Journal of Electronic Testing (2019) 35:335–347https://doi.org/10.1007/s10836-019-05799-8

Contact-Less Near-Field Test of Active Integrated RF Phased ArrayAntennas

Maryam Shafiee1 · Sule Ozev1

Received: 26 December 2018 / Accepted: 28 April 2019 / Published online: 24 May 2019© Springer Science+Business Media, LLC, part of Springer Nature 2019

AbstractFuture RF transceivers are expected to integrate the entire system, from baseband to antenna. Many emerging applicationsuse beam forming, which necessitates RF phased arrays and multiple antennas integrated on the same die. This integrationpresents a challenge in testing the entire system including antennas. The electromagnetic signal output is combined in theair and no longer can be separated by physically connecting to the test equipment. Testing each element in isolation does notexercise the interaction between the elements and cannot characterize important parameters such as phase mismatch. Thus,systems with multiple integrated antennas need to be tested using wireless means. This paper presents a novel contact-lessnear-field test method for measuring the gain and phase mismatch of RF phased array antennas. The proposed method isbased on using a known good die (KGD) receiver phased array antenna to capture the combined EM output of the transmitterantenna as the device under test (DUT). The mathematical model of mutual impedances and signal propagation is presentedfor a 16-element phased array to determine both gain and phase mismatches. The feasibility of the method is shown usinghardware measurement. The accuracy of the method under process variations and imperfections in the test set-up, includingnoise and error in test set-up dimensions, is further investigated through electromagnetic (EM) simulations of a coplanarpatch antenna array of sixteen elements.

Keywords Integrated phased-array antennas · Array antenna mismatches · Integrated antenna test and calibration ·Post-production test · Near-field antenna test

1 Introduction

Phased-array antennas play a significant role in communica-tion systems that rely on beam forming. By controlling therelative phase excitation between the elements, the maxi-mum radiation beam can be oriented in any direction to forma scanning array. Due to improved signal-to-noise ratio,effective isotropic radiated power, antenna pattern shaping,wider channel bandwidth, and spatial interference cancel-lation, phased arrays have been widely used in high endcommunications equipment (i.e. military systems) and areproliferating into the consumer electronics domain [19]. It is

Responsible Editor: K. Chakrabarty

� Maryam Shafieemshafiei@asu.edu

Sule OzevSule.Ozev@asu.edu

1 Arizona State University, Tempe, AZ, USA

expected that future communications systems will employbeam forming at several tens of GHz frequencies [2, 24].Beam forming is enabled via RF phased arrays where thephase shift of each antenna element is adjusted to steer thebeam in the desired direction.

Design and manufacturing of integrated phased arrayshave been widely explored and demonstrated in the pastdecade [1, 16, 18]. Integration of antennas together withthe phased arrays eliminates the need for additional off-chipinterconnects which contributes to more loss and introducesadditional phase error. At the target frequencies, even asmall deviation in interconnect dimensions would resultin significant phase shift [1]. Silicon integration solvesthe problems that exist with resolution and dimensionalcontrol but brings about new challenges. Increasing processvariations in finer geometries makes it difficult to matchthe gains and phases of the phase shift elements whichare typically implemented using active circuitry [16]. Evena few degrees of error could degrade the phased arrayoperation. Hence, it is necessary to calibrate the phase andgain imbalances [13] (Table 1).

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Table 1 Reported phased arrays and calibrated performance

Ref [23] [17] [6, 7] [25]

#Element 16 16 32 32

Gain Error N/A 16% 9% 8%

Phase Error 4◦ 9◦ 5◦ 5◦

This calibration process requires direct measurement ofphase and gain mismatches between elements in the RFdomain, which includes the phased-array as well as theantennas. This is a challenging problem due to two reasons.First, the phase and gain mismatches between RF elementshave a non-linear effect on the radiated power in the desireddirection. However, calibration requires decoupling themfrom one another. Second, due to the integration of theantenna, the signal is no longer accessible via an electricalconnection, which necessitates measuring radiated power.

Unfortunately, the effective combination of antenna sig-nals occurs only in the far field, which can be tens ofmultiples of the wavelength. For instance, for a 60 GHz, 16-element array system with half-wavelength separation, theeffective far field region starts at a distance of approxi-mately 56 cm. Clearly, placing the measurement equipmentat this distance is not practical in an automatic test equip-ment (ATE) environment. Hence, the radiated power needsto be measured in the near-field while in the normal mode ofoperation, the RF system is likely to be used in the far-field.Hence, it is also necessary to include the effect of near-fieldmeasurement and extrapolate the measurements to far field.

While there is extensive work on testing phased arraysusing electrical connections [9, 12, 14, 21, 23], contact-less near-field testing of phased array systems including theantenna has not garnered much attention. This is due tothe fact that until recently, phased array systems with manyantennas have been primarily used in military applicationswhere more resources can be devoted to testing.

In this work, we aim at closing this gap. We present amethodology for contact-less near-field testing of phasedarray systems without mechanically moving the receiverantenna, which would make it suitable for high volumeproduction environment. We propose a fast and cost-efficient test method to characterize active phased arrayantenna elements in terms of their gain and phase mismatch.Our proposed technique uses near-field measurement ofradiated power from antennas, thus the test path includesmismatches in the antennas as well as in active modules.Unlike existing contact-less measurement methods, ourapproach requires a single test setup and a short testduration. These qualities make the proposed approachviable for high volume production testing. Our proposedmethod is based on analytical derivation of mutual

impedances of radiated signals and measuring the amplitudeand phase of the signals at the receiver end. Using thismathematical model and the measured signal power, wedecouple the contribution of each phased array elementon the transmitter side. We determine the gain and phasemismatches using analytical solutions. In this paper, themodel has been derived for a 16-element system and canbe easily generalized to an N-element system. We evaluatethe accuracy of the proposed approach using MATLAB andANSYS HFSS simulations under various environment noiseand process variation scenarios.

The rest of the paper is organized as follows. In Section 2,we present an overview of related work. In Section 3,we present the physical model of the two antennas innear-field and their mutual impedance. In Section 4, themathematical model for our test setup including two arraysof sixteen elements is extracted. In Section 5, we verify themodel by hardware measurement using a 4-element setup.In Section 6, we describe the flow of the proposed testmethodology and in Section 7, we present experimentalresults evaluating its accuracy using MATLAB and HFSSsimulations. In Section 8, we conclude our paper.

2 RelatedWork

Majority of recent work on phased array testing has assumedelectrical connection to the phased array elements, eitherwith switches, or via on-chip coupling [9, 12, 14, 21].Hence, there is generally no antenna present during testingfor these methods.

In [12, 14], the authors present a built-in-self test methodfor phased arrays. The BIST signal is generated using aring oscillator and is coupled to all phased array portsvia directional couplers. The DC test signal is measuredafter self-mixing using an on-chip I/Q down-converter. Amatched resistor instead of actual antennas are used atantenna ports to get the coupling factors. In [23], the fullyintegrated 60-GHz receiver phased array is tested with theelectrical connection of the test RF signal to the LNA inputs.In order to calibrate the phase shift of elements, the RF isapplied to two elements at once, the phase of one elementis shifted gradually until the combined signal reaches itsdesired power. The receiver IC is packaged with a 16-element patch antenna array and entire transceiver systemwith the antennas present is tested at the far field, wherethe separation between the receiver and transmitter systemis 8 m. In [22], a 77GHz phased array transceiver with on-chip antennas is introduced. Similarly, for electrical testingthe transceiver, the antennas are bypassed. In [14], theauthors present a phased array BIST method using a simpleself-mixing down converter. Using resistive couplers and amatched switch network, the RF signal is first applied to

J Electron Test (2019) 35:335–347 337

each element separately. The next step is to apply the RFsignal to a pair of antennas and measure the combined signalpower. Using a mathematical model, the phase and gainmismatches are extracted from three measurements for eachantenna pair. The BIST work in [14] also requires electricalconnection (via a directional coupler) to the phase arrayoutput and bypasses the antennas.

Contact-less antenna test has been explored over pastdecade mostly in military applications. Antennas havetraditionally been tested using far-field measurement set-ups [4, 11]. These test methods require placing thereceiver antenna at distance where the existing fields aretransverse to direction of propagation and the angularfield distribution is independent of the radial distancefrom antenna. The measurement equipment is mechanicallymoved to test the radiated power at various angles todecide whether the elements are operating properly. Itis more convenient to measure phased array transmitterand receiver signals in a close distance with respect toeach other. Near-field measurement techniques have beendeveloped to provide a more effective method to cut downthe production and development costs of testing antennasystems [20]. There is an increasing trend to replace farfield measurement with near field measurement facilities.The near field antenna test technique, is performed indoorand provides a controlled environment which reducesproduction and development costs compare to its far-field counterpart. The near-field measurement test data iscollected via scanning RF field probe over a pre-selectedsurface. The measurement data is then transferred to far-field using Fourier transform methods. Application of thistechnique includes element failure diagnosis and phasedarray calibration [15]. The methods proposed in [15, 20]also require a mechanically moving RF probe. Due tothe need for mechanical movement and time-consumingdata collection, these techniques require both expensive testset-up and long test times.

In [27], a method for near-field measurement of dipoleantennas for a 2-element array is presented. In this method,the RF signal is applied to each antenna individually. Theamplitude and phase of the voltage due to each element atthe receiver end are measured. Using superposition, the totalreceived voltages are calculated to form a system of fournonlinear independent equations. Gain mismatch and phasemismatch are calculated from the measurements and usingthe cosine signal power combination. However:

• Antenna mutual impedances are not taken into accountas the signal is applied to a single element in the firststep

• A 2-element array cannot be a good representativefor a general array since it does not account for theintermediate element’s interactions

• The previously proposed test method is not investigatedon an actual coplanar setup and is limited to dipolesantennas only

• The hardware measurement is validated for a small2-element array

Unfortunately, none of the existing methods address theproblem of fast and cost-effective contact-less near-fieldtesting of integrated RF phased array mismatches includingthe antennas in a large scale. Testing on-chip antennasintegrated with phased-arrays requires new methods toinclude antenna mismatches as well as phased-arraymismatches. Since the output power is combined in radiatedform and cannot be separated, a new approach is desirableto detect all mismatches based on radiated measurements.

3 Physical Model

3.1 Test Setup

The proposed phased array test setup is depicted in Fig. 1.The transmitting phased array antenna is the device undertest (DUT). An identical phased array antenna system,coplanar with the DUT, is used as the probe antenna onthe receiver side. The probe antenna is a known gooddie with fully characterized parameters. Since the test set-up is shared by many thousand dies, the cost of thischaracterization is not an issue. The DUT is placed on theload board via a socket and the probe antenna is fixedonto the load board. The input RF signal is applied at theinput of the phased array via a direct electrical connection.The output RF signal is captured at the output of theprobe antennas via directional couplers or direct electricalconnection, whichever one is available. The captured outputis processed with respect to the mathematical model todetermine gain and phase mismatches in the DUT.

3.2 Mutual Impedance of Two Dipoles

Finding the mutual impedance between elements requiresknowledge of the near-field radiations since they are usuallya fraction of the wavelength apart. The geometry of thetwo identical (l1 = l2 = l) parallel diploes in the nearfield is shown in Fig. 2. The antennas are placed withina horizontal distance D, and a vertical distance d fromeach other. For a finite dipole with a sinusoidal currentdistribution, the magnitude of the tangential electric fieldcan be expressed in terms of its geometric properties andthe current that is flowing through it. Equation 1 defines thecurrent distribution of a thin dipole and Eq. 2 defines theelectric field of the dipole [3].

I (z′) = Im sin [k(l/2 − |z′|)] (1)

338 J Electron Test (2019) 35:335–347

Ez = −jηIm

4π

[e−jkR1

R1+ e−jkR2

R2− 2 cos

(kl

2

)e−jkr

r

]

(2)

Where l is the length of the dipole, R1 =√x2 + D2 + (z − |l/2|)2, R2 = √

x2 + D2 + (z + |l/2|)2,and r = √

x2 + D2 + z2.The induced open circuit voltage at antenna 2, referred to

its current at input terminals, due to radiation from antenna1 is given by Eq. 3.

V21 = −1

I2i

∫ l2

−l2

Ez21(z′)I2(z′)dz′ (3)

Where Ez21(z′) is the electric field component radiated by

antenna 1 along antenna 2, I2(z′) is the current distributionof antenna 2, and z′ = z − d. Hence, the mutual impedancereferred to the input current at antenna 1 is given by Eq. 4.

Z21i= −1

I1iI2i

∫ l2

−l2

Ez21(z′)I2(z′)dz′ (4)

By substituting Ez21(z′) from Eq. 2 and I2(z

′), I1i , I2i fromEq. 1, the expression for the mutual impedance, referred tothe input current, is obtained in Eq. 5.

Z21i= j

30

sin2(kl/2)

∫ l2

−l2

sin [k(l/2 − |z′|)][e−jkR1/R1

+e−jkR2/R2 − 2 cos (kl/2)e−jkr/r]dz′ (5)

Therefore, the mutual impedance referred to the currentmaxima is achieved in Eq. 6.

Z21m = Z21isin 2(kl/2) (6)

The closed form solution for the integral in Eq. 5 ispresented in [10] for any arbitrary length dipole bothfor parallel and collinear configurations. To simplify thecomplex expressions, a dipole length of λ/2 is assumedas it is the case for most phased arrays. The closedform expression for mutual impedance of a λ/2 dipoleis presented using induced EMF method [3]. It is shownthat the mutual impedance is reliant on the antennas type

Fig. 2 Two dipole antennas in staggered parallel position

(dipoles here), antenna length, and horizontal and verticaldistances between antennas.

4Mathematical Model

Considering the test setup configuration in Fig. 2, themeasurements are performed at the ports of the receivingprobe antennas(O1 − O16) which are assumed fullycharacterized. The phase and amplitude of the signals at theport of the transmitting phased array antennas (i1 − i16)

are target parameters. The coupling between antennas isdescribed by the mutual impedance matrix. An analyticalmodeling approach is used to solve for the target parameters.

The proposed approach is based on determining thetransfer matrix which links source currents to the outputvoltages using the mutual impedance model explained inSection 2. The coupling matrix between the transmitter andthe receiver which corresponds to the test setup in Fig. 1, isa 16 × 16 matrix and has the following form:

ZmT R =

⎡⎢⎢⎢⎢⎢⎣

Zi1,O1 Zi2,O1 Zi3,O1 . . . Zi16,O1

Zi1,O2 Zi2,O2 Zi3,O2 . . . Zi16,O2

Zi1,O3 Zi2,O3 Zi3,O3 . . . Zi16,O3...Zi1,O16 Zi2,O16 Zi3,O16 . . . Zi16,O16

⎤⎥⎥⎥⎥⎥⎦

(7)

Fig. 1 16-element transmitting and receiving phased array antennas test setup

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Fig. 3 Model Verification aHardware setup b Experimentalmethod illustration

(a)

(b)

Where Zin,Om represents the mutual impedance betweennth antenna at the transmitter side and mth antenna at thereceiver side. Due to the symmetry, Zin,Om = Zim,On . It canbe expressed by the real and the imaginary parts as shownin Eq. 8.

Zin,Om = Rin,Om + jXin,Om (8)

Rin,Om = −η/8π cos (w0n,m )[−2Ci(w1n,m ) − 2Ci(w′1n,m

)

+Ci(w2n,m ) + Ci(w′2n,m

) + Ci(w3n,m ) + Ci(w′3n,m

)]+η/8π sin (w0n,m )[2Si(w1n,m ) − 2Si(w

′1n,m

) − Si(w2n,m )

+Si((w′2n,m

) − Si(w3n,m ) + Si(w′3n,m

)] (9)

Xin,Om = −η/8π cos (w0n,m )[Si(w1n,m ) + Si(w′1n,m

)

−Si(w2n,m ) − Si(w′2n,m

) − Si(w3n,m ) − Si(w′3n,m

)]+η/8π sin (w0n,m )[2Ci(w1n,m ) − 2Ci(w

′1n,m

) − Ci(w2n,m )

+Ci((w′2n,m

) − Ci(w3n,m ) + Ci(w′3n,m

)] (10)

Where Ci(x) and Si(x) are the cosine and sine integrals andw0n,m , w1n,m , w

′1n,m

, w2n,m , w′2n,m

,w3n,m , w′3n,m

are functionsof the physical properties of the test setup. Equations 11a

to 11g expresses this dependency. Due to the symmetryof the array configuration and identical antenna elements,extracting the first column of the matrix of Eq. 7, gives usthe rest of the elements as well.

w01,m = k((m − 1)d + (m − 1)l) (11a)

w11,m =k(

√D2 + ((m − 1)d + (m − 1)l)2+(m−1)(d+l))

(11b)

w′11,m = k(

√D2 + ((m − 1)d + (m−1)l)2−(m−1)(d+l))

(11c)

Table 2 Actual vs. estimated added mismatch

Evaluation method Mismatch phase Mismatch gain

VNA Characterized 95◦ 0.95

Measured at Rx1 95.6◦ 0.94

Measured at Rx2 94.7◦ 0.92

Measured at Rx3 93.8◦ 0.93

Measured at Rx4 94.3◦ 0.93

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Fig. 4 Diagram of the test flow

w21,m = k(

√D2 + ((m − 1)d + (m−2)l)2+(m−2)(d+l))

(11d)

w′21,m = k(

√D2 + ((m − 1)d + (m−2)l)2−(m−2)(d+l))

(11e)

w31,m = k(

√D2 + ((m − 1)d + ml)2 + (m − 1)d + ml)

(11f)

w′31,m =k(

√D2 + ((m−1)d+ml)2−(m−1)d−ml) (11g)

5Model Verification

We verify the mathematical model derived in Section 4using hardware measurements. In order to verify,we expectto observe the characterized mismatch equally induced ateach element, at the receiving side. At least a systemof four antenna array is required to build a symmetricalmodel. The hardware setup is implemented by off-the-shelfcomponents. Splitter ZFSC-2-4-S+ is used for distributing

the input signal among antennas and to branch out inputas the phase reference. Four dipole antennas are used toform the transmitting array. The existing gain and phasemismatches in the antennas as well as the cables andsplitters used in the original set-up form the baseline. Thebaseline measurement also includes the effect of mutualimpedance. For our experiment, we inserted a characterizedmismatch (characterized by a VNA) at each element’s pathand read the output at the receiver side multiple times. Thecalculated mismatch from measurement is compared withthe original injected characterized mismatch.

Figure 3a shows the hardware setup. It includes fourdipole antennas at the transmitting side and one movingantenna at the receiving side to measure the transmittedsignal at four different locations. Figure 3b shows thediagram of the comparative analysis.The antenna separation(d) is λ/10 and the transmitter-receiver near-field distance(D) is equal to λ/3. The RF signal is generated usingsignal generator N5182A. The signal is captured atthe receiving end using digital oscilloscope DSO9254A.The oscilloscope has an 8-bit amplitude resolution. Themeasurements are repeated four times each and averaged,providing an additional bit of resolution. The results aresummarized in Table 2. Hardware measurements confirmthat gain mismatch and phase mismatch are calculated bymeasurements within 3.1% and 1.2◦ error respectively.

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Fig. 5 Matlab emulationplatform

Fig. 6 Estimated vs. actual again mismatch b phasemismatch at −84 dBm noisepower

(a)

(b)

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Fig. 7 a Total estimated gainmismatch b Total estimatedphase mismatch with respect toambient noise

(a)

(b)

6 Test Flow

The flow of the proposed near-field test methodology isshown in Fig. 4. Prior to high volume manufacturing testing,in the off-line phase, the mutual coupling is establishedbased on the antenna physical properties, and dimensions ofthe test set-up. The receiver probe antenna is characterizedin terms of its mismatches and mutual antenna impedance.These mismatches are included in the measurements whichcan be de-embedded from the mutual impedance model.This characterization is done once per tester load boardand the same probe antenna is used during the test process.During production testing (the online phase), the RF signalis applied at the input of the phased array. If the phasedarray is integrated with an active transmitter, a directionalcoupler can be used to inject the RF signal, as in priortest approaches [8, 9, 12, 14, 21, 23]. The output of eachantenna element is measured at the output of the probeantenna.

The source currents at the transmitting array are obtainedby multiplying the mutual impedance inverse matrix by themeasured voltage at each probe antenna in the receivingarray, as in Eq. 12.

−→Is = Z−1

m,T R

−→Vm (12)

Each element of−→Vm is represented by an amplitudeArxi and

a phase φrxi , plus the gain factor, Grxj , and a path phaseαrxi due to the on-chip circuitry on the signal path to theprobe.

Vmj= GrxiArxie

−j (αrxi+φrxi ) (13)

As shown in Eqs. 9 to 11, Zm,T R depends on physicalproperties of the test setup including antenna separation, d,distance between the transmitting array and the receivingarray, D, antenna element dimension, l, and antenna elementtype. Next, source voltages are obtained by Eq. 14 byemploying the self and mutual couplings between antennaswithin the DUT.−→Vs = Zm,T

−→Is (14)

Where Zm,T is a 16 × 16 matrix as well and is correlatedto the dimensions of the transmitting array. Each element of−→Vs is represented by a source amplitude Ain, a gain factorGtxi , a phase φtxi and a phase mismatch �φi .

Vsj = (Gtx + �Gtxi)Aine−j (iφtx+�φtxi ) (15)

The �Gtxi and �φtxi are our target parameters and areestimated as explained in the next section.

The proposed technique requires sixteen measurementsover a single time frame and several matrix multiplications.

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Fig. 8 Effect of error in ‘D’ ona estimated mean gain error bestimated mean phase error

(a)

(b)

The size of the matrix is determined by the phase arrayelement size. Currently, for commercial systems, thesematrices are 16×16, and for military systems, these matricescan be as large as 256×256. Since the number of elements islimited by physical dimensions, the matrices will not growsignificantly regardless of application (Fig. 5).

To compute test time, we make the following assump-tions: (a) RF signal is above 1 GHz, (b) 1000 periods aresampled, (c) tester RF resource is limited to 4 channels,which requires 4 sequential measurements, (d) tester relaysettling time is 50 ms. Under these assumptions, each RFmeasurement will take 16μs, plus the 50 ms relay settlingtime, resulting in an overall test time of roughly 200 ms.Computational time is negligible compared to the overallmeasurement time.

7 Evaluation of theMeasurement Method

In order to demonstrate and evaluate the proposed testmethodology, we have derived the mathematical model andemulated a 16-element array. Although we experiment witha 16-element system, we strive to obtain a test accuracy that

can be suitable up to 32-element systems. Table 1 showsreported post-calibration element gain and phase errors forvarious 16-element and 32-element systems reported in theliterature. Note that, measurement and calibration are eitherconducted using electrical connection [6, 7, 17, 23], or overthe air by measuring main lobe and side lobe powers usinga movable RF probe in the far field [25]. We strive toprovide measurement accuracy that can enable this level ofcalibration with the antenna in the loop, and in the near field.In order to achieve this, we set our maximum error goalas half the calibrated phase and gain error for the reportedwork. Thus, our goal is to measure gain mismatch within4% error and phase error within 2◦ error. The operationfrequency used in the experiments is 30 GHz with a 10 MHzbandwidth. Antennas are laid out as λ/2 dipoles, separatedwith d = λ/4 on-chip distance. With these variables, thefar field of the antenna system is established approximatelybeyond 28 cm. The distance between the arrays in the testenvironment (D) is set as D = 3λ (3 cm), which placesthe receive antenna system in the near-field of the transmitantenna system. Phased array noise figures reported in theliterature are generally below 10 dB [12, 23]. To account foradditional environment noise, the thermal noise in the test

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Fig. 9 Effect of error in ‘d’ on aestimated mean gain error (b)estimated mean phase error

(a)

(b)

environment is set at 20 dB above the thermal noise level at−84 dBm (KTB+20 dB). We have experimented with up to10◦ phase mismatch and 25% gain mismatch for the DUT.Figure 6 shows the comparison between estimated andactual gain and phase mismatches between transmitter arrayelements for various steering beam directions. Figure 5shows the MATLAB emulation platform for the proposedmethod.

To verify our model, the estimated and actual gain andphase mismatches between transmitter array elements arecompared for ambient noise at −84 dBm. Figure 7 shows an

estimation accuracy of less than 0.05◦ and 0.1% for phaseand gain mismatches respectively.

7.1 Effect of Measurement Noise

The effect of measurement noise power on estimated sourcevoltages is investigated at main beam direction θs = 0◦.In order to evaluate the methodology for a wide set ofrandom gain and phase mismatches, we use Monte-Carlosimulations for 500 samples. Figure 7a shows the totalamplitude RMS error of the source voltages with respect

Fig. 10 Patch antenna geometryunder process variation

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Table 3 Gain and phase mismatches estimation error accounting forprocess variation, load board variation and noise power at θs = 0

�w1, �w2, �w3, �l1 = 0.6μm

�t = 0.5μm,D = 1μm, Noise Floor = − 84 dBm

�G1 0.67% �φ1 0.99◦

�G2 0.93% �φ2 1.13◦

�G3 0.62% �φ3 1.46◦

�G4 1.27% �φ1 0.99◦

�G5 0.67% �φ5 0.87◦

�G6 0.84% �φ 1.54◦

�G7 1.12% �φ7 0.57◦

�G8 0.78% �φ8 0.29◦

�G9 0.88% �φ9 0.33◦

�G10 1.96% �φ10 0.42◦

�G11 1.3% �φ11 0.29◦

�G12 0.65% �φ12 0.57◦

�G13 2.27% �φ13 0.68◦

�G14 4.1% �φ14 0.45◦

�G15 3.9% �φ15 0.97◦

�G16 3.46% �φ16 1.75◦

to the noise power. Figure 7b shows the total phase RMSerror of the source voltages with respect to the noise power.Based on our accuracy target, the proposed method workswell up to −50 dBm noise power, which is much larger thanwhat we expect in a production test environment even whenmultiple such devices are tested on the same floor. Despitethe fairly low SNR at -50dBm noise power, the proposedtechnique produces the desired accuracy. We conclude thatenvironment noise is not a significant source of error for theproposed technique.

We have further investigated the effect of error in distancebetween antennas, D, and error in antenna separation, d,on gain and phase estimation RMS errors. Figure 8 showsthe effect of errors in distance between transmit and receiveantennas. In order to meet the outlined accuracy requirement(2◦ error in phase mismatch measurement and 4% errorin gain mismatch measurement), D needs to be knownwithin less than 0.5% error. This distance is set by thetester load board, as well as the DUT socket dimensions.Theexpected error in these dimensions in the load board isless than 1um. Thus, the maximum error we expect inthis test set-up parameter is less than 0.05%. The effect oferror in antenna separation, d, is shown in Fig. 9. Antennaseparation, d, is a design parameter and will be affected bylithographic process variations. However, this separation istypically in the order of millimeters for higher frequencies,where lithographic errors are in terms of nanometers.Hence, we do not expect that the antenna separation woulddeviate significantly from the design-specified value. The

(a)

(b)

(c)

Fig. 11 Array pattern with and without estimation errors a φtxi = 0◦b φtxi = 30◦ c φtxi = −30◦

346 J Electron Test (2019) 35:335–347

proposed technique is applicable to any arbitrary setup andarray configuration as long as the mutual impedance is char-acterized. The mutual impedance between antennas dependonly on the physical characteristic of the test setup such asantenna type, antenna dimension, distances between antennas,etc. For instance, the mutual impedances between elementsof an array of patch antennas, are demonstrated in [26, 28].

7.2 Effect of Process Variation

Since the mutual impedance obtained during production testis fixed for all chips, the accuracy of our method is subjectto chip-to-chip process variations. To illustrate the effect ofprocess variation on the accuracy of the proposed method,the test setup of Fig. 1 is simulated in ANSYS HFSS. Thepatch antenna array of 16-by-1 is designed at 30GHz on aRogers3006 substrate. Up to 10◦ phase mismatch and 25%gain mismatch are injected into the DUT.

Further, the process corner is extracted from 130 nmCMOS process design manual [5]. Length variation equalto the half of required minimum space (600 nm) is injectedin all the dimensions. Metal thickness variation is alsoinserted (4μm ± 0.5μ m). Figure 10 shows the patchantenna structure and geometric variations. The impedancematrices Zm,T and Zm,T R are obtained before and afterprocess variation and the gain and phase mismatches arecalculated in both cases to find the estimation error dueto process variation. On top of process variations, othersources of error including thermal noise, receiver noisefigure, quantization noise and load board variation, areadded and the DUT antennas mismatches are calculated.The estimation errors are tabulated in Table 3. It is observedthat the maximum phase mismatch estimation error is within2◦ and gain mismatch estimation error is within 4%. Thus,this measurement technique is suitable to replace the costly,far-field measurements with mechanical moving arm RFprobe, at least up to 32-element systems.

Finally, the effect of overall measurements error andprocess variation is investigated in the array far-field pattern.Estimation error is achieved at different beam directions.Figure 11 illustrates the antennas E-plane pattern withoutand with estimated mismatches error at three main beamdirections. For this 16-element system, it is observed thatfor 2◦ error in phase mismatch estimation and maximum 4%error in gain mismatch estimation, the main beam directionmisplacement is �θs < 0.1◦. Its difference on array gain is|�G| < 0.1dB which is very insignificant in practice.

Note that the patch antenna behavior will deviate fromthe ideal dipole model that we used due to lack ofsymmetricity. However, since we are interested in extractingmismatches, the relative changes in the signal behaviorare largely preserved in the simplified model. Thus, oursimulations using the patch antenna results along with

the dipole antenna model is still able to extract the pathmismatches accurately.

8 Conclusion

Integration of the entire transmitter system, includingthe phased array and antennas on the same die is theonly viable solution to meet the stringent requirementsof future wireless systems. Examples of phased arrayantenna integration have already been demonstrated forradar systems. These integrated systems pose a significanttest challenge as the RF phased arrays which need tobe calibrated for effective beam forming. This calibrationrequires detailed characterization of the phased arrayelements. While phased array testing and even built-in self-test has been demonstrated in the literature, there has beenscant work on characterizing phased arrays when thereis no physical connection to the antenna’s output. For alow-cost test solution, it is desirable to place the test set-up in the near field in a fixed location. However, themeasured result needs to be extrapolated to the far field.Mismatches in the phased array and the antennas makethis extrapolation even more difficult. In this paper, wepresented a method for modeling the near-field radiation ofphased array antennas. This model is then used to extract thegain and phase mismatches with the aim of calibrating themat the transmitter. We conclude that with the proposed testmethod, the total gain mismatches can be estimated within4% error and total phase mismatches can be measured withless than 2◦ error at 20dB above the ambient noise level.We also conclude that based on analysis of phased arrayantennas, this accuracy is more than adequate to calibratetoday’s and future phased array systems in the commercialdomain. The proposed method is further explored in acoplanar environment to investigate the effect of the processvariation on the accuracy of mismatch estimation. It showsthat the accuracy is beyond adequate for up to 32-elementsystems. Current silicon based high frequency phased arrayapplications include up to 32 elements [6, 7, 25].

Acknowledgments Authors would like to thank professor RodolfoDiaz for his support and expertise which greatly assisted this research.This work is supported by National Science Foundation with GrantNumber 1617562 and by Semiconductor Research Corporation byTask Number Task 2712.003.

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Maryam Shafiee received the B.S. degree from National Universityof Iran in 2009 and M.Sc. degree from Iran University of Science andTechnology in 2013 both in electrical engineering. She received herPhD degree from Arizona State University in 2018. Her research areasinclude RF/analog design, test and debug. She is currently working asa R&D IC design engineer at Broadcom Ltd.

Sule Ozev received the Ph.D. degree from the Department ofComputer Science and Engineering, University of California at SanDiego, La Jolla, CA, USA, in 2002. She was an Assistant Professorwith the Department of Electrical and Computer Engineering, DukeUniversity, Durham, NC, USA, from 2002 to 2008. Since 2008,she has been an Associate Professor with the School of Electrical,Computer, and Energy Engineering, Arizona State University, Tempe,AZ, USA. Her current research interests include system-level testingand characterization of radio frequency (RF)/analog circuit, testingcost reduction for RF circuits, and RF/analog circuit design. Dr.Ozev has been involved in the organization of many workshopsand conferences, including the IEEE International Conference onComputer Design and the IEEE VLSI Test Symposium. She is aMember of the IEEE.