two methods for calculating broadband antenna … antenna radiation efficiency without using ......
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Two Methods for Calculating Broadband Antenna Radiation
Efficiency without Using Far-Field Monitors
Constantine Kakoyiannis a,b
a Institute of Communication & Computer Systems, National Technical University of Athens, Greece
b Institute of Informatics & Telecommunications, National Centre for Scientific Research “Demokritos”,
Athens, Greece
Introduction
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The importance of antenna efficiency
Fundamental attributes of compact antennas for mobile terrestrial and satellite communications Impedance bandwidth, BW Radiation efficiency,ηrad
Size (physical and electrical)
Antenna efficiency contributes decibel-for-decibel to… Overall system power efficiency Receiver noise figure Link budget
Example: Antennas for satellite systems Expected efficiency 97–98% Inefficiency subtracts no more than 0.1 dB from link budget
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E- and H-fields on PML boundary are transformed to the equivalent far-field quantities
Integration of normal component of Poynting’s vector, S = E×H*, over all (θ,φ) space Total radiated power (TRP) is obtained
Division by available, Pin, and accepted, Pacc, power… … gives the total, ηtotal, and radiation, ηrad, efficiency,
respectively Single-frequency (narrowband) approach based on the
total radiated power (TRP) Requires a multitude of far-field monitors to yield a
broadband result
Standard efficiency calculation
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Severe criticism from academia on commercial E/M software
E/M software is unable to accurately estimate the efficiency of low-loss antennas
Efficiency easily exceeds 100% and thus violates energy conservation A. Galehdar, D. V. Thiel, and S. G. O’Keefe, “Antenna efficiency calculations
for electrically small, RFID antennas,” IEEE Antennas Wireless Propag. Lett., vol. 6, pp. 156–159, 2007.
R. Maaskant, D. J. Bekers, M. J. Arts, W. A. van Cappellen, and M. V. Ivashina, “Evaluation of the radiation efficiency and the noise temperature of low-loss antennas,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 1166–1170, 2009.
A. Sutinjo, L. Belostotski, R. H. Johnston, and M. Okoniewski, “Efficiency measurement of connected arrays using the improved Wheeler cap method,” IEEE Trans. Antennas Propag., vol. 60, no. 11, pp. 5147–5156, Nov. 2012.
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Should we demonize the Poynting vector approach?
Previous claims certainly not totally unfounded, but… An antenna model properly configured in MWS will avoid
this pitfall Various degrees-of-freedom available as countermeasures
Average MWS user may lack the experience, time or computing power for this task
Far-field ηrad calculations provide only coarse frequency resolution, e.g., Δf = 0.2 GHz
The multiplicity of far-field monitors creates computational overhead
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Scope of the presentation
Two alternative methods for efficiency estimation Applicable to both T- and F-solvers
Broadband at practically zero computational overhead
Offer arbitrary frequency resolution
Methods rely solely on the core competence of EM solvers Calculation of the near field surrounding the antenna
Are indifferent towards material losses
First method enabled by MWS version 2013 Replaces far-field monitors by either E-/H-field or Powerflow monitors
Estimates efficiency via the total power dissipated on the antenna
Second method is completely monitorless ηrad estimated via the equivalent circuit at the input to the antenna
Requires each model to be solved twice, i.e., it is a differential method.
Total dissipated power (TDP) method
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Energy conservation applied to any single-port antenna
Kurokawa (1965): Power waves and scattering parameters
By substitution of Pout we obtain
TDP theory (1)
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TDP theory (2)
Definition of radiation efficiency
|S11| and Pin are readily available after simulation ends, therefore all that’s missing is the total dissipated power
MWS v2013: the calculation dielectric loss was automated like metal loss
Final result
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TDP theory (3)
Pℓ,d
Total dissipated power on dielectrics [Wrms]
Pℓ,m
Total dissipated power on lossy metals [Wrms]
Fraction denominator is power accepted by AUT
All three involved powers are calculated at the near-field of the antenna
Core competence of any E/M solver
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TDP implementation in STUDIO
Either E-/H-field monitors or Powerflow monitors must be added to the frequencies once occupied by far-field monitors
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Application of TDP method (1)
Antenna description
GSM 900 PIFA
f0 = 0.906 GHz
εr = 4.35, tanδ = 0.025 (FR-4)
Conductors: Annealed Cu
T-Solver, DC–1.8 GHz
Distance to PML boundary was λ0/4
Variable substrate loss 10−4 ≤ tanδe ≤ 1
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Application of TDP method (2)
Efficiency result at f0 as a function of the angular resolution of the far-field pattern
Log sampling of tanδe at 10 samples/decade (37 values)
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Application of TDP method (3)
Same result, zoomed-in on the loss tangent range 10−4 ≤ tanδ ≤ 10−1
Both TDP and Poynting methods proved insensitive to PML distance
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Application of TDP method (4)
Selected subset of eight values of tanδe
10% ≤ ηrad ≤ 100% (10% is tremendous loss for a PIFA!)
Poynting and TDP results are highly correlated
Poynting (Δφ = Δθ = 4) TDP
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Limitations of TDP method
Currently not applicable to anisotropic magnetic materials
Gyromagnetic materials described by Polder’s 3×3 tensor (gyrotropic model)
Calculation of dissipated power considers only diagonal elements of tensor
Omission of off-diagonal elements produces dissipated power on ferrite greater than stimulated one
Negative efficiency results
CST development team will provide a fix
Quality factor method (QFM)
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QFM theory (1)
Origins of QFM
E. H. Newman, P. Bohley, and C. H. Walter, “Two methods for the measurement of antenna efficiency,” IEEE Trans. Antennas Propag., vol. AP-23, no. 4, pp. 457–461, Jul. 1975.
G. S. Smith, “An analysis of the Wheeler method for measuring the radiating efficiency of antennas,” IEEE Trans. Antennas Propag., vol. 25, no. 4, pp. 552–556, Jul. 1977.
QFM was proposed as an alternative to H. A. Wheeler’s method for experimental characterization of antenna efficiency (a.k.a. the “Wheeler cap”)
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Comparison of free-space Q-factors of the actual and corresponding ideal (lossless) AUT
W: time-average stored energy, Pr: radiated power, Pℓ: dissipated power
Assumption: the addition of losses to the ideal AUT is a small perturbation
QFM theory (2)
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QFM theory (3)
QFM is an indirect method of ηrad characterization Does not involve energy or power calculations
Relies solely on frequency response of the equivalent circuit at the input to the antenna
Experimental verification of QFM is practically impossible Requires operation of AUT at or below the critical
superconductivity temperatures of all materials
Virtual implementation of QFM in an E/M simulation environment is trivial Turn all conductive parts to PEC
Set all dielectric and magnetic loss tangents to zero
Antenna response maintains causality
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Q-Factor calculations (1)
Various ways to estimate Q exist Method applied herein relies on Zin = Rin + jXin
Approximate, yet efficiently accurate, formula for computing antenna Q A. D. Yaghjian and S. R. Best, “Impedance, bandwidth, and Q of
antennas,” IEEE Trans. Antennas Propag., vol. 53, no. 4, pp. 1298– 1324, Apr. 2005.
H. R. Stuart, S. R. Best, and A. D. Yaghjian, “Limitations in relating quality factor to bandwidth in a double resonance small antenna,” IEEE Antennas Wireless Propag. Lett., vol. 6, pp. 460–463, 2007.
Method holds regardless of matching and tuning status of the antenna
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Q-Factor calculations (2)
Formula based on AUT resistance & reactance and frequency derivatives thereof
Provides an inherently wideband calculation of Q
…where the magnitude of dZ/dω is given by:
If Zin is readily computable, then the result is so accurate
that it makes evaluation of exact Q unnecessary Limitation: formula does not work well when AUT
exhibits multiple closely-spaced resonances
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QFM validation in TD & FD (1)
Actual AUT, tanδe = 0.1
Lossless AUT, tanδe = 0
Freq. band 0.6–1.3 GHz (74%)
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QFM validation in TD & FD (2)
QFM estimations of ηrad in TD and FD correlate very well
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QFM vs Poynting & TDP (1)
tanδe = 0.0003
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QFM vs Poynting & TDP (2)
tanδe = 0.05
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QFM vs Poynting & TDP (3)
tanδe = 0.1
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QFM vs Poynting & TDP (4)
tanδe = 0.2
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QFM vs Poynting & TDP (5)
tanδe = 0.3
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QFM vs Poynting & TDP (6)
tanδe = 0.5
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QFM vs Poynting & TDP (7)
tanδe = 0.7
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QFM vs Poynting & TDP (8)
tanδe = 1.0
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Conclusions of head-to-head comparison
tanδe < 0.1 QFM results match those of
the other 2 methods
0.1 ≤ tanδe ≤ 0.7 QFM predicts lower
efficiency by max. 5 p.p.
tanδe > 0.7 QFM predicts a slightly
greater result
When tanδe > 0.1, the “small perturbation” hypothesis breaks down
Broadband efficiency of the GSM900 PIFA for increasing material loss calculated by application of QFM
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Limitations of QFM method
Ferrites, again! But, for a totally different reason
Making a ferrite lossless can be very tricky
Zero loss means zero Landau-Lifschitz damping factor, α Zero linewidth, ΔΗ = 0
Ferromagnetic resonance becomes infinitely narrow
Simulation misbehaves
Magnetic materials described by generalized dispersion models? (instead of gyrotropic) Lossless antenna response exhibits false resonances
Artifact of zero loss; reflects on Q; not E/M solver–related
Some more examples
1. Linear tapered slot antenna (LTSA)
2. Antipodal Vivaldi antenna
3. Balanced antipodal Vivaldi antenna (BAVA)
4. Wideband, closely-spaced, quasi-Yagi antenna
5. Horn antenna
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Linear TSA (1)
PCB size 630 mm × 300 mm
Flare length/height 450 mm × 236 mm
Copper and Isola IS400 (h = 1.51 mm) εr = 3.9, tanδ = 0.022 @ 0.5 GHz
0.6–4.0 GHz, mesh λmin/14
PML distance = λ/8 @ 0.7 GHz
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Linear TSA (2)
tanδe = 0.0220
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Linear TSA (3)
tanδe = 0.0001
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Antipodal Vivaldi (1)
PCB size 169 mm × 222 mm
Copper and Isola IS400 εr = 3.9, tanδ = 0.022 @ 0.5 GHz
h = 1.51 mm
0.5–4.0 GHz, mesh λmin/12
PML distance = λ/8 @ 0.7 GHz
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Antipodal Vivaldi (2)
tanδe = 0.0220
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Antipodal Vivaldi (3)
tanδe = 0.0001
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Balanced antipodal Vivaldi (1)
J. Bourqui et al., “Balanced antipodal Vivaldi antenna with dielectric director for near-field microwave imaging,” IEEE TAP, Jul. 2010
PCB size 74 mm × 44 mm × 9 mm
Copper and Rogers RT6002 (4 layers) εr = 2.94, tanδ = 0.0012 @ 10 GHz
1–8 GHz, mesh λmin/16
PML distance = λ/8 @ 2 GHz
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Balanced antipodal Vivaldi (2)
tanδe = 0.0012 0.0001
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Wideband closely-spaced Yagi (1)
PCB size 49.7 mm × 48 mm
Antenna size 43.7 mm × 42 mm
Copper and Isola IS400 (h = 1.51 mm) εr = 3.9, tanδ = 0.022 @ 0.5 GHz
DC–4.0 GHz, mesh λmin/20
PML distance = λ/8 @ 2 GHz
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Wideband closely-spaced Yagi (2)
tanδe = 0.0220
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Wideband closely-spaced Yagi (3)
tanδe = 0.0001
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Horn antenna (1)
Macros > Construct > Demo Examples > Horn Antenna (Aluminum, σ = 35.6 MS/m)
WG width/height 20 mm × 10 mm fco = 7.49 GHz
Horn length 30 mm, taper angle 30
7.5–10 GHz, mesh λmin/20
PML dist. = λ/4 @ 7.5 GHz + 45 mm in front
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Horn antenna (2)
Poynting, Δφ = Δθ = 4
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Horn antenna (3)
TDP
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Horn antenna (4)
Poynting (4) vs TDP, variable aluminum conductivity
Conclusion
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Conclusion (1)
Efficiency calculation via Poynting vector Solid mathematical foundation; tried-and-tested
Relies on accurate estimation of TRP @ far-field
Can cause problems when material losses are low
Two alternative methods were described Applicable to T- and F-solvers (what about I-solver?)
Broadband w. arb. freq. resolution, zero overhead
Rely on the estimation of near-field quantities in and around the antenna, i.e.,
Exploit the basic strength of E/M solvers
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Conclusion (2)
Method #1: TDP Enabled by MWS v2013
Replaces far-field monitors by either E-/H-field monitors or Powerflow monitors
Relies on accurate estimation of TDP on coductors and dielectrics @ near-field complementary to Poynting vector
Method #2: QFM Completely monitor-less
Relies solely on properties of equivalent circuit @ AUT input
Requires each model to be solved twice (actual/ideally lossless)
Poynting, TDP and QFM form a set of three independent methods for the numerical estimation of efficiency
Thank you.
Questions, please!
Inquiries, doubts, objections, crazy ideas?