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1

Mixed-Mode Sensitivity Analysis of a CombinedDifferential and Common Mode Active Receiving

Antenna Providing Near-HemisphericalField-of-View Coverage

D. S. Prinsloo Student Member, IEEE, R. Maaskant Senior Member, IEEE, M. V. Ivashina Senior Member, IEEE,and P. Meyer Member, IEEE

Abstract—A theoretical framework for a mixed differential andcommon mode sensitivity analysis of active receiving antennas ispresented, which includes the derivation of a novel set of noiseparameters for dual-mode balanced amplifiers. The analysis isapplied to an example of a mixed-mode active wire antennadesign, consisting of an integrated monopole and dipole structure.Results of numerical simulations and experimental measurementsare presented which show that, for a single-polarized design, thejudicious use of both differential and common modes enables thefield-of-view coverage to be extended over the entire hemispherewith a variation in receiving sensitivity of less than 3dB in theE-plane.

Index Terms—Receiving antennas, sensitivity, active antennas,differential amplifiers, microwave circuits.

I. INTRODUCTION

THE vast majority of present-day receiving antennas arebalanced in nature and therefore require baluns for use

with Single-Ended (SE) Low-Noise Amplifiers (LNAs). TheCommon Mode (CM) component of the signal in such a sys-tem is then rejected by the antenna+balun and/or differentialLNA, so that it suffices to optimize the antenna DifferentialMode (DM) radiation and impedance characteristics only.However, baluns compromise compactness and increase ohmiclosses, thereby reducing the antenna signal-to-noise ratio [1],[2].

Direct differential feeding obviates the use of baluns andrepresents a potential low-loss, low-cost antenna topologywhich allows for high integration with differential front-endelectronics. Differential low-noise amplifiers (dLNAs) havetherefore become increasingly popular amongst the microwavecommunity during the last years [3]–[5]. However, the absenceof baluns removes the suppression of CM signals in thesystem, and therefore an accurate analysis and design of theseactive antennas require proper handling of both common and

Manuscript received September 03, 2013.This work is based upon research supported by the South African Research

Chairs Initiative of the Department of Science and Technology and theNational Research Foundation, as well as the Swedish VR and VINNOVAfunding agencies.

D. S. Prinsloo and P. Meyer are with the Department of Electrical andElectronic Engineering at the University of Stellenbosch, Stellenbosch, SouthAfrica (e-mail: 16238087@sun.ac.za, pmeyer@sun.ac.za).

R. Maaskant and M. V. Ivashina are with the Signals and Systems De-partment at Chalmers University of Technology, Gothenburg, Sweden (email:rob.maaskant@chalmers.se, marianna.ivashina@chalmers.se).

differential modes of the antenna. Furthermore, an understand-ing of how these modes propagate through the entire receiversystem is crucial; for instance, it has been observed that CMsignals can have a detrimental effect on the DM antennaperformance when these undesired CM signals are excited atcertain frequencies [6]–[9].

In this paper, we propose a novel dual-mode antenna designintrinsically supporting both the DM and CM signals, therebycreating an additional beamformer degree-of-freedom for im-proving the antenna impedance and radiation characteristics.The dual-mode antenna is based on a dipole combined witha parasitic monopole antenna to effectively exploit – ratherthan reject – the CM response. It should be noted thatthe associated common and differential mode patterns aredissimilar to the difference and sum patterns in monopulseradar tracking systems, where one typically employs a pair ofidentical antennas [10]. In wireless communication systems,the combination of a dipole and monopole into a singleantenna element provides antenna diversity that can improvethe reliability of the system in rich isotropic multipath (RIMP)environments [11], [12]. Furthermore, by combining the CMand DM patterns with arbitrary complex-valued weights, thebeam may potentially be steered electronically over the entirehemisphere [13]. This extended scan range is of significantimportance for the next generation radio telescopes requiringfull sky surveys through the use of wide-scan phased arrayantenna systems [14], [15]. It is worth mentioning that S. Hayhas shown that the aperture efficiency of the AustralianCheckerboard phased array feed increased by 10–20 percentwhen all the outputs of pairs of SE LNAs making up thedifferential LNAs were beamformed individually, even thoughthe antenna elements in that system were aimed to suppressCM signals [16].

Low-noise design for dense antenna arrays is in general acomplex procedure due to the presence of mutual couplingbetween array elements [17]. Moreover, the introduction ofan antenna element utilizing both common and differentialmodes adds extra complexity, as its design would require theknowledge of a full noise model, including all four noiseparameters for both DM and CM cases, a full S-parameterdescription for both modes, as well as both DM and CM activeimpedances over a range of frequencies and scan angles.

While Mixed-Mode (MM) S-parameter theory is well es-

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tablished [18], the work on the MM noise performance ofdifferential active antennas has been limited to the reportingof the presence of CM associated noise effects [6], [7]. Thispaper therefore presents a theoretical framework that can beused for the analysis and experimental characterization ofreceiving sensitivity of active antenna elements utilizing bothCM and DM excitation. The framework includes a novel MMformulation of the standard noise parameters and extends theequivalent system representation of SE active array antennas,as proposed by [19], to the MM case.

The developed model has been validated numerically andthrough measurements, both by using a SE modeling approach.Note that the practical noise characterization of dLNAs,nonetheless, remains a challenging task because: (i) standardmeasurement techniques apply to two-port devices only, and;(ii) new methods for modeling and experimental characteri-zation of the multi-port noise behavior reported thus far arelimited to SE antenna-amplifier combinations with uncorre-lated noises sources [3]–[5], [20]–[23].

The MM model introduced in this paper is applied to thenewly proposed dual-mode antenna, showing that the receivingsensitivity increases significantly over the Field-of-View (FoV)relative to the purely differentially excited case.

II. MIXED-MODE FORMULATIONS

A. Mixed-Mode Antenna Analysis

The operation of the proposed dual-mode antenna is illus-trated in Fig. 1. The antenna consists of a dipole over groundand a parasitic monopole antenna integrated with a balancedtransmission line feed. When excited differentially, no currentis present on the monopole, creating a pure dipole-over-groundradiation pattern. In the case of a CM excitation, the dipolearms are excited in-phase and the monopole out-of-phase withrespect to the dipole arms, realizing a near pure monopoleradiation pattern.

(a) (b)

Fig. 1. Operation principle of the considered dual-mode antenna: (a)differential mode (dipole) radiation; (b) common mode (monopole)radiation.

When excited by two SE wave sources, two EmbeddedElement Patterns (EEPs) f1 (θ, φ) and f2 (θ, φ) result, and aSE two-port description is obtained in the form of the S-matrixSant

SE . Due to linearity, the DM and CM patterns and S-matrixare obtained by superposition of the SE excitations, to yieldf d (θ, φ), f c (θ, φ), and Sant

MM as:

f d (θ, φ) =1√2

[f1 (θ, φ)− f2 (θ, φ)] (1a)

f c (θ, φ) =1√2

[f1 (θ, φ) + f2 (θ, φ)] , (1b)

and

SantMM =

[Sant

dd Santdc

Santcd Sant

cc

], (2)

where from [18]

Santdd = (Sant

11 − Sant12 − Sant

21 + Sant22 )/2 (3a)

Santdc = (Sant

11 + Sant12 − Sant

21 − Sant22 )/2 (3b)

Santcd = (Sant

11 − Sant12 + Sant

21 − Sant22 )/2 (3c)

Santcc = (Sant

11 + Sant12 + Sant

21 + Sant22 )/2. (3d)

Using the complex-valued beamforming weights wd (θ, φ) andwc (θ, φ) for the DM and CM EEPs, the receiving sensitivitycan be optimized over the FoV as explained in Sec. III. Whilethe mechanism of combining weighted antenna patterns toachieve a new pattern follows that of standard arrays, theapproach presented here differs in the fact that the arrayelements are collocated and the EEPs which are combinedare not the same. This allows the MM receiver to exploitthe different DM and CM element patterns to achieve animproved FoV coverage.

B. Mixed-Mode Circuit Analysis

The active antenna system comprises a balanced DifferentialLow-Noise Amplifier (dLNA), whose mathematical model in-volves the formulation of the MM S-parameters and an equiv-alent set of MM noise parameters. The combined antenna-amplifier model, in turn, enables the receiving sensitivity tobe modeled as explained in Sec. III.

The theory presented in [18] is used to derive the MM S-parameters of the balanced dLNA. Fig. 2 shows two SE Low-Noise Amplifiers (LNAs) with the corresponding SE incidentand reflected power waves, and an equivalent LNA with MMincident and reflected waves.

The MM S-parameters can be derived from the SE onesusing the transformation

SdLNAMM = MdLNA

S SdLNASE

(MdLNA

S

)−1

, (4)

where the transformation matrix MdLNAS is defined as

MdLNAS =

1√2

1 0 −1 00 1 0 −11 0 1 00 1 0 1

. (5)

3

a3

b3

a1

b1

a2

b2

SLNA1

SdLNA

SE

SLNA2

a4

b4

bd;1bc;1

ac;1ad;1

ad;2ac;2

bc;2bd;2

SdLNA

MM

Fig. 2. Incident and reflected power waves at the SE and MM input andoutput ports of the corresponding LNAs.

It is useful to block-partition the MM scattering matrix as

SdLNAMM =

[SdLNA

dd SdLNAdc

SdLNAcd SdLNA

cc

](6)

where SdLNAdd , SdLNA

cc , and SdLNAcd ,SdLNA

dc , denote the 2×2 DM,CM, and cross-mode S-parameter matrices of the dLNA, re-spectively. For the balanced system considered in this analysis,the two SE LNAs are assumed to be identical and perfectlyisolated, i.e. SLNA1 = SLNA2 = SLNA, so that the four-port SEscattering matrix takes the form

SdLNASE =

SLNA11 SLNA

12 0 0SLNA

21 SLNA22 0 0

0 0 SLNA11 SLNA

120 0 SLNA

21 SLNA22

, (7)

which, after the application of (4), renders the cross-termsSdLNA

cd = SdLNAdc = 0 in (6).

In addition to the MM S-parameters, a corresponding setof MM equivalent noise parameters of the dLNA is required.The derivation of such a set of noise parameters is presentedin the Appendix, and summarized in (8) for the case of twoidentical and isolated LNAs of which the noise contributionsare uncorrelated. In (8), Rn, Fmin, and Yopt are the standardSE noise parameters.

DM Noise Parameters CM Noise ParametersF d

min = Fmin F cmin = Fmin

Rdn = 2Rn Rc

n = Rn/2Y d

opt = Yopt/2 Y copt = 2Yopt

(8)

In general the LNAs in active antenna systems are fed bycoupled transmission lines. The DM and CM characteristicimpedances of a pair of coupled transmission lines can,respectively, be related to the odd mode (Zo

0 ) and even mode(Ze

0) characteristic impedances of each line, i.e., [18]

Zd0 = 2Zo

0, and Zc0 = Ze

0/2 (9)

from which the equivalent SE characteristic impedance iscalculated as [24]

Z0 =√Zo

0Ze0 (10)

where Z0 is the real-valued SE characteristic impedance. As-suming uncoupled transmission lines results in Zo

0 = Ze0 = Z0.

Together with (8), and for identical SE LNAs, each withoptimum source reflection coefficient Γopt, this results in

Γdopt = Γc

opt = Γopt. (11)

III. RECEIVING SENSITIVITY MODELING

Modeling the receiving sensitivity requires a detailed de-scription of the receiver noise. In [17] it is shown that highersensitivity is achieved when the receivers are noise matched tothe active reflection coefficient of a beamforming array ratherthan the passive reflection coefficient of the array antennas.This section applies a similar analysis to the dual-modeactive antenna to solve both the SE and MM active reflectioncoefficients, effectively noise-decoupling the two channels (ormodes). The noise analysis presented in [19] is then appliedto the noise-decoupled receivers, of both the SE and MM rep-resentations, in order to evaluate the respective receiver noisetemperatures. In the analysis to follow, [p, q] denotes either thechannels [1, 2] or the modes [d, c], and S(p),S(q) representthe scattering parameters SLNA1,SLNA2 or SdLNA

dd ,SdLNAcc

for the SE and MM representations, respectively.

A. Receiver Noise

Fig. 3(a) shows the dual-mode active antenna connectedto two SE LNAs with complex beamforming weights w1

and w2 applied to the respective channels. The correlatednoise waves emanating from the input and output of eachLNA are denoted by [c(1)

1 , c(1)2 ] and [c(2)

1 , c(2)2 ], respectively. The

equivalent MM representation of the active dual-mode antennais shown in Fig. 3(b) with the respective DM and CM complexbeamforming weights wd and wc applied to each mode. Inthe MM representation each antenna represents one of the twomodes and their coupling is defined by the cross-mode antennascattering parameters. The equivalent DM and CM correlatedinput and output noise waves are denoted by [c(d)

1 , c(d)2 ] and

[c(c)1 , c

(c)2 ], respectively.

+

c(2)2

c(2)1

ctot = c(1)tot + c

(2)tot

c(1)1

c(1)2

w2

SLNA2SLNA1

w1

+

wc

c(d)1

c(d)2

c(c)1

c(c)2

ctot = c(d)tot + c

(c)tot

SccSdd

wd

(a) (b)Fig. 3. Propagation paths of the (a) single-ended noise waves and (b) mixed-mode noise waves in the coupled dual-mode active antenna.

The active reflection coefficients of the individual chan-nels/modes are solved by expressing the noise wave at theoutput of the ideal power combiner – due to the respective

4

channel/mode – as the superposition of three noise wavecontributions, i.e.,

c(p)tot = Direct Part + Reflected Part + Coupled Part (12)

= wpc(p)2 + wpc

(p)1 Sant

ppS(p)21 + wqc

(p)1 Sant

qpS(q)21 ,

For identical LNAs, with gains SLNA21 , the expression in (12)

reduces to

c(p)tot = wp

[c(p)2 + c

(p)1 SLNA

21

(Santpp +

wqwpSantqp

)]

= wp

[c(p)2 + c

(p)1 SLNA

21 Γ(p)act

], (13)

from which it follows that for a reciprocal antenna, the activereflection coefficient of channel p equates to Γ

(p)act = Sant

pp +wq

wpSantpq . Similarly, the active reflection coefficient of channel

q can be shown to equal Γ(q)act = Sant

qq +wp

wqSantqp . Using these

active reflection coefficients the antenna can be represented astwo noise-decoupled channels/modes, as illustrated in Fig 4.

+

S(p)

wp

Γ(p)act

Γ(q)act T

(q)LNA

T(p)LNA

G(q)av

G(p)av

TLNAout

Z0

S(q)

wq

Fig. 4. Equivalent noise-decoupled representation of the dual-mode activeantenna.

Fig. 4 can be used to calculate the equivalent input referrednoise contributed by the receiver for both the SE and MMrepresentations. The total noise contribution due to the LNAsis given by the weighted sum of the uncorrelated noisecontributions

T LNAout = G(p)

av T(p)LNA +G(q)

av T(q)LNA, (14)

where the noise temperature T (ν)LNA is referred to the input of

channel/mode ν = p, q and is weighted by the respectiveavailable gain G(ν)

av – defined from the output of the antennato the output of the ideal power combiner, i.e.,

G(ν)av =

1

2|S(ν)

21 |2|wν |2(

1− |Γ(ν)act |2

), for ν = p, q. (15)

The input referred noise temperature of each channel (ormode) is obtained using the well-known formula for noisytwo-ports:

T(ν)LNA = Tmin +

4R(ν)n T0

Z(ν)0

|Γ(ν)

act − Γopt|2

|1 + Γopt|2(

1− |Γ(ν)act |2

)

(16)

for ν = p, q, where R(ν)n , Tmin, Γopt are the noise parameters of

the LNA, T0 is the standard temperature (290 K) and Z(ν)0 the

real-valued characteristic impedance for the specific channelor mode.

Dividing (14) by the equivalent available gain of the LNAsyields the equivalent input referred noise of the receiver, i.e.,

Teq = T LNAout /Geq

av, (17)

where

Geqav =

1

2

[|wp|2|S(p)

21 |2(

1− |Γ(p)act|2

)

+ |wq|2|S(q)21 |2

(1− |Γ(q)

act|2)]. (18)

Furthermore, for equal SE LNA gains, (17) reduces to

Teq =|wp|2

(1− |Γ(p)

act |2)T

(p)LNA + |wq|2

(1− |Γ(q)

act |2)T

(q)LNA

|wp|2(

1− |Γ(p)act |2

)+ |wq|2

(1− |Γ(q)

act |2) .

(19)

B. Receiving Sensitivity

The receiving sensitivity of the active antenna is definedas the ratio of the effective antenna area to the total sys-tem noise temperature, i.e., Aeff/Tsys, where the well-knownreciprocity relation Aeff = (4π)−1λ2G relates the effectivearea to the antenna gain G(Ω), defined as the ratio of theradiated power per solid angle, P (Ω), to the accepted inputpower of the antenna, Pin. Here, P (Ω) can be expressedin terms of the weighted EEPs for wave excitations, i.e.,P (Ω) = (2η)−1|wpfp(Ω) + wqf q(Ω)|2, with η denoting thefree-space impedance. The effective area is therefore expressedas

Aeff =λ2

2η

|wpfp(Ω) + wqf q(Ω)|2Pin

, (20)

where λ denotes the wavelength, and Pin = wH(I − SHS)wis the total accepted input power, with I the 2 × 2 identitymatrix, and where w,S either denotes [w1, w2]T ,Sant

SEor [wd, wc]

T ,SantMM for the SE and MM representations,

respectively.Generally, Tsys consists of three main contributions: (i) the

spillover noise; (ii) the noise due to dissipation losses of theantenna, and; (iii) the noise due to the LNAs which dependon the noise properties of the LNAs and active reflectioncoefficients at the antenna ports [19]. Since the focus of thispaper is on the MM receiver characterization of an active dual-mode antenna, only the latter noise contribution is taken intoaccount, so that Tsys = Teq, where the equivalent input referrednoise of the receiver, Teq, is calculated using (19). Hence, thefinal receiving sensitivity is given by

Aeff

Tsys=

λ2

2ηTeq

|wpfp(Ω) + wqf q(Ω)|2

wH(I− SHS

)w

. (21)

IV. DUAL-MODE ANTENNA DESIGN WITH LARGEFIELD-OF-VIEW COVERAGE

In [13], a simple proof-of-concept dual-mode antenna, con-sisting of a balanced microstrip transmission line feed and aninverted-V dipole on the top layer of a Rogers Duroid RO4003substrate, and a monopole which extends out from a groundplane on the bottom layer, was demonstrated theoretically and

5

verified experimentally. Whilst demonstrating the viability ofa dual-mode structure, this antenna exhibited limited band-width and significant sensitivity variation over the FoV. Thepresent paper proposes an improved dual-mode antenna designexhibiting a smaller gain variation and receiving sensitivityvariation over the FoV.

A. Dual-Mode Antenna Design

Fig. 5. Cylindrical dual-mode antenna design with cut planes at the bottom,middle (semi-rigid coaxial to air-core twinaxial transition) and top of theantenna feed.

TABLE ICYLINDRICAL DUAL-MODE ANTENNA DESIGN PARAMETERS.

Parameter Value [mm] DescriptionL1 141 Dipole lengthL2 75 Dipole heightL3 70 Feed/Monopole heightL4 5 Dipole-Monopole separationL5 35 Height of twinaxial transitionW1 3 Coaxial dielectric diameterW2 0.91 Coaxial conductor diameterW3 10 Feed ground shield outer diameterW4 5 Dipole/Feed line separationW5 13.66 Monopole sleeve inner diameterW6 15 Monopole sleeve outer diameterW7 2 Twinaxial inner conductor diameterW8 1.15 Dipole arm diameterW9 8 Twinaxial ground shield inner diameterd1 1 Monopole Teflon supportd2 2 Twinaxial conductor Teflon supportd3 5 Twinaxial conductor Teflon supportd4 1 Monopole-Feed ground cap thicknessg1 2 Monopole-Ground plane gap height

The improved dual-mode antenna is realized by combininga cylindrical dipole and monopole element with a singletwinaxial feed, as depicted in Fig. 5. The cylindrical dual-mode antenna is realized by a single balanced transmissionline feeding a dipole element – where each of the two centerconductors is connected to one of the dipole arms. Ratherthan extending the monopole from the ground conductor ofthe transmission line, as is done in the planar design [13], themonopole is realized by folding the ground conductor backtowards the ground plane – leaving a small gap between themonopole and the ground shield of the feed as well as theground plane (g1). To keep the monopole sleeve in place,a small Teflon spacer is placed at the foot of the antenna.The antenna is excited through two 3 mm semi-rigid coaxial

cables extending midway into the antenna feed, from whichpoint the center conductors of the semi-rigid coaxial cablesextend further to form an air-core twinaxial transmission line.To ensure the stability of the center conductors of the twinaxialtransmission line, another Teflon spacer is placed at the top ofthe monopole sleeve. Table I summarizes the antenna designparameters illustrated in Fig. 5.

(a) (b)

(c) (d)

Fig. 6. Simulated electric field distributions (a) DM antenna near field (b)CM antenna near field (c) DM port excitation (d) CM port excitation.

Fig. 6 illustrates the MM operation of the antenna topology,shown in Fig. 5, simulated over an infinite ground plane usingCST. The DM field distribution in the balanced transmissionline feed [c.f. Fig. 6(c)] is seen to excite the dipole arms outof phase, realizing a typical dipole radiated electric near field[c.f. Fig. 6(a)]. A CM excitation realizes the field distributionof the feed as depicted in Fig. 6(d) and is shown to excitethe dipole arms in-phase, but out-of-phase with respect to themonopole sleeve, resulting in a monopole-like radiated electricnear field [c.f. Fig. 6(b)].

−100 −50 0 50 100−30

−25

−20

−15

−10

−5

0

5

10

15

Mag

nit

ud

e [d

B]

θ , deg

Gain (Principal Planes)

H − DM excitationH − CM excitationE − DM excitationE − CM excitation

Fig. 7. Differential and common mode E-plane and H-plane gain simulatedat 1 GHz.

Fig. 7 shows the normalized E- and H-plane MM gainpatterns resulting from the DM and CM excitations depictedin Fig. 6. The curves in Fig. 7 clearly illustrate that a typicaldipole-over-ground radiation pattern is realized by a DMexcitation, and that a CM excitation results in a monopole-over-ground radiation pattern.

6

B. Experimental Verification

In order to measure the performance of the antenna, thedesign illustrated in Fig. 5 is placed in the center of a circularground plane with a diameter of 500 mm, and excited throughtwo 3 mm semi-rigid coaxial cables shown in Fig. 8.

Fig. 8. Dual-mode antenna on finite circular ground plane with 3 mm semi-rigid coaxial feeds.

Using (3a) and (3d), the DM and CM input reflectioncoefficients can be solved from the measured SE S-parametersof the antenna, respectively. The graph in Fig. 9 compares themeasured MM input reflection coefficients to the simulatedresults obtained using MM excitations in CST. Fig. 9 showsthat the measurements agree very well with the simulatedresponse, with both differential and common modes matchedat the center frequency of 1 GHz. Also shown in Fig. 9 isthe measured isolation between the DM and CM excitationscalculated using (3b). It is seen that an isolation below -30 dBis achieved.

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2−45

−40

−35

−30

−25

−20

−15

−10

−5

0Mixed−Mode Input Reflection Coefficient and Isolation

[dB

]

Frequency [GHz]

DM − MeasuredCM − MeasuredIsolation − MeasuredDM − CSTCM − CST

Fig. 9. Measured and simulated differential and common mode inputreflection coefficients and isolation.

Similar to the MM reflection coefficients, the DM and CMradiation patterns are obtained by measuring the SE radiationpatterns of the antenna and applying (1a) and (1b), respec-tively [13]. The co-polar MM radiation patterns measured andsimulated, at 1 GHz, in both principal planes are compared inFig. 10.

The measured differential and common mode radiationpatterns are seen to be in good agreement with the simulatedresponse [c.f. Fig. 10] in both principal planes. It should benoted that the differences in the common mode pattern of themeasured antenna, shown in Fig. 10, and the radiation patternsdepicted in Fig. 7 can be attributed to the finite ground planeused for the physical antenna. Regardless of these differences,

−100 −50 0 50 100−30

−25

−20

−15

−10

−5

0

5

10

15

Mag

nit

ud

e [d

B]

θ , deg

Normalized Gain (E−Plane)

DM − MeasuredCM − MeasuredDM − CSTCM − CST

(a)

−100 −50 0 50 100−30

−25

−20

−15

−10

−5

0

5

10

15

Mag

nit

ud

e [d

B]

θ , deg

Normalized Gain (H−Plane)

DM − MeasuredCM − MeasuredDM − CSTCM − CST

(b)

Fig. 10. Measured and simulated co-polar differential and common moderadiation patterns (a) E-plane and (b) H-plane.

the measurements still illustrate the dipole- and monopole-like radiation characteristics of the antenna resulting fromdifferential and common mode excitations, respectively.

V. DUAL-MODE ACTIVE RECEIVER

A schematic representation of the MM active receiveranalyzed in this section is shown in Fig. 3(b), where theactive antenna element is realized using the cylindrical antennadesign in Fig. 5, placed on an infinite ground plane andconnected to two identical SE LNAs. For the purpose ofthis investigation, an LNA model with typical noise-parametervalues for Fmin and Rn is chosen, while Γopt is selected toprovide a noise-match to the passive differential antenna inputimpedance. In addition, idealized S-parameters are used, asshown in Table II. The use of these ideal values does notaffect the conclusions of the analysis.

TABLE IISINGLE-ENDED LNA NOISE AND S-PARAMETERS.

Noise Parameters S-ParametersTmin = 37 K S21 = 20Rn = 3 Ω S12 = 0

Γopt = Sddant S11 = S22 = 0

In order to analyze the MM sensitivity, the SE parametersshown in table II are transformed into the equivalent MM S-and noise parameters using (4) and (8), respectively.

7

−100 −50 0 50 1000

1

2

3

4

5

6

7

8

9

10

Mag

nit

ud

e [d

B]

Scan angle [deg]

Gain (Principal planes)

H − Purely Differential AntennaH − Weighted MM AntennaE − Purely Differential AntennaE − Weighted MM Antenna

Fig. 11. Weighted MM E- and H-plane gain optimized for each scan anglecompared to purely differential excitation.

A. Effective Area

By solving the MM beamforming weight vector w =[wd, wc]

T for maximum sensitivity at each scan angle [25],the performance of a MM receiving element – allowing forboth DM and CM propagation – can be compared to thatof a conventional purely differential receiver. Fig. 11 com-pares the MM antenna gain, with the respective MM weightsoptimized for maximum sensitivity using the DM and CMEEPs predicted by CST, to the antenna gain realized for apurely differential excitation, in both the E- and H-planes. Thecurves show the antenna gain at 1 GHz, and clearly indicatethe improved FoV realized by allowing CM propagation. Withthe weighted MM antenna gain deviating by less than 3 dBin the E-plane and by only 4 dB in the H-plane, this antennaeffectively realizes near hemispherical FoV coverage.

B. Equivalent Noise Temperature

Since this increase in effective area is maximized by apply-ing complex-valued beamforming weights to each of the twomodes, the equivalent noise contribution of the MM receivershould be computed using the active reflection coefficientas discussed in Sec. III, rather than the passive reflectioncoefficient considered in the purely differential receiver. UsingSant

MM as calculated by CST, the noise contributed to the receivernoise temperature due to the weighted differential and commonmode is shown for both the E- and the H-planes in Fig. 12.

Fig. 12 indicates that equivalent noise contributed by thepurely differential receiver remains constant at the minimumnoise temperature of the SE LNA listed in Table II. Thisis to be expected given that the optimum source reflectioncoefficient of the LNA equals the passive differential reflectioncoefficient of the antenna.

For the MM noise contribution, first consider the E-planenoise contribution in Fig. 12. The weighted MM antenna gainin Fig. 11 (E-plane) is seen to be almost equal to a purelyDM excitation for scan angles of 0 ≤ θscan ≤ 20 fromzenith. For these scan angles the DM weights are found to besignificantly more dominant than the CM weights, resulting in

Fig. 12. Purely differential and MM equivalent input noise temperature inboth the E- and H-planes.

an active differential reflection coefficient close to the passivereflection coefficient of the antenna. Together with low CMweight values, this results in the MM receiver being noisematched in the E-plane at 0 ≤ θscan ≤ 20 from zenith.For 20 ≤ θscan ≤ 50 from zenith, the MM antenna gainis seen to be greater than that of the the purely DM receiver.This increase in gain is due to the addition of CM propagationrealized through an increase in the complex CM weight values.Since the LNAs are noise matched to the passive differentialimpedance of the antenna, the CM noise mismatch resultsin a larger CM noise contribution. Considering Fig. 12 at20 ≤ θscan ≤ 50 from zenith, this CM noise is seen toincrease the MM equivalent input noise proportionally to theCM weight values applied at these scan angles. The E-planegain in Fig. 11 shows that the MM antenna gain is dominatedby a CM excitation at scan angles 50 ≤ θscan ≤ 90 fromzenith, realizing CM weights that are substantially larger thanthe DM weights, and in turn resulting in CM noise dominatingthe MM equivalent input noise. This behavior is noted inthe increase of the equivalent noise temperature of the MMreceiver in Fig. 12.

Next, consider the H-plane antenna gain patterns and equiv-alent receiver noise contribution shown in Figs. 11 and 12,respectively. Fig. 11 shows that the weighted MM gain equalsthe gain of the purely differentially excited antenna for scanangles 0 ≤ θscan ≤ 60 from zenith. The CM weights atthese scan angles are therefore nearly negligible compared tothe DM weights, and hence the equivalent noise contributionof the weighted MM receiver equals that of the DM receiveras shown in Fig. 12. For scan angles 60 ≤ θscan ≤ 90 fromzenith, the H-plane MM antenna gain is realized primarilydue to a CM excitation, resulting in dominating CM weights.Analogous to the E-plane, the increase in CM weights at theselarger scan angles are seen to result in CM noise dominatingthe MM equivalent noise contribution in Fig. 12.

C. Receiving Sensitivity

As indicated in (21), the receiving sensitivity is approxi-mated by only accounting for the noise contributed by the

8

LNA. The normalized sensitivity, in both the E- and H-planes, of the MM receiver is compared to the sensitivityof a conventional differential receiver in Figs. 13(a) and (b),respectively.

(a)

(b)

Fig. 13. Purely differential and dual-mode sensitivity (a) E-plane and (b)H-plane.

Fig. 13 indicates that, regardless of the increase in theequivalent noise temperature attributed to the CM presentin the MM receiver, the utilization of CM propagation canresult in an increase in the sensitivity over the entire FoVcoverage when compared to the conventional receivers whereCM is completely rejected – realizing a variation in sensitivityof less than 50% in the E- and 60% in the H-plane. Acomparison between the variation in sensitivity in Fig. 13 andthe gain variation depicted in Fig. 11 shows that the variationin sensitivity corresponds to the gain variation in both planes.

As a final validation of the MM receiver model presentedin this paper, Fig. 13 shows that the MM sensitivity analysisproduces the same result obtained when analyzing the antennaand receiver using the equivalent SE S-matrix Sant

SE and EEPsf1 (θ, φ) and f2 (θ, φ) with the corresponding SE complexbeamforming vector w = [w1, w2]T solved for maximumsensitivity at each scan angle.

VI. CONCLUSIONS AND RECOMMENDATIONS

With the theoretical framework presented in this paper,single-polarized active receiving antennas can be modeled

using a mixed differential and common mode analysis. Theproposed mixed-mode model has been used to investigatethe sensitivity of a novel active dual-mode receiving antennautilizing, rather than rejecting, CM propagation. It was shownthat, regardless of the additional noise contributed by thepresence of a CM channel, the active dual-mode antennaexhibits only a 3 dB sensitivity loss at 60 E-plane scan, ascompared to a 10 dB loss for a conventional active receiverrejecting CM propagation.

Previous works [26], [27] have shown that similar an-tenna structures, referred to as tripole antennas, were foundto have good polarimetric beam properties and polarizationdiscrimination capabilities over the field of view when usedas a receiving antenna, which is of particular importance inradio astronomy applications [28]. Hence, the polarimetricanalysis of a dual-polarized mixed differential and commonmode active receiving antenna will be considered in future, aswell as an array thereof operating over an increased frequencybandwidth.

APPENDIX

In addition to the MM S-parameters, we derive a cor-responding set of MM equivalent noise parameters of thedLNA. Toward this end, the equivalent MM noise parametersof the balanced dLNA are expressed in terms of the SE noiseparameters of the constituent SE LNAs shown in Fig. 2 (left).Note that the derivation presented here assumes that the SELNAs are identical, isolated, and with their noise contributionsuncorrelated.

- -

+ +

- -

+ +

I3

V3

I4

V4

en2

in2

ASE2

CA2

en1

V1

I1 I2

V2in1

ASE1

CA1

CA;DM CA;CM

- -

++

- -

++

CY2

in4

YdLNASE CdLNA

Y;SE

I4

V4

I2

V2in1

V3

V1

I3

I1

in3

in2

YSE1

CY1

YSE2

(a) (b)Fig. 14. Equivalent noise sources and corresponding noiseless network for twoisolated LNAs in (a) chain representation, and; (b) admittance representation.

Each SE LNA can be represented by a noiseless ABCD-matrix with a noise voltage and current source applied to theinput of the noiseless two-port, as shown in Fig. 14(a). Thisrepresentation is referred to as the chain representation [29].A physically significant representation of these noise sourcesis given by their self and cross-power spectral densities, whichwhen arranged in matrix form constitutes the so-called noisecorrelation matrix, henceforth referred to as the correlationmatrix. One of the fundamental advantages of the chainrepresentation of the correlation matrix is the direct relationof its elements to the noise parameters of the two-port device,

9

i.e.,

CA1 =1

2

[〈en1, e

∗n1〉 〈en1, i

∗n1〉

〈in1, e∗n1〉 〈in1, i

∗n1〉

]=

[CA;11 CA;12CA;21 CA;22

]

= 2kBT0

RnFmin − 1

2−RnY

*opt

Fmin − 1

2−RnYopt Rn|Yopt|2

,

(22)

where 〈en1, e∗n1〉, 〈in1, i

∗n1〉 and 〈en1, i

∗n1〉, 〈in1, e

∗n1〉 denote

the auto- and cross-correlated spectral power densities, re-spectively, of the noise sources en1 and in1, and where kB isBoltzmann’s constant, T0 is the standard temperature (290 K),Fmin is the minimum noise figure, Rn is the noise resistance,and Yopt is the optimal source admittance [29].

To derive the MM noise parameters, the chain correlationmatrix is transformed to the equivalent admittance correlationmatrix CY1 using the transformation matrix TY introducedin [29]. In the equivalent admittance representation, shownin Fig. 14(b), the LNAs are represented by their noiselesstwo-port admittance matrices with two noise current sourcesapplied to the input and output ports, respectively. The admit-tance correlation matrix is given by

CY1 = TYCA1THY , (23)

where TY is expressed in terms of the SE admittance param-eters, i.e.,

TY =

[−YSE;11 1−YSE;21 0

]. (24)

Solving the admittance correlation matrix of the second LNAin a similar manner, the total admittance correlation matrix ofthe two uncorrelated LNAs can be formulated as

CdLNAY;SE =

[CY1 00 CY2

], (25)

where 0 denotes a 2×2 zero-matrix. To obtain the MM admit-tance correlation matrix, the transformation matrix MdLNA

I isused, where MdLNA

I relates the DM and CM input and outputcurrents to the respective SE currents. That is,

IdLNAMM = MdLNA

I IdLNA, (26)

where IdLNAMM = [Id1, Ic1, Id2, Ic2]T , IdLNA = [I1, I2, I3, I4]T ,

and

MdLNAI =

12 0 − 1

2 01 0 1 00 1

2 0 − 12

0 1 0 1

. (27)

Hence, for identical LNAs, the MM admittance correlationmatrix is given by

CdLNAY;MM = MdLNA

I CdLNAY;SE

(MdLNA

I

)H

=

〈id1, i*d1〉 0 〈id1, i

*d2〉 0

0 〈ic1, i*c1〉 0 〈ic1, i

*c2〉

〈id2, i*d1〉 0 〈id2, i

*d2〉 0

0 〈ic2, i*c1〉 0 〈ic2, i

*c2〉

. (28)

The non-zero terms in (28) can be grouped into two equivalentDM and CM two-port admittance correlation matrices that canbe related to the SE admittance correlation matrices, i.e.,

CY;DM =

[〈id1, i

*d1〉 〈id1, i

*d2〉

〈id2, i*d1〉 〈id2, i

*d2〉

]=

1

2CY1 (29a)

CY;CM =

[〈ic1, i

*c1〉 〈ic1, i

*c2〉

〈ic2, i*c1〉 〈ic2, i

*c2〉

]= 2CY1. (29b)

Since the LNAs are isolated, the DM and CM admittancematrices can be expressed in terms of the SE admittance matrixYSE, where, similar to the correlation matrices, the DM andCM admittance matrices, respectively, result in

YDM =1

2YSE, and YCM = 2YSE. (30)

The DM and CM admittance correlation matrices can nowbe transformed to their equivalent chain representations, afterwhich the MM noise parameters can be solved through com-parison with (22). From [29] it follows that the DM chaincorrelation matrix is given by the transformation

CA;DM = TA;DMCY;DM (TA;DM)H (31)

where the transformation matrix TA;DM is expressed in termsof the DM ABCD-parameters:

TA;DM =

[0 BDM1 DDM

](32)

where, on account of (30), BDM = −1/YDM;21 = −2/YSE;21,and DDM = −YDM;11/YDM;21 = −YSE;11/YSE;21. Substitut-ing (23) in (29a), and then in (31), enables us to relate theelements of the DM chain correlation matrix CA;DM to thecorresponding SE ones. That is, for CA1 = CA2 = CA,

CA;DM = 2kBT0

Rdn

F dmin − 1

2−Rd

n

(Y d

opt

)∗

F dmin − 1

2−Rd

nYd

opt Rdn|Y d

opt|2

=

[2CA;11 CA;12

CA;2112CA;22

]

(33)

Finally, by using (33), the DM noise parameters, and similarlythe CM ones, can be expressed in terms of the standard two-port SE noise parameters Fmin, Rn, Yopt, yielding the ratherintuitive result:

F dmin = Fmin

Rdn = 2Rn

Y dopt =

1

2Yopt

F cmin = Fmin

Rcn =

1

2Rn

Y copt = 2Yopt.

(34)

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David S. Prinsloo (S’11) received the B.Eng. degreein Computer and Electronic Engineering from thePotchefstroom campus of North-West University,South Africa, in 2009 and the M.Sc.Eng. degreein Electronic Engineering from the University ofStellenbosch, Stellenbosch, South Africa in 2011. Heis currently pursuing the Ph.D. degree in ElectronicEngineering at the University of Stellenbosch. Since2012 he has spent several months as a visitingresearcher with the Antenna Group at the ChalmersUniversity of Technology, Gothenburg, Sweden. His

current research interests include multi-port noise theory, receiving antennaarrays, and active receiving antennas.

Rob Maaskant (M’11-SM’13) received his M.Sc.degree (cum laude) in 2003, and his Ph.D. degree(cum laude) in 2010, both in Electrical Engineeringfrom the Eindhoven University of Technology, Eind-hoven, The Netherlands. His Ph.D. has been awarded“the best dissertation of the Electrical EngineeringDepartment, 2010.” From 2003–2010, he was em-ployed as an antenna research scientist at the Nether-lands Institute for Radio Astronomy (ASTRON),Dwingeloo, The Netherlands, and from 2010–2012as a postdoctoral researcher in the Antenna Group

of the Signals and Systems Department at the Chalmers University ofTechnology, Sweden, for which he won a European Commission FP7 MarieSklodowska-Curie Actions Outgoing – Rubicon Fellowship from the Nether-lands Organization for Scientific Research (NWO), 2010. He is currently anAssistant Professor in the same Antenna Group. He is the primary authorof the CAESAR software; an advanced integral-equation based solver forthe analysis of large antenna array systems. His current research interest isin the field of receiving antennas for low-noise applications, meta-materialbased waveguides, and computational electromagnetics to solve these typesof problems.

Dr. Maaskant received the 2nd best paper prize (’best team contribution’)at the 2008 ESA/ESTEC workshop, Noordwijk, and was awarded a YoungResearcher grant from the Swedish Research Council (VR), in 2011. He is anAssociate Editor of both the IEEE Transactions on Antennas and Propagationand the FERMAT journal.

11

Marianna V. Ivashina (M’11-SM’13) received aPh.D. in Electrical Engineering from the SevastopolNational Technical University (SNTU), Ukraine, in2000. From 2001 to 2004 she was a PostdoctoralResearcher and from 2004 till 2010 an AntennaSystem Scientist at The Netherlands Institute forRadio Astronomy (ASTRON). During this period,she carried out research on an innovative PhasedArray Feed (PAF) technology for a new-generationradio telescope, known as the Square KilometerArray (SKA). The results of these early PAF projects

have led to the definition of APERTIF - a PAF system that is being developedat ASTRON to replace the current horn feeds in the Westerbork SynthesisRadio Telescope (WSRT). Dr. Ivashina was involved in the developmentof APERTIF during 2008-2010 and acted as an external reviewer at thePreliminary Design Review of the Australian SKA Pathfinder (ASKAP) in2009. In 2002, she also stayed as a Visiting Scientist with the EuropeanSpace Agency (ESA), ESTEC, in the Netherlands, where she studied multiple-beam array feeds for the satellite telecommunication system Large DeployableAntenna (LDA). Dr. Ivashina received the URSI Young Scientists Award forthe GA URSI, Toronto, Canada (1999), an APS/IEEE Travel Grant, Davos,Switzerland (2000), the 2nd Best Paper Award (’Best team contribution’) at theESA Antenna Workshop (2008) and the International Qualification Fellowshipof the VINNOVA - Marie Curie Actions Program (2009) and The VR projectgrant of the Swedish Research Center (2010). She is currently an AssociateProfessor at the Department of Signals and Systems (Chalmers Universityof Technology). Her interests are wideband receiving arrays, antenna systemmodeling techniques, receiver noise characterization, signal processing forphased arrays, and radio astronomy. She is an Associate Editor of the IEEETransactions on Antennas and Propagation and the FERMAT journal.

Petrie Meyer (S’87-M’88) received his Ph.D. in1995 from the University of Stellenbosch, on numer-ical analysis of microstrip circuits using the Method-of-Lines. He has since worked actively in the fieldsof passive network design, optimization, and sur-rogate modelling, and has authored or co-authoredmore than 90 technical journal and conference pa-pers. Since 2010 he has been involved in the designof microwave filters and ultra-low-noise amplifiersfor the planned Square Kilometre Array (SKA) radioastronomy antenna, and the South-African precursor

telescope, MEERKAT. In 2004, he was awarded the South African THRIPprize for human resource development, and in 2007 the international CSTprize for a published journal paper making use of CST. In both 2009 and 2010,he was awarded the University of Stellenbosch Rectors award for research.He has served as chairman for the local IEEE AP/MTT conferences since2005 and as technical chair for the 1999 IEEE Africon conference, as well aschairman of the IEEE South Africa Section during 1996-1997. He serves asregular reviewer for IEEE, IET and Wiley microwave journals. In 2009, hewas elected Fellow of the South African Institute for Engineers. Since 2003he holds the position of Professor in Microwaves and Electromagnetics atStellenbosch University.