Calibration Procedure for Complex Permittivity Extraction Using an Open-Ended Coaxial Probe. Arjen Kremers Mai-Han Truong

Transcription

1 Calibration Procedure for Complex Permittivity Extraction Using an Open-Ended Coaxial Probe Arjen Kremers Mai-Han Truong June 15, 216

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3 Calibration Procedure for Complex Permittivity Extraction Using an Open-Ended Coaxial Probe by Arjen Kremers Mai-Han Truong June 15, 216 Students: Arjen Kremers Mai-Han Truong Project duration: April 18, 216 July 1, 216 Supervisor: dr. Marco Spirito, TU Delft An electronic version of this thesis is available at

4 Γ L

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6 Γ Γ 1 Γ 2 Γ 3 Γ c Γ M1 Γ M2 Γ M3 ω σ ε ε ε ε ε c ε r ε s e e 1 e 1 e 11 f S S 11 y L

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9 2. Requirements 2.1. Features The following features are desired in the product. i The radiating device used to measure reflection coefficients should be able to scan along two dimensions and should provide a good spatial resolution. ii The radiating device does not influence measurements on skin and does not react with the skin tissue. iii Measurement calibration should be performed real-time and calibration takes up to one minute. iv Range of detectable relative permittivity must consist of the permittivity of some reference liquids and of skin. The real part of the relative permittivity must cover 1 to 4 and the imaginary part must cover to 15. v The device should be wideband with the operational frequency ranging from.5 GHz to 2 GHz. vi The measured permittivity values should be visually represented. Figure 2: Pictures of the used open-ended coaxial probe Design Choices The first design choices have been made to give the project a well-defined direction. An open-ended coaxial probe with a polytetrafluoroethylene dielectric, better known as Telfon, between the conductors has been chosen as the radiating device. The probe has an outer diameter of 3.58 mm and a length of 1 cm. This because such a probe is able to measure a small area precisely and thus could provide a good spatial resolution. Teflon is also a safe material to use when in contact with skin, it does not irritate and it is not hazardous, as long as it is not overheated during operation [7]. Pictures of the probe are shown in figure 2. 9

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11 ε c ε ε r ε ε r ε σ f ω 2πf ε c = ε j σ ω ε ε ε = σ ω ε ε ε c = ε jε....

12 N 2 S 11 S 22 S 12 S 21 [ ] S11 S 12 = S 21 S 22 S 11 Γ c Γ c S ij Γ c = S 11 + S 12 S 21 Γ 1 S 22 Γ S 11 Γ Γ Γ = S 11 Γ c S 11 S 22 S 22 Γ c S 12 S 21

13 ε s ε s Γ Γ Γ c S 11

14 e e 11 e 1 e 1 Γ Γ Γ M = e e Γ 1 e 11 Γ e e = e e 11 e 1 e 1 Γ M Γ Γ 1 Γ 2 Γ 3 Γ M1 Γ M2 Γ M3 Γ M e e 1 e 1 e 1 Γ M1 = e + Γ 1 Γ M1 e 11 Γ 1 e Γ M2 = e + Γ 2 Γ M2 e 11 Γ 2 e Γ M3 = e + Γ 3 Γ M3 e 11 Γ 3 e e e 1 e 1 e 1

15 Γ Γ e Γ = Γ M e Γ M e e

16 ..... Γ 1 Γ 3 S 11 Γ 1 Γ 2 Γ 3

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18 S 11 ε ε S 11 Lookup table ǫ Phase of S Frequency [GHz] -3 ε = S 11

19 ...

20 S 11.. S 11 d S11 m S11 k ref k d = S11 m S11 k ref 2 ε c ε c

21 Frequencies [GHz] Frequencies [GHz] S 11

22 ε S 11 ε S 11 ε ε S 11 S 11 S 11.. S 11

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25 S 11 S 11 S S 11 S 11 S 11

26 S S 11 Γ = S 11 y L y L = 1 Γ 1 + Γ

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28 S 11 ε ε. ε ε S 11

29 ϵ 15 1 ϵ ϵ 15 1 ϵ ϵ ε ϵ ϵ ε ϵ ε ε ε

30 ϵ 15 1 ϵ ϵ ϵ ε ϵ ε ϵ ε ε

31 ϵ ϵ ϵ 15 1 ϵ ε ε ϵ ϵ ε ε

32 .. S 11 MAE = 1 n n e i i=1 e i = ε meas ε ref ε meas ε ref ϵ ϵ

33 ϵ ϵ ε.. ε.

34 ϵ 3 ϵ ϵ ϵ

35 ±2 S S 11 S 11 ( ± )

36 S 11 S 11 S 11

37 ϵ ϵ ϵ

38 8 6 ϵ ϵ 4 ϵ

39 ± = =

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44 e = Γ 1 (Γ 2 Γ M3 (Γ M1 Γ M2 ) + Γ 3 Γ M2 (Γ M3 Γ M1 )) + Γ 2 Γ 3 Γ M1 (Γ M2 Γ M3 ) Γ 1 (Γ 2 (Γ M1 Γ M2 ) + Γ 3 (Γ M3 Γ M1 )) + Γ 2 Γ 3 (Γ M2 Γ M3 ) e11 = Γ 1 (Γ M3 Γ M2 ) + Γ 2 (Γ M1 Γ M3 ) + Γ 3 (Γ M2 Γ M1 ) Γ 1 (Γ 2 (Γ M1 Γ M2 ) + Γ 3 (Γ M3 Γ M1 )) + Γ 2 Γ 3 (Γ M2 Γ M3 ) e1e1 = (Γ 1 Γ 2 ) (Γ 1 Γ 3 ) (Γ 2 Γ 3 ) (Γ M1 Γ M2 ) (Γ M1 Γ M3 ) (Γ M2 Γ M3 ) (Γ 1 (Γ 2 (Γ M1 Γ M2 ) + Γ 3 (Γ M3 Γ M1 )) + Γ 2 Γ 3 (Γ M2 Γ M3 )) S S 11

45 S S S S 11

46 ϵ 15 1 ϵ ϵ ϵ ϵ

47 ϵ ϵ ϵ

48 ϵ 7 ϵ

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