Injection-locked coupled microstrip leaky-mode antenna
array
C.-N.Hu and C.-KCTzuang
Abstract: Thc papcr prescnts a novel design for an injection-locked microstrip leaky-mode antenna array. It demonstrates that the coupling parametcrs can be obtained numerically, leading to the analysis or the steady-state phasc relationships of the coupled oscillators based on Van der Pol equations for determining the excitation signals of the array. ln particular, it applies the coupled- modc approach to investigating the clcar and considerable mutual coupling effect on the radiation characteristics of the microstrip leaky-mode array. This, in turn. produces a very efficient and accurate assessment of the radiation far-Geld patterns. Finally, a proof-of-concept design using a two- elemcnt injection-locked microstrip leaky-mode array is presentcd for experimental verification, showing excellent agreenient bctweeu theoretical data and measured results.
1 Introduction
Matured MMIC (monolithic microwave integrated circuit) and quasi-optical techniques offer the prospect of reducing construction costs for active phased arrays [ 11, making the application of such arrays a rapidly growing area of rcsearcli [24]. However, the complcxity of the distribution network required increases as the element number of the phased array system grows. Thus a challenge confronts us in designing the signal distribution for large phased array systems. Given tlic large size, high loss and dispersion in conventional transmission mediums, designers are seeking improved methods for high combination efficiencics using quasi-optical spatial power combining techniques [5, 61 and a simpler distribution network layout
[7].
From this perspective, the microstrip Icaky-mode antenna based array becomes attractive bccause it employs a liiicar array to achieve thc pencil beam that otherwise can only bc obtained by conventional two-dimensional arrays incorpo- rating patch resonators or othcr means, grcatly reducing component account. This paper describcs a new design for beam scanning array based on the concept of quasi-optical power combining using tlic microstrip lcaky-mode antenna array. As Fig. I shows, an injection signal from an external stablc source feeds into one end of the activc h e a r array with a unit element comprised of a free-running oscillator and a microstrip leaky-mode antenna. The injection signal couples into and locks the nearest active devices of the microstrip leaky-modc antenna. The latter then synchro- nises with the next sequential unit of the activc antenna element, and so on. As the frequency of the external signal varies, the beam-scanning characteristic is derivcd from thc naturc or the leaky-wave antenna array.Y I
/.
I
C P W s h o r t c i r c u i t9
a ; CPW Xin I open-circuitedU
s h o r t - c i r c u i t e dtin
bFig. 1 Generic; .W-clenieiit injectiuiz lodtecl microstrip leciky-mode anreninrw cirru.y, including CP W q~ici.ri-o/~t~ctil oscil1ator:r; CP W-to-slotline transitions, and slotlirzc,s, fbr excifirix EH, niocle qf indiviclurrl micrmiril, lines, irnd .sirnIJlfied sclie-
rnritic d i q p n i , f i ~ uri/mitw integrcitc.rl with yua,+optic(iI oscillator Lr Antcnna array
I> Schematic diagram of array integratcd with oscillator
I CPW (coplanar wavcguidc) quasi-optical oscillators on back side of suhstratc 2 Microstrip Icaky-modc antciina? with length L , widlh Wand gap S o n top sidc of subslratc
2
Theoretical analysis2.1 Mode coupling
of
complex-wave andcoupling parameters
As Fig. 1 shows, microstrips are placed as close as possible to achieve sufficient coupling Ftrength for an acceptable locking bandwidth. lHowever, coupling between the adja- cent microstrip lines alters the modal spectra of the micros- trip's EH, mode, which is the first higher order of the microstrip mode leaking powcr away in the form of a space wave. By rigorous full-wave analysis [8], one can always obtain both the undisturbed (before coupled) EH, mode of a single microstrip line and all coupled EH1 modes of the microstrip array with fewer elements. Fig. 2 plots the theo- retical results of a 3-element array, clearly indicating the
0 LEE, 2000
LEE Pinceetlings online no. 20000599
DOL IO. 1049/ip-iiiap:20000599
P a p liwl rcccived 14th January and in revised bin1 20111 April 20(N The authors are with tlic Institute of t':lcctiical Coinmunication Engiiieering, Nalional Chiao Tung University, Hsinchu, l'hiwan
effect of mode coupling of complex waves inherent in a microstrip leaky-mode array. The coupled-mode approach [9, IO] states that mode coupling of complex waves inherent in N-element leaky lines is governed by a systcm oT linear differential equations and expressed a s follows:
j = 1
where I,(z) is the modal current vector on microstrip i and C,, is the mutual coupling interaction betwccn the ith and jth elements. Using matrix notation, eqn. 1 is abbreviated as
where B = [diag(X) - [C,]] and
7
= [ I , , 12,...,
I,,,](. When all the coupled microstrips are in equal width, ‘/r must be equal tox
where y is the complcx propagation constant of the EH, leaky mode of a singlc microstrip. On the other hand,N coupled leaky-mode solutions should exist in the iV-ele- ment array, denoted as A,,
4,
...,AN.
For a specific mode with complex propagation constant A,, the modal solution mandates_
d I / t l % = y7
.
I (3) Substituting eqn. 3 into eqn. 2 for i = I , 2, ..., N , we obtainwhere
2
= [diag(A) ~ diag(x)+
[C,]. The source-free rnodalsolutiog require nontrivial solutions for the modal current vcclor
I(z).
Therefore eqn. 4 leads to a standard cigcnvaluc problem by solving( k t
(=>
A = 0(5)
Eqn. 4 clearly demonstrates that one can either attain the A (coupled EH, modes) given [Cy] (the square matrix of coupling parameters) or deducc [Cy] givenA.
Thus, substi- tuting the rigorous data of thc coupled EH, modes(A
shown in the solid line of Fig. 2) into eqn. 4, one can deduce all coupling parameters numerically. The Appendix (Section 8) carries out the detailed formulation for dedic- ing all coupling parameters. By using eqn. 13, Fig. 3 plots the theoretical results of the coupling parameters CI2 and Cl3, revealing that thc strcngth of CI1 ~ coupling due toother-adjacent-element ~ is much smaller than that of Cl2,
nearest-neighbour coupling. 0.8 0.6- 0.L 0 . 2
-
Y \ - - 1 l . O - 0.8 -0.6 c, \ - 0.4 0.2 - UI 9 .I 9.2 9.3 9.1 9 . 52.2 Coupled oscillator theory
A competent theory of coupled oscillators nccds to predict the steady-state phase relationships in the array niinieri- cally. York et al. [6] indicated that coupled Van der Pol
equations adequately describe the coupled oscillator arrays for power combining. With predicted coupling paniineters
Cji (Cji = pjj.LC~ji) by eqn. 13, the equations describing the ainplitude and phase dynamics for an array of N elements can be achieved. From the theoretical results shown in Fig. 3, this work only considers the nearest-neighbour coupling, with pij = 0 for all
1;
~ ,jl # 1. Furthermore, thecoupling is reciprocal. Since the oscillators in the linear array arc cquidistaiit, all of the coupling terms are identical, and the following simplifications are possible: pi,
+
p
and ‘Pi/ =a.
Thus, one can (to first order) ignore the amplitude dynamics. The systcm is then described by [6] as follows:.if i
whcrc i = 1, 2, ..., N , and whcrc I, is the instantaneous amplitude, U, is thc frcc running frequency, and 0; =
wif
+
4;
is the instantaneous phase of oscillators i. Meanwhile Q is the Q-fiictor of the oscillator embcdding circuits. Eqn. 6 allows the steady-state phase diffcrcnccs between each oscil- lator to be solved, given the Tree-running frequencies and computed coupling parameters by cqn. 13.m U
-15
2.3 Radiation pattern
of
an active, coupled,microstrip leaky-mode array
For a coupled microstrip array, each coupled EH, mode is supported by a particular modal current distribution on the strips. This can be viewcd as an eigenvalue corresponding to a specified eigenvector. For instance, another view for distinguishing the two leaky modes of a two-element array is based on the eigenvectors of the modal current distribu- tions on the strips, either in-phase ([1/42, 1/42]) for the EHl even-niodc or out-of-pliasc ([l/42, -11421) Tor the EH, odd- mode. These in-phase and out-of-phase modal current distributions are two orthogonal eigenvectors of the two- elcinent microstrip array from the perspective of the coupled-mode approach. Thus the excitation signal ( P ( O ) ) , which is obtained by eqn. 6 provided that active devices oscillate equal amounts of instantaneous amplitude ([,), may be expressed by superpocitioii of N eigenvectors based on tlic cigcnfunctioii approach, i.e.
2:l
where I / i f ( ( 0 ) is the oscillating signal on the z = 0 plane,
5
is the eigenvector of [A], and LL, represents the modal anipli-tude of the ith coupled EHI modc. Thus, applying Huygcn's principle to an cquivalent current distribution travclling along the microstrip makes it possible to obtain the far-zone electric fields of the Icth microstrip with a length of L [l 11 expressed as follows:
E,
?Eo N 0whcre
z
z
= j (cos B - p i ) - Q;k = 27r/X,
where A, is the free-space wavelength,
p,
(a,)
is the phase (attenuation) constant of tlie ith coupled EH, mode and represents the kth element at the ith eigenvector. Mean- while, the total far-zone electric field E< is the supcrposi- tion of the N-element microstrip leaky-mode array expressed asN
(9)
k l
where x/< is the location of tlie lcth microstrip. Thus, the radiation charactcristics of thc coupled microstrip array can be simulated by tlie following procedures:
(a) Solving the coupled EH, modes of a three-element array by using rigorous full-wave analysis makes it possiblc to deduce the coupling paranicters using cqn. 13.
(b) Substituting thc computed coupling parameters (step (a)) into tlie characteristic equation of [A] in eqn. 4 allows the computation of all the coupled EH, modes
(A!,
i = 1, 2, ..., N) and their corresponding cigenvectors (<,, i = 1, 2,...,
N)
by solving the standard eigenvalue problem (eqn. 5). (c) By substituting computed coupling parameters (in step (a)) into eqn. 6, we can solvc the steady-state phase differ- ence (6,) between oscillators for an empirically determined Q-factor to obtainIIn((O).
(d) With computed ri"'(0) and
E,,
we obtain N excited modal amplitudes (a,, i = 1, 2,...,
N) by solving N linear independent equations derived by eqn. 7.(e) Substituting computed values of U,,
A,
andEl
into cqn. 8makes it possible to simulate thc far-field pattern of thc injection-locked microstrip leaky-mode array.
3
two-element active array
3.
I
Antenna designA two-element niicrostrip leaky-mode antenna array intc- gratcd with a quasi-optical oscillator presents the prototypc of a proof-of-concept design. The slotline underneath the microstrip is employed to excite the EH, mode efficicntly [SI, and also acts as a short-circuited tuning stub to coni- pensate for the imaginary part of the input impedaiicc of thc antenna. Thus, an L-type matching circuit is establishcd in a very compact fashion. Followed by a CPW-to-slotline transition, the slotline is transformed into a CPW (coplanar waveguide) h e to integrate with a quasi-optical oscillator. Fig. lh shows the single antenna impedance matching scheme dcscribed above.
Proposed proof-of-concept design of a
Realising the compact antenna design (as Fig. lh shows) needs the quantitative assessment of the characteristic impedance for the microstrip lcaky mode to provide an insightful circuit-domain view of the leaky line. The input impedance of thc microstrip leaky-mode antenna with length L is exprcssed as
Z,,(w) = - j Z c ( w ) cot
(k,L)
(10) where 2, is the characteristic impedance of the microstrip leaky mode given by [12, 131 aswhere It is the total current on the metal strip, and S is the cross-sectional arca of the microstrip. It is well known that the Icaky line exhibits nonstandard growing behaviour along the transverse plane, resulting in invalid computation of Poyntiiig power. Das [12] reported the method for obtaining tlie leaky-mode characteristic impedance by decomposing the transverse fields into bound fields and leaky fields and considering bound fields only for Poyiiting power computation. Applying this definition, the character- istic impedance of the microstrip leaky mode can be computed by using the 2-D integral equation method [I 31. Fig. 4 plots the theoretical results of the input impedance for this particular design, where the solid line (dashed line) represents the real (imaginary) part of the input impedance for tlie microstrip leaky-mode antenna of length 145mm. With
Z,,
(92.135 - j16.36R) computed at the desirablefrequency of 9.4GHz, the value of shunt inductance (Ls) can be calculated based on circuit theory so that the micro- strip leaky-mode antenna is matched to tlie slotline imped- ance of R,y (95Q). The calculated values of R,s and L,? allow thc dimensions of the slotline of width 15" and length 142nini to be determined.
A
.-
-901
3.2 Quasi-optical oscillator design
Various oscillator designs share similar design procedure regardless of the problem being solved. We first employ lin- ear analysis to obtain the first-order design parameters of the proposed circuit schematic diagram as shown in Fig. 1 h and then apply harmonic balance analysis to predict the oscillation frequency and to optimise the output power. The simulation result indicates the first harmonic at a fre- quency of 9.403GHz with power level of 12.44dBm. The quasi-optical oscillator was optimised to maximise power output for thc desirable pointing direction of the leaky- mode antenna. The complete quasi-optical oscillator was built on a 25"-thick RT/Duroid 6010 substrate with a 366
relative dielectric constant of 10.2. For a frcc-running situa- tion, the near-field pick-up measurement shows that the unlocked source oscillates at 9.415GHz with I1.XdBni power level, which is very close to the simulated result. Meanwhile, the measurement also observes DC-to-RF effi- ciency of 23%) and phase noise of -90dBc/Hz at a IOkHz offset from the carrier.
4 Measurement results
The theoretical prediction of the coupling parameters for the leaky-mode antenna array was first validatcd cxperi- mentally using an imaging technique [6]. A single active microstrip leaky-modc antenna was tuned to a measured free-running frequency of 9.41 5GHz; the microstrip leaky- mode antenna was then positioned near a vertical ground plane, thus simulating two identical, in-phase (for tlic odd- symmetrical nature of the microstrip EHI mode) coupled oscillators. With varying position of the microstrip leaky- mode antenna, a frequency shift was evident which relates to the coupling parameters. Fig. 5 displays the results, and indicates that the theoretical prediction by this approach and by the empirically determined Q-factor of 14. I compares very favourably with array measurement. Subse- quently a prototype, two-element, active array was built for experimental validation. 30 I
9
1 0 - 0- p -10-z
- 2 0 - 0 - 3 0 - x " CT + L L - L O -LEVEL FREQUENCY SPAN1 D I V
HEN ODBM CEN 9 4 2 5 7 8 6 H z
TEK 494AP
IO DBI 20DB 5 4-18 INT IO KHz
VERTICAL R F FREQ REF RESOLUTION DISPLAY ATTEN. RANGE OSC BANDWIDTH
For a free-running situation, the near-field pick-up nieas- urement shows that the unlocked source oscillates at
9.415GHz with 1 I .8dBni output power. Then, an injection locking nicasurcmeiit is talicn. As an external stable source of 12dBm at 9.426GHz is injected into one end of the array, the oscillator is locked and synchronised to the frc- quency of the injection signal through the mutual-coupling interaction between antennas. Fig. 6 shows the spectrum of an injection-locked oscillator, demonstrating 23MHz lock- ing ranges. Furthermore, the measured ERP (effective radi- ated power) of a single- and two-element array is 22.5dBm and 27.3dBm, respectively. Fig. 7 (Fig. 8) plots tlie nieas- ured far-field pattern in the azimuth (clcvation) plane cut at the peak valuc of the main lobe as a comparison with ones by using the rigorous analysis described in Section 2, and good agreement is achieved. As the frequency oT the exter- nal source sweeps, the antenna will siniultancously scan it by phase control in azimuth and by frequency control in elevation. Fig. 9 plots the measurcd far-field patterns in the azimuth plane (x-y plane) cut at the peak valuc or the main beam corresponding to the injected frequencies at 9.406, 9.410 and 9.41 SGHz, respectively. The antcnna beam is scanned to (x-J) planeiy-z plane) equal to 4.6"/44.5", 15.3"/40.9" and l7.5"/36.7", respectively, as the injected fre- quency changes l'rom 9.406 to 9.415GHz. The thcorctical prediction of the beam scanning direction points towards
$/&L (x-y planeiy-z plane) at 3.9"/43.9", 13.4"/4 I .4" and 19.5"/39.2" for tlie respective injection signal frequencies, showing good agreement with measured results.
- 6 0 - L 8 -36 - 2 L -12 0 12 2 L ~ ~ 36
-1
a z i m u t h , deg.Meusured jur$eld bean? scanning patterns controlled by frequencies Fig. 9
of injection sknul
F = (i) 9.406GHz; (ii) 9.41GHz; (iii) 9.415GHz; (iv) 9 .4 1 GH~ (single element)
5 Conclusion
This work has presented an injection-locked microstrip leaky-mode antenna array in which beam scanning has been achieved without using dedicated phase shifters. The coupled-mode approach is adopted to analyse and design an injection-locked coupled microstrip leaky-mode antenna array that considers the mutual coupling of the leaky lines. Finally, this study experimentally verifies the novel design via a two-element, proof-of-concept design, exhibiting 23MHz locking bandwidth, 27.3dBm ERP and one-sided continuous H-plane beam scanning from 5” to 17” for 1 OMHz offset from the free-running frequency of 9.415GHz.
6 Acknowledgement
The authors would like to thank Dr. G.J. Chou and S.D. Chen for their helpful discussion. This work was supported by National Council of the ROC under grant NSC 88- 221 3-EOO9-073 (-101).
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1471-1478 7
8
Roots of thc characteristics polynomial function of
2
are essentially the complex propagation constants for the coupled microstrips array. Thus wc can rewrite eqn. 5 asAppendix: Formulation of coupling coefficients
N
= (A - A,)
z = l
(12) where
AI
(i = 1-N) are eigenvalues to be solved and b, (i = 1-N) are the constant coefficients which are a function of the ‘undisturbed’ leaky mode (y) and gupling coefficients(C,,). Expanding the determinant (det(2 )), and comparing order b; order-at both sides of eqn: 12 for N = ‘3, we obtain the following equations for solving the known cou- PliW c 1 2 and c13, representing the coupling parameters of adjacent and other-than-adjacent elements, respectively: References
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DARYOUSH, A S . : ‘Optical synchronization of’ millimeter-wave oscillators for distributed architectures’. IEEE Trans., 1990, MTT-38, (3), pp. 467476
LIAO, P., and YORK, R.A.: ‘A six-element beam-scanning array’, IEEE Microw. &id. Wuve Lett., 1994, 4, (l), pp. 2&22
y = (A1
+
A 2+
A,) / 37 3 - 2C,2,C13 -
@cf,
+
C&)y = A l A 2+
A 2 X 3 + A 1 A3372 - 2Cf2 -
c&
= X I A 2 A3(1-3)
