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Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Lecture #6 Engineering Approach for Analytical.

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Presentation on theme: "Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Lecture #6 Engineering Approach for Analytical."— Presentation transcript:

1 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Lecture #6 Engineering Approach for Analytical Electromagnetic Modelling of THz Metal Structures The main objective of this lecture is to teach a useful tool for enabling a student to derive analytical expressions for a number of electromagnetic problems relating to THz metal structures. The traditional approach when using the classical relaxation-effect model can be mathematically cumbersome and not insightful. This lecture briefly introduces various interrelated electrical engineering concepts as tools for characterizing the intrinsic frequency dispersive nature of normal metals at room temperature. This Engineering Approach dramatically simplifies the otherwise complex analysis and allows for a much deeper insight to be gained into the classical relaxation- effect model. Problems with worked-though solutions will be given in class.

2 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 OVERVIEW  Drude’s frequency dispersion model  The Engineering Approach  Equivalent transmission line model  Q-factor for metals  Kinetic inductance  Complex skin depth  Boundary resistance coefficient  Applications  Metal-pipe rectangular waveguides  Cavity resonators  Single metal planar shield  Conclusions

3 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Classical relaxation-effect frequency dispersion model: Drude’s Model

4 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Compare vector Helmholtz equations (for an unbounded plane wave in one-dimensional space) with those of the telegrapher's equations. Electromagnetic Characterisation of Homogenous Materials #1 Line Modelling

5 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Generic Equivalent Transmission Line Model

6 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Generic equations: Intrinsic Modelling for Normal Metals at Room Temperature

7 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Classical skin-effect model:

8 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Classical relaxation-effect model:

9 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Classical relaxation-effect models:

10 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Distributed-element parameters for the classical relaxation-effect model Distributive shunt inductance

11 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Propagation Delay Per Unit Wavelength

12 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Circuit-based Simulation Results for Gold at Room Temperature Equivalent Transmission Line model Elementary Lumped-element Circuit Values Z IN [  ] (Theory: j1.1124)  pR [fs/ R ] (Theory: 170:494) R R  z [  ] L R  z [fH] G R  z [mS] C R  z [fF] L SHUNT_R  z [pH] Z T = Z SR Extracted model   j Alternative Extracted model   j with  = 1, depth l = R,  z = R / 400 = [nm]

13 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 and Kinetic inductance is created from the inertial mass of a mobile charge carrier distribution within an alternating electric field (i.e. classical electrodynamics). #2 Kinetic Inductance

14 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Gold at room temperature Intrinsic classical skin-effect model overestimates ohmic losses and Detuning. Also, underestimates extrinsic losses.

15 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Gold at room temperature Intrinsic classical skin-effect model underestimates perturbation detuning

16 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授

17 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Material Q-Factor #3 Q-factor

18 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Component Q-Factor Classical relaxation-effect model: and

19 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Gold at room temperature

20 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Complex Skin Depth: #4 Complex Skin Depth

21 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Classical relaxation-effect model:

22 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Gold at room temperature

23 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Boundary resistance coefficient: Surface dissipative power density per unit area: Po = Power flux density per unit area in air Forward E-field and average power tilt angle: For a cube in any mode (with perturbation theory only): #5 Resistance Coefficient

24 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Elementary Lumped-element Circuit Line Model Validation

25 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 When the terminating impedance is equal to the complex conjugate of the characteristic impedance of the transmission line:

26 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Gold at room temperature

27 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Parameters for l = R,  = 1, Z T = Z* SR Theory Synthesized Transmission Line ABCD Parameter Matrix Calculations Microwave Office® No. of Sections, N Z SR [  ] j j j  R R [ R -1 ] j j j S j j j j Return Loss [dB] S 11 = e -2  (1+  2)  [1+j(1+  2)]  j j j j j6.239 G MAX [dB] Absorption Loss [dB]  S 11 = tan -1 (1+  2)[ o ] Comparison of modelled parameters for gold at room temperature, at THz, determined from theory, direct ABCD parameter matrix calculations and synthesized equivalent transmission line models using commercial circuit simulation software

28 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 d x y z b a and THz MPRWGs

29 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 New Waveguide Standard for Terahertz Frequencies No extension of industry standards above 325 GHz (WR-3) No compatibility among hardware Impractical transitions Defined in inches, rounding errors Why New Standard ? 5 THz horns and coupler (C. Walker U. Arizona) 1.5 THz Frequency Multiplier Chain (JPL) John Ward, JPL 2006

30 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Widely used global industry standard Logarithmic scale Infinitely extendable Repeats every decade Decision tree with range of coarse and fine spacing New Waveguide Standard for Terahertz Frequencies: ISO 497 Preferred Metric Sizes

31 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Proposed air-filled MPRWG and cavity resonator definitions and specifications

32 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Variational Methods for Calculating Propagation Constant for the TE mo Mode

33 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Calculated attenuation constants for the dominant TE 10 mode

34 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Resulting errors in attenuation constant calculations Classical skin-effect: 108% error at 12 THz Simple relaxation-effect: 373% at 12 THz Power Loss Method (for simplicity)

35 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 with for Classical skin-effect: 108% error at 12 THz e.g. Calculated error using this approximation is 110% at 12 THz Errors in attenuation constant

36 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 HFSSTM electromagnetic simulations of attenuation constant for JPL 100  m band

37 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 With Perturbation model, unloaded Q-factor in the mnl mode : Geometric factor : where For all modes! THz Cavity Resonators

38 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授

39 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Complex Resonant Frequency As determined by Eigenmode solution in HFSS TM Overall frequency detuning takes into account both perturbation (represented by Xs) and detuning due to Ohmic losses (represented by Rs) Due to

40 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Over-simplified Solution (O. Klein et al.,1993, and M. Dressel & G. Gruner, 2002) Simplified Solution (J. C. Salter, 1946) whereis due to perturbation

41 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Exact Solution Self-consistent analytical solution for all dispersion models Self-consistent analytical solution With and Usinginstead of Change in Surface Impedance: Cavity Perturbation Formula

42 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Derivation of Driven Frequency of Oscillation After equalizing equations for surface reactance:

43 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Self-consistent Solution for General Case of Metal

44 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Gold at room temperature

45 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Gold at room temperature

46 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授

47 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Errors in Unloaded Q-factor Classical skin-effect: 41% error at 7.3 THz e.g. Calculated error using this approximation is 40% at 7.3 THz

48 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 HFSS TM current versions (v.10 & 11) cannot accurately predict the performance of structures operating at terahertz frequencies Intrinsic dispersion models: Classical skin-effect & simple relaxation-effect inflate the attenuation. Therefore, extrinsic loss effects (e.g. surface roughness) may be underestimated

49 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 RF metal shielding is found in many applications; ranging from: Construction of high isolation subsystem partitioning walls Efficient quasi-optical components (e.g. planar mirrors and parabolic reflectors for open resonators and antennas) Creating guided-wave structures that have (near-)zero field leakage (e.g. metal-pipe rectangular waveguides and associated closed cavity resonators) Embedding ground planes within compact 3D multi-layer architectures. THz Metal Shielding

50 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授  Metal shields should be made as thin as possible, while meeting the minimum values for figures of merit within the intended bandwidth of operation, in order to reduce weight and cost.  For reasons of structural integrity, thin metal shielding can be deposited onto either a solid plastic/ceramic or even honeycomb supporting wall.  Thin metal shielding embedded between dielectric layers (e.g. to create conformal ground planes or partition walls) can avoid issues of poor topography when integrating signal lines within 3D multi-layered architectures.  Shielding effectiveness, return loss and absorptance (or absorptivity) are important figures of merit that are quoted to quantify the ability to shield electromagnetic radiation.  An electrical engineering approach, which can include network analysis and the synthesis of predictive equivalent transmission line models, can accurately solve specific EM problems.

51 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Uniform plane wave at normal incidence to an infinite single planar shield in air Physical representationEquivalent 2-port network model Voltage transmission coefficients: Voltage-wave reflection coefficients:

52 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Transient response solution Steady-state solution S-Parameters Analysis for Single Planar Shield

53 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Boundary resistance coefficient and Therefore, e.g. S-Parameters Analysis for Single Planar Shield a = thickness normalized to normal skin depth

54 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Approximation error : < 0.4% up to a R = 10, frequency less than 12 THz S-Parameters Analysis: Classical Relaxation-effect Model

55 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 S-Parameters Analysis: Classical Skin-effect Model Approximation error : < 0.6% up to a R = 10, frequency less than 12 THz

56 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Analysis of Shielding Effectiveness (SE) Cross-boundary reflections Absorption Multiple reflections

57 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Correction Factor for Multiple Reflections Calculations Classical-relaxation Model Error using Approximation

58 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Screening Effectiveness Calculations Classical Relaxation-effect Model Classical Skin-effect Model Less shielding as frequency increases and/or thickness decrease

59 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Due to absorption, a peak value ). Beyond the peak region Linearly increase, 11.7% at T = l m = 1.6  SR Screening Effectiveness Calculations-Error using Approximation 7.8% at a R = 10

60 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Reflection Characteristics: Return Loss Calculations Less reflected power as frequency increases and/or thickness decrease

61 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Reflection Characteristics: Return Loss Calculations Error using Classical Skin-effect 109% at T = 10  SR Thickness invariant above

62 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Absorptance Calculations More absorbed power as frequency increases and/or thickness decrease

63 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Absorptance Calculations: Error using Classical Skin-effect 14% at T = 10  SR Thickness invariant above

64 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Synthesis Modelling of Metal Shielding Walls Classical Relaxation-effect Model: Equivalent transmission line model For example, at THz, gold at room temperature

65 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Comparison of modelled parameters for gold at room temperature, at THz, determined from theory, direct ABCD parameter matrix calculations and synthesized equivalent transmission line models using commercial circuit simulation software

66 Radio Frequency Engineering Lecture #6 Engineering Approach Stepan Lucyszyn ステファン・ルシズィン インペリアル・カレッジ・ロンドン准教授 Conclusions An electrical engineering approach to the modelling of specific electromagnetic problems at THz frequencies is introduced, using 5 interrelated concepts (transmission line modelling, kinetic inductance, Q-factor, complex skin depth and boundary resistance coefficient). The Engineering Approach has 5 main advantages: –Excellent pedagogical tool –Greatly reduces otherwise lengthy mathematical derivations –Reduces risk of introducing mistakes –Avoids the need for poor approximations –Can replace the need for slow numerical computations (with simple structures) –Gives new perspectives and deeper insight While the focus has been on the characterization of normal metals (magnetic and non- magnetic) at room temperature, it is believed that the same methodology may also be applied to metals operating in anomalous frequency-temperature regions, superconductors, semiconductors, carbon nanotubes and metamaterials.


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