divided to resonant cavity methods,

measurement in a cross-section of a waveguide, and free space measurement methods, to

measure S-parameters for extracting the dielectric constant of materials [10]. The Free Space

Measurement (FSM) method is commonly used for measuring of dielectric properties of

materials in free space [11].

A FSM method has been used for material characterization for a long time in microwave and

mm wave (sub-THz) frequency range. Accurate measurement of dielectric properties in a wide

frequency band range can be achieved by using FSM system. The usage of FSM method has

become possible in mm and THz wave frequency range by fast new developments of the used

devices [4,12]. It is obvious that, only one measurement method is not able to characterize all

materials over a broad frequency band. Moreover, properties of lossy and low loss materials

are difficult to measure accurately. Therefore, different methods are required for each frequency

band and material loss. FSM method is a common used method belonging to the non-resonant

group which is more appropriate to use for low or high frequency, at high temperature etc. It

should be considered that the sample size limitation will be not a problem at THz frequencies,

however the distance is important between antennas for composing of plane wave [3,5,13].

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This paper describes a new data correction method using the 𝑆21 parameter which is measured

by Vector Network Analyzer (VNA) in free space. The experiment was performed in 325-500

GHz frequency range to show the ability of proposed model in the THz frequency range. The

main goal of this study is to obtain accurate complex permittivity evaluation with new estimated

𝑆21 parameter using a simple process. Thus, the availability of FSM method has been shown

with accuracy and stability criteria. Furthermore, the extracted results of complex permittivity

show highly accurate agreement the values found in literature for each sample (Teflon, PMMA,

and PVC). In addition, the parabolic mirrors were used to eliminate the disadvantages of FSM

that are related to the sample size and collimating of electromagnetic wave.

2. Measuring of S-Parameters

A non-contact and non-destructive FSM method was used to measure the dielectric properties

of thin samples [14]. In order to achieve the frequency 325 GHz, frequency extenders should

be used. The frequency range is increased up using these extenders, while the maximum

frequency of the VNA is 60 GHz. The receiving and transmitting antennas are connected to the

rectangular waveguides. A lens can be preferred to collimate the electromagnetic wave to the

surface of sample, however in the present set-up, two parabolic mirrors were used. The

measurement process was implemented over a frequency range 325-500 GHz using a frequency

extender. A VNA, two horn antennas, two frequency extenders, two parabolic mirrors, and a

sample holder are used to compose the measurement system as shown in Fig. 1. The horn

antennas are connected to the VNA using coaxial cables, extender and waveguide adapters.

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Fig. 1 The setup of measurement system

Spot focusing lenses can be used to minimize the diffraction effect for high accuracy

measurement. It is known that, lens, collimating beam and reducing beam diameter, increases

antenna gains. In addition, during these processes, the errors can be reduced with Thru Reflect

Line (TRL) calibration method and VNA gating technique. Although the diffraction effect is

minimized by using large sample size, the measurement performance may diminish due to

sagging of soft materials. Effective thickness causes another problem that is non-planarity of

phase incident on sample surface when high accuracy results are required. Thickness effect

should be considered for the spot where the collimated beam passing through the lens is

thinnest, to coincide with the midpoint of the sample thickness [2,15,16].

On the other hand, the measurement method can be supplied with optical components in THz

frequency range like this study. This method can be called as a quasi-optical FSM as it consists

of a parabolic mirror that is an optical component. A parabolic mirror has some advantages for

FSM method which are the compact size, collimation of the radiation onto sample, and thus

minimizing the sample size. If an off-axis parabolic mirror has large solid angle and lower focal

length (<10 cm), it will be useful for measurement system to align the radiation.

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3. Extracting of Complex Permittivity

The transmission and reflection coefficients obtained from S-parameters are used to calculate

the dielectric constant. Many methods such as Nicolson Ross Weir (NRW), NIST Iterative,

New Non-Iterative, Genetic Algorithm (GA), Root Finding Algorithm (RFA), Newton-

Raphson, and Particle Swarm Optimization (PSO) are used to obtain these coefficients and

dielectric properties [17]. These extraction techniques can be divided into two main groups:

analytical and numerical extracting techniques.

The analytical extracting techniques are based on certain and specific expressions which are

easy to use and comprehensible for extracting the complex permittivity of samples. When the

thickness of the sample reaches multiples of the half wavelength, the magnitude of the reflection

coefficient approaches to zero. At this condition, the formulas, which are used in extraction

process, are inaccurate and unstable for a specific range of sample thicknesses as in the NRW

method [9,18]. However, a new method has been proposed called the iterative method. This

method eliminates the resonances occurring when the thickness of dielectric materials is larger

than half [19]. In spite of analytical techniques, solutions of numerical techniques such as RFA

and GA cover a wide range of algorithms. The major deficiency of these calculation techniques

the is necessity to estimate permittivity before starting the calculation process [17].

The Newton-Raphson theory uses an iterative procedure process to find the best solution of

function. The real and imaginary part of complex permittivity can be calculated using reflection

coefficient (𝑆11) or transmission coefficient (𝑆21). Therefore, the Newton-Raphson technique

has a significant advantage with this feature over NRW extracting algorithm because NRW

technique requires 𝑆11 and 𝑆21 parameters simultaneously. When the reflection of material

(high-loss) is high, the 𝑆11 coefficient can be used to determine the dielectric properties of

materials. On the other hand, when a material (lossless) has small reflection, the 𝑆21 coefficient

is satisfactory for extracting process [20]. The extraction process can be describe using

transmission coefficient 𝑆21 which is stated as follows [21]:

𝑆21 =T(1 − Γ2)

1 − T2Γ2 (1)

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where Γ is the reflection coefficient of between air-sample interface and T is the transmission

coefficient of the wave propagating along the environment in free space. The initial equations

of Newton-Raphson algorithm can be expressed as:

𝜑(휀𝑟, 휀𝑖) = 𝑆21_𝑟(휀𝑟 , 휀𝑖) − 𝑆21𝑚_𝑟 (2)

𝜙(휀𝑟 , 휀𝑖) = 𝑆21_𝑖(휀𝑟, 휀𝑖) − 𝑆21𝑚_𝑖 (3)

where 𝑟 and 𝑖 indicate the real and imaginary parts of 𝑆21 magnitue and 𝑚 indicates measured

data. The Equations 2 and 3 are about real and imaginary parts of permittivity, respectively.

Their derivatives (dS21_r/dεr, dS21_r/dεi, dS21_i/dεr and dS21_i/dεi) are calculated with respect to 휀𝑟

and 휀𝑖 to compute the tolerance value:

𝐷 = ||(

𝑑𝑆21_𝑟

𝑑휀𝑟) (

𝑑𝑆21_𝑟

𝑑휀𝑖)

(𝑑𝑆21_𝑖

𝑑휀𝑟) (

𝑑𝑆21_𝑖

𝑑휀𝑖)

|| (4)

The first corrections are determined for unknowns (휀𝑟 , 휀𝑖) as follows:

휀𝑟 = 휀𝑟_0 + ℎ (5)

휀𝑖 = 휀𝑖_0 + 𝑘 (6)

where, h and k are corrections for real and imaginary parts of permittivity, respectively. The

initial guesses are 휀𝑟_0 and 휀𝑖_0 to start the Newton-Raphson algorithm process. This value is

obtained with each point as a function of frequency by the algorithm. The whole process is

shown in Fig. 2 which is a flowchart of the Newton-Raphson extracting technique to obtain the

complex permittivity of samples. This process is repeated until the conditions are met which

are the number of iterations and a tolerance.

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Fig. 2 The flowchart of Newton-Raphson technique

The actual goal of this technique is to compute a root of set of functions in Newton-Raphson

technique. This algorithm is very useful when the dielectric constant of materials is extracted.

Additionally, this algorithm can generate a new initial value every point of data. Newton-

Raphson technique allows characterizing the object depending on the type of the material and

the measurement accuracy. The same procedure, which is described above, applicable to 𝑆11.

For instance, 𝑆11 can be used to measure high-loss dielectric materials (called lossy materials)

because the transmission is very low. On the other hand, when a material has a small reflection

(or lossless), it is sufficient to use 𝑆21.

Before the using of Newton-Raphson technique, the Singular Spectrum Analysis (SSA) was

applied to original data to obtain smoothed signal. The original data series is separated into a

sum of small number of independent components by SSA. These independent components have

a meaningful interpretation of original data. The SSA algorithm has two steps which are

decomposition (embedding and SVD-Singular Value Decomposition) and reconstruction

(grouping and diagonal averaging). In diagonal averaging stage, the raw data (transmission

parameter - 𝑆21) is recovered from unwanted ripples and noises. Briefly, after disposing of

unwanted data, the new estimated data is obtained which is similar to raw (measured) data

without any noise and ripple. Thereby, when all steps of SSA algorithm are performed, the

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smoothed signal wave form is gathered after the ripple and noise are eliminated. This algorithm

has been described in detail [22–24].

4. Results and Discussion

All raw data was collected for three material samples in 325-500 GHz frequency range.

Generally, Teflon sample is used to verify the accuracy of measurement and extraction process.

The parabolic mirrors were used to align the radiated electromagnetic wave (THz). Hence, THz

wave can be focused onto sample with quasi-optical system. The position of parabolic mirrors

must be adjusted well. Therefore, it may be necessary to take measurements several times while

the position of the parabolic mirror is being determined.

It will be useful to give some mathematical approaches before analyzing the results of

measurement. The errors and noises should be removed which are in measured signals since

considering the difficulty of generating THz signals by the FSM method. Thus, the following

procedures must be carried out in order to correct the measured signals. Then, the acquired

signal is used to extract the complex permittivity. To perform the signal correction process, two

different measurements were taken with and without sample which are named material (m) and

air (a), respectively. The value of transmission parameter (𝑆21) is used as following:

𝑆21_𝑐 =𝑆21_𝑚

𝑆21_𝑎𝑒(𝑗𝛽𝑑) (7)

Hence, the correction value of 𝑆21 parameter is obtained using above equation. Here d is the

thickness of material, c is correction, m is material, and a is air. The 𝛽 value is calculated as

𝛽 = 2𝜋𝑓√휀0𝜇0 (8)

The transmission parameter (𝑆21) of three (PVC, Teflon, and PMMA) samples are sufficient

since the Newton-Raphson can extract the complex permittivity using just 𝑆21 parameter. There

are two ways to run Newton-Raphson algorithm for obtaining permittivity value of samples.

Firstly, the initial guesses were set for each sample such as PVC (2), PMMA (2.6), and PVC

(2.9). These values complied from literature. Secondly, initial value estimating algorithm can

be used to find the best initial guess. The convergence was achieved less than 1% of the error

value.

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A filtering method may be needed to reduce the remaining noise which are occurred after the

correction process. Although, the correction steps given above have been performed between

325-500 GHz, the SSA was used in second step as shown in Fig. 3. Hence, the smoothed signal

will be obtained from corrected data (raw 𝑆21). It is important for material characterization that

the environmental noises and measurement errors should be eliminated using the SSA

technique. When this technique is used, the magnitude of the 𝑆21 parameter can be obtained as

smoothed and the permittivity can be calculated with smaller error. Hence, the goal of using of

SSA is to obtain the accurate, reliable and smooth data to extract the complex permittivity.

Fig. 3 The flowchart of proposed model

The quasi-optical FSM was used to measure the signals for three samples (Teflon, PVC,

PMMA). The using of PM is a good choice since THz wave can be attenuated due to ambient

conditions such as temperature and moisture. The plane wave was composed in short distance

using two parabolic mirrors. Moreover, this wave was collimated onto surface of sample easily

to obtain high accuracy data. Hence, the distance between antennas can be reduced for a

compact setup system. The empty measurement processes were repeated for each samples to

use in Eq. 7. The number of data points was selected as 1601 in order to collect a dense

frequency grid and small differences of the S21 phase between adjacent data points. The

correction process was separately implemented for Teflon sample in Fig. 4 to clarify the

proposed model. If we pay attention, there is a problem around 342 GHz according to Fig. 4. It

was also determined for PMMA and PVC samples. This will affect the extraction of complex

permittivity.

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Fig. 4 Magnitude of 𝑆21 parameter for Teflon after correction process

The imaginary part was also corrected using proposed model as shown in Fig. 5. When the two

zoom regions are examined around 420 GHz, the difference between the wave propagation in

the material and in the empty space can be easily seen.

Fig. 5 Magnitude of 𝑆21 parameter for PMMA after correction process

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Actually, the measurement performance is not good after 480 GHz as shown in Fig. 6. Although

the correction signal is bad between 480-500 GHz, the SSA is able to obtain a smooth signal

successfully. The narrower useful frequency band of 380-480 GHz is most probably caused by

unexpected resonances in the lower and upper part of the frequency band due to low-grade

cables used for the frequency converters.

Fig. 6 Magnitude of 𝑆21 parameter for PVC after correction process

As seen from figures, the 𝑆21 transmission parameter is different for particular materials. The

difference of repeatability was shown for each sample in this study. This can be described as

the effect of multiple reflections inside the material layer. Teflon has almost two peak values

between 325-500 GHz frequency range, while this value is four and eight for PMMA and PVC,

respectively. Furthermore, the transmission parameter magnitude values of samples are

decreasing towards 500 GHz.

The complex permittivity of three samples was calculated using 𝑆21 parameter after performing

the four steps which can be sorted as correction of signal, filtering signal, estimated new 𝑆21

parameter, and extracting the permittivity, respectively. The results of Newton-Raphson

technique are shown in Fig. 7. The dielectric constant value of Teflon is approximately 2.02

with average value whole frequency band. This value is detected as 2.6 for the PMMA sample.

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And it is determined as 2.9 for the PVC sample. The solid line is the real part of permittivity

and the dashed line is the imaginary part of permittivity for three samples.

Fig. 7 The permittivity values for Teflon, PVC, and PMMA samples

It should be noted that the transmission parameter (𝑆21) of the materials provide an advantage

with high amplitude. Thus, the transmission parameter is collected easily in the whole

frequency band. In addition, the transmission and reflection parameters should be purified from

noise and error in order to use the FSM method in THz frequency range (0.1-0.5 THz) actively.

5. Conclusion

Newton-Raphson extraction technique allows high accuracy level calculation of the dielectric

constant for thin samples at millimeter and THz wave frequency ranges. The usage capability

of Newton-Raphson technique is better than an analytical method, which is NRW, since it can

be run using just reflection or transmission parameter of the material under test. The magnitude

of the 𝑆21 parameter can be gathered easily, when the air and material measure values of a

sample are used in a simple equation. Hence, the corrected signal can be used to calculate the

dielectric properties of a material. If the Newton-Raphson technique is applied to a corrected

signal, which is achieved using Eq. 7, the complex permittivity is extracted as fluctuated

because of the fluctuating transmission parameter (𝑆21). When the SSA is used to filter the

corrected signal, the complex permittivity is extracted correctly as smoothed.

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Acknowledgements

Part of the work has been supported by the EMRP joint research project “NEW07 Microwave

and terahertz metrology for homeland security”. The EMRP is jointly funded by the EMRP

participating countries within EURAMET and the European Union.

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