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Wave Analysis of Open-ended Coaxial Time Domain Reflectometry Probes

Wave Analysis of Open-ended Coaxial Time Domain Reflectometry Probes. Hiruy Abdu. Dept. of Plants, Soils and Biometeorology Utah State University; Logan, Utah, USA FOC at USU day, April 19, 2005. Introduction.

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Wave Analysis of Open-ended Coaxial Time Domain Reflectometry Probes

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  1. Wave Analysis of Open-ended Coaxial Time Domain Reflectometry Probes Hiruy Abdu Dept. of Plants, Soils and Biometeorology Utah State University; Logan, Utah, USA FOC at USU day, April 19, 2005

  2. Introduction • Time Domain Reflectometry (TDR) provides permittivity and electrical conductivity measurements based on travel-time analysis and signal attenuation and frequency analysis. • The large contrast between the permittivities (eb) of water and those of soil constituents typically provide excellent water content measurement accuracy.

  3. Permittivity of Porous Media • Soils composed ofsolid particles, (relative perm.,εr= 4-10) gaseous phase (εr = 1) liquid water phase (εr = 80) Thus permittivity of soil strongly influenced by its water content

  4. Δz z z + Δz Transmission Line Equations lΔz Using Kirchhoff’s Laws I(z + Δz,t) I(z,t) + + cΔZ --- V(z,t) V(z + Δz,t) ---- _ _

  5. Transmission Line Equations (cont) • General Solution for a line connecting a source to a load Where the characteristic impedance is And the velocity of propagation is

  6. rw ε, μ0 rs Per-unit-length parameters for a coax • for a homogeneous medium

  7. TDR Wave Analysis • Travel-time-based Permittivity Measurement • Frequency Domain • DFFT of Scatter Function

  8. Travel-time-based Permittivity Measurement Permittivity

  9. Extending the Permittivity Measurement Range in Lossy Porous Media • Travel time analysis limitations • Standard probes > 10 cm • ECw < 6 dS m-1 • Permittivity information lost in the time domain due to signal attenuation may be extracted in the frequency domain. • The key for implementation of such an approach is the use of very short probes, unsuitable for standard travel time analysis, coupled with waveform transformation.

  10. Waveform Transformation • The discrete fast Fourier transform (DFFT) of the system response and input signal yield their equivalent in the frequency domain. DFFT Time Domain Frequency Domain

  11. Scatter (s) parameters

  12. Experimental Setup • coaxial probes • εr values of 1, 21.5, 40, 62, 70, 80 • Tektronix 1502B TDR and WINTDR 6.1 software • HP 8752C Network Analyzer • TDRConverter for Analysis

  13. r1=1 mm r2=5.5 mm r3=7.5 mm r1 ε1 ε2 r2 r3 Open-ended Coaxial TDR Probe Volume measured ~ 500mm3 • Advantages over wire Probe • Close to ideal transmission line • Adaptable for mobile platforms

  14. TDR Converter (15 cm probe) In air In water

  15. S11 function

  16. 2 cm Coaxial Probe

  17. Open-ended Coaxial Probe

  18. Open-ended Coaxial Probe (cont)

  19. Noisy S11 Wave

  20. Summary Slide • Time Domain Reflectometry (TDR) provides permittivity and electrical conductivity measurements based on travel-time analysis and frequency analysis. • Frequency analysis useful in recovering information lost due to high EC or short length probes. • Problems analyzing signals from flat probes • Geometry? • Signal conditioning?

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