Magdalena Salazar-Palma - Modern Characterization of Electromagnetic Systems and its Associated Metrology

7 Chapter 9Table 9.1 The Norm of the Mean Squared Error between the Free Space Results a...

8 Chapter 10Table 10.1 Reconstruction error for the helical antenna in the angular domain...Table 10.2 Reconstruction error for the Yagi antenna in the angular domain at...

1 Chapter 1 Figure 1.1 Discretization of the letter X on a 20×20 grid. Figure 1.2 Rank‐1 approximation of the image X. Figure 1.3 Rank‐2 approximation of the image X. Figure 1.4 Rank‐3 approximation of the image X. Figure 1.5 Rank‐4 approximation of the image X. Figure 1.6 Rank‐5 approximation of the image X. Figure 1.7 Rank‐6 approximation of the image X. Figure 1.8 Rank‐7 approximation of the image X. Figure 1.9 Rank‐8 approximation of the image X. Figure 1.10 Mean squared error of the approximation.

2 Chapter 2 Figure 2.1 Normalized singular values from the SVD of matrix [ Y ]. Figure 2.2 Comparison between the original data and the estimated data by ap... Figure 2.3 Comparison between the original data and the data with added whit... Figure 2.4(a) Normalized singular values from the SVD of matrix [ Y ]. Figure 2.4(b) Comparison between the original data, the data with additive n... Figure 2.5 Z 0as a function of h / λ 0using various definitions for the ... Figure 2.6 De‐embedding of a device under test. Figure 2.7 Plot of the propagation constant β for the incident and refl... Figure 2.8 Characterization of a 90 ∘radial stub with x = 0 starting f... Figure 2.9 Mode decomposition shown in equation (2.28) of the current in the... Figure 2.10 Geometry of a right angled bend. Figure 2.11 Mode decomposition shown of the current in the microstrip feed l... Figure 2.12 Geometry of a mitered bend. Figure 2.13 Multiple reflections from the Beatty standard terminated with a ... Figure 2.14 Calculated Impulse Response from (2.13) using MPM for the Beatty... Figure 2.15 The Magnitude and the Phase Response of the Beatty Standard from... Figure 2.16 Time Domain Impulse Response using the standard built‐in bandpas... Figure 2.17 The Magnitude and Phase response of the Beatty standard measured... Figure 2.18 Time Domain Impulse Response using the standard built‐in band‐pa... Figure 2.19 Time Domain Impulse response obtained using the MPM with 2 GHz b... Figure 2.20 The magnitude and the Phase response of the Beatty standard from... Figure 2.21 Time domain impulse response of the shorted Beatty standard usin... Figure 2.22 Time Domain impulse Response obtained using the Matrix Pencil me... Figure 2.23 Time Domain Response for the Fourier Technique Based method as a... Figure 2.24 Multiple reflections from the Beatty standard terminated with a ... Figure 2.25 Calculated Impulse Response of the Beatty Standard terminated wi... Figure 2.26 The Magnitude and the Phase Response of the Beatty Standard term... Figure 2.27 Time‐domain impulse response using the internal built‐in band‐pa... Figure 2.28 The magnitude and phase response of the shorted Beatty standard ... Figure 2.29 Time‐domain impulse response of the shorted Beatty standard. usi... Figure 2.30 Time‐domain impulse response of shorted Beatty standard obtained... Figure 2.31 Time‐domain impulse response of shorted Beatty standard obtained... Figure 2.32 An anechoic chamber in ANTEM‐LAB, with the AUT on a rollover azi... Figure 2.33 An anechoic chamber in ANTEM‐LAB, with the probe on a polarizati... Figure 2.34 A top view of the antenna‐measurement scheme in (a). The copper ... Figure 2.35(a) The steps followed in the FFT‐Based Method: S 21( f , φ ), t... Figure 2.35(b) The steps followed in the FFT‐Based Method: S 21( f , φ ) m... Figure 2.35(c) The steps followed in the FFT‐Based Method: S 21( t , φ ), ... Figure 2.35(d) The steps followed in the FFT‐Based Method: S 21( t , φ ), ... Figure 2.36 Example 1, d = 2.05 m: The radiation pattern measured in reverbe... Figure 2.37 Example 1, d = 2.05 m: A comparison between the processed result... Figure 2.38 Bandwidth required by the MPM to carry out the processing is dis... Figure 2.39 Example 1, d = 2.05 m: A comparison between the processed result... Figure 2.40 Example 2, d = 1 m: The radiation pattern measured in reverberan... Figure 2.41 Example 2, d = 1 m: The time response as a function of azimuth a... Figure 2.42 Example 2, d = 1 m: A comparison between the processed result us... Figure 2.43 Bandwidth required by the MPM to carry out the processing is dis... Figure 2.44 Example 2, d = 1 m: A comparison between the processed result us... Figure 2.45 The variance ‐ 10log 10(var( ϕ 1)), 3‐D MP and the CRB are plo... Figure 2.46 The variance ‐ 10log 10(var( θ 1)), 3‐D MP and the CRB are plo... Figure 2.47 The variance ‐ 10log 10(var( λ 1)), 3‐D MP and the CRB are plo... Figure 2.48 The scatter plots of elevation and azimuth angles for (a) SNR = ...Figure 2.49 Histogram of azimuth angle for (a) SNR = 5, (b) 10, (c) 15, and ...Figure 2.50 Histogram of elevation angle for (a) SNR = 5, (b) 10, (c) 15, an...Figure 2.51 Histogram of wavelength for (a) SNR = 5, (b) 10, (c) 15, and (d)...Figure 2.52 Path for typical Sommerfeld integration.Figure 2.53 Functional samples of the tails of the Sommerfeld integral used ...Figure 2.54 Normalized errors for the tail integration, to1 = 10 −14.Figure 2.55 Comparison of CPU times for the two methods, to1 = 10 −14....Figure 2.56 Number of functional evaluations for the two methods, to1 = 10 −1...Figure 2.57 Normalized errors for the tail integration, to1 = 10 −12.Figure 2.58 Normalized errors for the tail integration, to1 = 10 −10.Figure 2.59 (a) Two sphere model. (b) One wire and one cone model.Figure 2.60 Pole Library vs. Computed poles of the unknown objects (two PEC ...Figure 2.61 Pole Library vs. Computed poles of the unknown objects (one PEC ...

3 Chapter 3Figure 3.1 Normalized singular values obtained from the SVD of matrix [ C ].Figure 3.2 Comparison between the original data and the estimated data from ...Figure 3.3 Normalized singular values from the SVD of matrix [ C ].Figure 3.4 Comparison between the original data and the estimated data from ...Figure 3.5 Comparison between the original data and the data added with whit...Figure 3.6 Normalized singular values from the SVD of matrix [ C ].Figure 3.7 Comparison between the original data and the estimated data from ...Figure 3.8 RCS of a sphere as a function of its radius and generated over a ...Figure 3.9 Scattering efficiency as a function of size parameter. (a) Input ...Figure 3.10 Generation of stopband response using passband data. (a) Reconst...Figure 3.11 Generation of passband response using stopband data. (a) Reconst...Figure 3.12 Broadband device characterization. Solid lines, extrapolation us...Figure 3.13 Comparison of theoretical PDF and numerically simulated PDF’s. S...Figure 3.14 Comparison of theoretical PDF and numerically simulated PDFs. SN...Figure 3.15 A Conducting Cube with a Square Hole.Figure 3.16 Radiated far‐field Power density of the PEC Box due to an incide...Figure 3.17 Comparison of Original and Interpolated Data (Down sample Rate =...Figure 3.18 Error Percentage Rate over the entire band (Down sample Rate = 1...Figure 3.19 Comparison of the Original and Interpolated Data (Down sample Ra...Figure 3.20 Error Percentage Rate (Down sample Rate = 20).Figure 3.21 Comparison of Original and Interpolated Data (Down sample Rate =...Figure 3.22 Error Percentage Rate (Down sample Rate = 30).Figure 3.23 Comparison of Original and Interpolated Data Around the First Nu...Figure 3.24 Comparison of Original and Interpolated Data Around the First Nu...Figure 3.25 A Horn Antenna.Figure 3.26 An input Gaussian Pulse.Figure 3.27 Power Spectrum Density of Horn Antenna.Figure 3.28 Actual, Reconstructed and Difference of Phase Functions.Figure 3.29 Time Domain Responses.Figure 3.30 Sifted Time Domain Responses.Figure 3.31 A Microstrip Patch Antenna.Figure 3.32 Power Spectrum Density of the Microstrip Patch Antenna.Figure 3.33 Actual, Reconstructed and Difference of Phase Functions.Figure 3.34 Aligned Time Domain Response from the Patch Antenna.Figure 3.35 Phase of the scattered fields from a Conducting Cubic Box with a...Figure 3.36 Time Domain Response from the Conducting Box with a hole.Figure 3.37 Flowchart of the proposed interpolation algorithm for adaptive i...Figure 3.38 The initial interpolation result for the patch antenna.Figure 3.39 The second interpolation result for the patch antenna, the inter...Figure 3.40 The error of the second interpolation result for the patch anten...Figure 3.41 The initial interpolation result for the hollow PEC box while th...Figure 3.42 The second interpolation result of the hollow box while the base...Figure 3.43 The third interpolation result of the hollow box from updated sa...Figure 3.44 The fourth interpolation result for the hollow PEC box with two ...Figure 3.45 The error of the final interpolation result for the hollow PEC b...Figure 3.46 A SDPA array with 11 elements.Figure 3.47 Far‐field radiation pattern of the SDPA array.Figure 3.48 The initial interpolation result of the SDPA array with base sam...Figure 3.49 The second interpolation result of the SDPA array with base samp...Figure 3.50 The third and final interpolation result of the SDPA array with ...Figure 3.51 The error of the last interpolation result for the SDPA array sh...Figure 3.52 Waveguide filter. Model of S 11and S 22with common denominator....Figure 3.53 Microstrip filter, the numerical based MoM model generating the ...Figure 3.54 Microstrip filter, result from the MoM model and its wide‐band r...Figure 3.55 (a) HOBBIES simulation model for the 0.15‐m‐diameter PEC sphere....Figure 3.56 Natural poles of the 0.15‐m‐diameter PEC sphere from the SEM and...Figure 3.57 (a) HOBBIES simulation model for the PEC wire with 0.1 m length ...Figure 3.58 (a) HOBBIES simulation model for the PEC disk with 0.1 m diamete...Figure 3.59 (a) HOBBIES simulation model for the PEC ellipsoid with 0.02 m d...Figure 3.60 (a) HOBBIES simulation model for the PEC sphere with 0.1 m diame...Figure 3.61 (a) HOBBIES simulation model for the PEC cone with 0.1 m diamete...