two methods for calculating broadband antenna … antenna radiation efficiency without using ......

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

29/04/2015 CST EUC 2015: Broadband Antenna Efficiency w/o Far-Field Monitors 3

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


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


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.


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


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


Energy conservation applied to any single-port antenna

Kurokawa (1965): Power waves and scattering parameters

By substitution of Pout we obtain

TDP theory (1)


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


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


TDP implementation in STUDIO

Either E-/H-field monitors or Powerflow monitors must be added to the frequencies once occupied by far-field monitors


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



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)



Same result, zoomed-in on the loss tangent range 10−4 ≤ tanδ ≤ 10−1

Both TDP and Poynting methods proved insensitive to PML distance



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


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)


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”)


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)


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


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


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


QFM validation in TD & FD (1)

Actual AUT, tanδe = 0.1

Lossless AUT, tanδe = 0

Freq. band 0.6–1.3 GHz (74%)


QFM validation in TD & FD (2)

QFM estimations of ηrad in TD and FD correlate very well


QFM vs Poynting & TDP (1)

tanδe = 0.0003



tanδe = 0.05



tanδe = 0.1



tanδe = 0.2



tanδe = 0.3



tanδe = 0.5



tanδe = 0.7



tanδe = 1.0


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


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


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


Linear TSA (2)

tanδe = 0.0220


Linear TSA (3)

tanδe = 0.0001


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



tanδe = 0.0220



tanδe = 0.0001


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


Balanced antipodal Vivaldi (2)

tanδe = 0.0012 0.0001


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



tanδe = 0.0220



tanδe = 0.0001


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


Horn antenna (2)

Poynting, Δφ = Δθ = 4


Horn antenna (3)

TDP


Horn antenna (4)

Poynting (4) vs TDP, variable aluminum conductivity

Conclusion


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


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?

[email protected]

[email protected]

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