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Design and Calibration of a Compact Quasi-Optical System for MaterialCharacterization in Millimeter/Sub-millimeter Wave Domain

Alireza Kazemipour∗, See-Khee Yee†, Martin Hudlicka‡, Mohammed Salhi∗,Thomas Kleine-Ostmann∗ and Thorsten Schrader∗

∗Physikalisch-Technische Bundesanstalt, Braunschweig, Germanyalireza.kazemipour@ptb.de

†Tun-H University (UThM), Johor, Malaysia‡Czech Metrology Institute, Prague, Czech Republic

Abstract—A compact spectrometer setup based on conven-tional rectangular horn antennas and two symmetrical parabolicmirrors is designed to provide a plane wave on the material-under-test. A commercial Vector Network Analyzer (VNA) andwaveguide frequency extension units are used to measure thescattering parameters. A simple practical calibration process isused to determine the S-parameters on the material surface with-out need of high-cost micrometer positioners. Several materialsare measured and the complex permittivity is presented.

Index Terms—Material Characterization, Free-space calibra-tion, Quasi-optical setup, Millimeter and sub-millimeter waves.

I. INTRODUCTION

Free-space measurement is a non-contact and non-destructive testing method to evaluate the intrinsic materialproperties such as complex permittivity and permeability. Thismethod has long been possible at microwave frequencies usinga VNA or in the terahertz range with ultrawideband pulses inthe time-domain [1]. With the advance of measurement instru-mentation, free-space systems for millimeter/sub-millimeterwaves became possible as well. They usually contain largeparabolic mirrors, high-cost corrugated horns and sophisticatedmicrometer positioners to perform the relevant free-spacecalibration [2].

In this paper, a system with conventional rectangular hornsand compact-size mirrors is presented to cover the widefrequency range from 50 GHz to 500 GHz and a reliablesimple calibration method is used without need for precisepositioning.

II. QUASI-OPTICAL SETUP

The system consists of a commercial VNA and sets ofwaveguide frequency converters: 50-75, 75-110, 110-170, 140-220, 220-325 and 325-500 GHz. The waveguide ports areconnected to conventional rectangular horn antennas and twosymmetrical parabolic mirrors are used to reduce the free-space transmission path-loss (Fig. 1). The system topology andthe shape and size of the mirrors must be designed to improvethe measurement accuracy for the whole frequency range andoptimize the cost and fabrication feasibility. Only two 90-degree parabolic off-axis mirrors are used to reduce the systemsize, cost and degrees of freedom of the adjustable parameters.Their distances to the antennas must be precisely determinedto satisfy the plane-wave conditions on the material-under-test

surface and to guarantee maximum energy passing throughfor a further improved sensitivity. Horn antennas are symmet-

sample�location

horn�2vector�networkanalyzer

horn�1

frequencyextender

frequencyextender

focal�distance f

foca

l�dis

tance

f

RF

LO MEAS

REF

REF

MEAS

LO RF

Fig. 1. Schematic overview of a quasi-optical measurement system.

rically put at the focal-points (f ) of parabolic mirrors whichthemselves are separated by a distance equal to 2f (Fig. 1).This topology is essential to provide a plane wave at themiddle of the two mirrors where the material-under-test mustbe placed. By using quasi-optical Gaussian relations it can beshown that the beam-waist (w0) is located slightly behind thehorn aperture. The beam diameter on the mirror is given asfollows assuming Gaussian expanding propagation [3]:

w (z) = w0

[1 +

(λz

πw20

)2]0.5

. (1)

The mirror aperture must be at least three times larger thanthe beam size to reduce diffraction effects and to providemaximum energy focused on the material surface. The systemhere is optimized with compact mirrors having a diameter ofless than 8 cm and a focal-point equal to 76 mm. As the phasecenter of horns depends on frequency, a manual horn-to-mirrordistance adjustment is necessary for every frequency range tomaximize the transmitted energy. Our observations show thatthis system can provide S12 better than -4 dB (50-325 GHz)and better than -8 dB (325-500 GHz). The transmission couldbe further improved by using high-cost long corrugated hornswhich have weaker side-lobes and higher gain.

483

III. CALIBRATION PROCESS

Several calibration methods exist in free-space and mostof them are very sensitive to the quality and the preciselocation/orientation of the “Short” standard for which a sophis-ticated micrometer positioner is needed in the sub-millimeterwave domain [4]. Here we use a new concept to shift thecalibration plane virtually from the VNA waveguide portsto the material-under-test surface. This is the complete de-embedding technique for which the overall scattering effects ofthe propagation path from the actual VNA ports to the materialsurface are evaluated experimentally. The key point is toevaluate the propagation path losses/diffraction by measuringthe S-parameters of the empty setup which is supposed to besymmetrical (Fig. 2) and then repeating the same process withthe material.

S

material�surface

11A S

12A

S21A S

22A

S11B S

12B

S21B S

22B

S11C S

12C

S21C S

22C

S11M S

12M

S21M S

22M

A B C

VNA�calibration�plane

VNA�Port�1 VNA�Port�2

Fig. 2. De-embedding of the S-parameters.

Symmetry of the empty system satisfies SA11 = SC

22;SA22 = SC

11; SA12 = SA

21 = SC12 = SC

21. After some matrixmanipulations, the S-parameters on the surface of the material(SB) can be derived as a function of the overall system S-parameters (SM ) and the free-space matrices A and C:

SB21 =

SM21(

SA21

)2 , SB11 =

SM11 − SA

11(SA21

)2 . (2)

In above relations, SM is known from the full-system(material loaded) measurements, and SB can be derived if SA

is known, as well. SA is the “de-embedding” factor whichcould be determined from the empty-system measurementassuming

SB =

[0 e−jkL

e−jkL 0

], (3)

where k is the free-space propagation constant and L is themeasured material slab thickness. The permittivity and perme-ability of the material can be extracted by taking into accountmultiple-reflection effects in the material slab. Concerning theapplied data-extraction method, both S11 and S12 are used oruniquely the S12 is used for the transmission-only method.

IV. MEASUREMENT RESULTS

Several material slabs were measured and we report theresults for six of them as representatives of thick andthin slabs as well as lossy and low-loss materials: teflon(L = 2 mm), polyvinylchloride (PVC, L = 8 mm), glass(L = 2 mm, lossy), bor-crown glass (BK7, L = 500 µm, lossy),quartz (L = 500 µm) and polymethylmethacrylate (PMMA,

L = 4 mm). The extracted real and imaginary parts of thepermittivity are shown in Figs 3 and 4.

100 200 300 400 5000

1

2

3

4

5

6

7

frequency (GHz)

ε r

eal part

(−

)

teflon

glass

BK7

quartz

PMMA

PVC

Fig. 3. Extracted real part of the permittivity.

100 200 300 400 500

0

0.1

0.2

0.3

0.4

0.5

frequency (GHz)

ε im

ag p

art

(−

)

teflon

PMMA

glass

BK7

quartz

PVC

Fig. 4. Extracted imaginary part of the permittivity.

V. CONCLUSION

A simple quasi-optical VNA spectrometer setup was intro-duced which is an alternative to existing time-domain THzsystems at low frequencies. The calibration of the systemconsists of a 2-stage process; first the VNA is calibrated atthe waveguide flanges and second a free-space calibration isperformed and the reference plane is shifted.

ACKNOWLEDGMENT

This work has been conducted within the EMRP jointresearch project “NEW07 Microwave and terahertz metrologyfor homeland security”. The EMRP is jointly funded bythe EMRP participating countries within EURAMET and theEuropean Union.

REFERENCES

[1] D. K. Ghodgaonkar, V. V. Varadan, and V. K. Varadan, “Free-space mea-surement of complex permittivity and complex permeability of magneticmaterials at microwave frequencies,” IEEE Trans. Instrum. Meas., vol. 39,no. 2, pp. 387–394, 1990.

[2] E. Saenz, L. Rolo, M. Paquay, G. Gerini, and P. de Maagt, “Sub-millimetre wave material characterization,” in European Conference onAntennas and Propagation (EuCAP), Rome, Italy, Apr. 2011, pp. 3183–3187.

[3] P. F. Goldsmith, Quasioptical Systems. New York: The Institute ofElectrical and Electronics Engineers, Inc., 1998.

[4] I. Rolfes and B. Schiek, “Calibration methods for microwave free spacemeasurements,” Advances in Radio Science, no. 2, pp. 19–25, 2004.