full characterisation of varactor-loaded, probe-fed, rectangular, microstrip patch antennas

Full characterisation of varactor-loaded, probe-fed, rectangular, microstrip patch antennas

R.B. Waterhouse N.V. Shuley

Indexing terms: Microstrip patch antennas, Varacfor diode

Abstract: A thorough investigation of the radiation characteristics of a probe-fed microstrip patch loaded with a varactor diode is presented. The theoretical analysis used to model this structure incorporates the full-wave spectral domain integral technique in conjunction with an equivalent circuit model of the varactor diode. Attach- ment modes are used to accurately model the current through the feed and load. Very good agreement between theory and measurement was obtained. From this investigation, the advantages and drawbacks of using varactor diodes to improve the radiation characteristics of a microstrip patch antenna were established. It was shown that large effective bandwidths can be achieved using varactor diodes, although at the expense of reduced antenna efficiency and increased cross-polarisation levels.

1 Introduction

Since the initial development of microstrip patch radiators, several successful techniques to improve their inherent narrow bandwidth have been proposed [l]. These methods are usually divided into two categories, the first of which may be considered as a means of improving the instantaneous bandwidth of the patch. Simplistically, enhancement of the instantaneous bandwidth can be interpreted as a lowering of the Q-factor of the microstrip element. The methods which improve the instantaneous bandwidth of the radiating element include: using low-dielectric material (for example, hard foam with E, = 1.05 [Z]): using a parasitic element (both horizontally [3] and vertically [4]); and using matching structures [S, 61. The second group of techniques to improve the impedance behaviour of the microstrip patch antenna involves increasing the effective bandwidth of the resonator. Here the instantaneous bandwidth generally remains the same (approximately 1-5%); however, the patch can now operate at different frequencies, thereby increasing its usefulness. Loading the microstrip patches with shorting pins [7] or varactor diodes [8] are methods to increase their effective bandwidth.

Q IEE, 1994 Paper 1305 (Ell) , first received 17th August 1993 and in revised form 6th April 1994 The work was done at the Department of Electrical and Computer Engineering, University of Queensland, Brisbane Q L D 4072, Australia R.B. Waterhouse is now with the Department of Communication and Electronic Engineering, Royal Melbourne Institute of Technology, Mel- bourne, VIC3000, Australia

IEE Proc.-Microw. Antennas Propag., Vol. 141, No. 5, October 1994

The possibility of loading microstrip patches with varactor tuning diodes was first proposed in Reference 8. Subsequently, these active devices have been incorpor- ated in several microstrip patch configurations to improve their radiation properties (see for example Refer- ences 9 and 10). Only recently, however, have accurate models of these structures been developed [11-141, thereby allowing the improved characteristics and also the potential drawbacks of a variety of diode-loaded microstrip patches to be thoroughly investigated. Such models have enabled the impedance behaviour of the patch antenna and other related characteristics to be simulated with accuracies to within a few percent. Another important advantage of implementing rigorous full-wave analyses is that they are not limited to thin substrate material.

In this paper the complete characterisation of a probe- fed, rectangular, microstrip patch loaded with a varactor diode is presented. A summary of the analysis method is given, including the technique for accurately modelling the current through the load. The tuning range, input impedance behaviour, co-polar and cross-polar far-field radiation patterns, efficiency and radar cross-section (RCS) for a particular example are displayed using the full-wave solution, and the predicted results are compared to experimental data when possible. From the results presented, the advantages and drawbacks of using varactor diodes to improve the radiation characteristics of microstrip patches become evident. It is shown that, although a varactor diode can be used to increase the effective bandwidth of a microstrip patch, at low applied bias levels the power dissipated in the diode can become large, thereby reducing the antenna efficiency as well as increasing the cross-polarisation currents.

2 Theory

Consider a probe-fed, microstrip, rectangular patch loaded with a varactor diode, as depicted in Fig. la. Here the patch of resonant length L and width W is fed by a coaxial probe positioned at (xplr ypl). The varactor diode used to load the microstrip patch is located at ( x p 2 , y p 2 ) and has an equivalent circuit as shown in Fig. l b [l5]. In Fig. l b Cj is the varactor diode junction capacitance, R,

The authors wish to acknowledge discussions on the concept of this topic with Drs. M. Majewski and D. Novak. The authors also wish to thank Dr. J. Aberle for the derivations of RCS and eff- ciency used in the analysis. Finally the authors wish to thank Mitec Ltd. for the construction of

361

is the spreading resistance associated with the ohmic contact and the finite thickness of the epitaxial layer, and L, and C , represent parasitics associated with the pack-

!'

ground plane a b

Fig. 1 diode a Illustration b Equivaknt circuit diagram of the varactor diode

Probe-jed rectangular microstrip patch loaded with a uaractor

aging of the device. As the diode is reverse-biased at all times, it can be assumed that the junction resistance will be very large and may therefore be ignored. The bias dependence of the junction capacitance in reverse bias can be simply expressed as [ 151

cjiv=f$J 1 - -

where C,{O) is the junction capacitance at 0 V bias and Qbi is the built-in voltage of the diode (for silicon mbi = 0.7 V).

To analyse the probe-fed patch loaded with the varactor diode, the varactor diode is modelled as a metallic conductor of the same diameter as the diode, which is subsequently loaded with the lumped equivalent circuit at the base of this probe. Thus to determine the radiation characteristics of the loaded patch, the port impedances of this system are required. For this antenna configuration a two-port network (as shown in Fig. 2) was implemented. -

two-port system load port

Fig. 2 Schematic representation of a two-port system

To model accurately the feed and load currents, the electric field integral equation (EFIE) is examined. The EFIE ensures the boundary condition, namely that the total tangential field on the patch, as well as the feed and load, must vanish, is enforced when either of the feed port or load port is excited. The two equations representing the EFIE can be written as:

on patch, feed and load. In eqn. 2, Er' is the electric field scattered by the feed port, the load port and the patch. The expression for the scattered electric field and the related Green functions can be found in Reference 16. The driving sources are assumed to be delta-gap gener- ators at the base of the feed or load, with incident fields

368

given by :

where ( x p k , ypk) are the x and y coordinates of the feed (k = 1) and load (k = 2) location on the patch. Thus in this analysis, as described above, the varactor diode is modelled as a lumped load at the base of a perfectly con- ducting pin.

Using the moment method, the current density on the feed, load and patch is expanded by a set of N vector basis functions:

Each expansion mode may have a component on the patch, feed and load.

The EFIE of eqn. 2 is discretised using the Galerkin method, and Can be written in matrix form as

CzlCrl = [U, k = 1 , 2 (5 ) where the impedance matrix elements and the voltage vector elements can be determined from eqns. 15-17 in Reference 16, generalised for a two-excitation case.

To model accurately the current on the feed and through the diode, two attachment modes of the form given in Reference 17 were implemented. The use of these modes ensures current continuity between the feed, load and the patch; it also enables accurate modelling of the singularities at these positions. The distribution of the attachment modes on the feed and through the load is assumed to be a pulse function; however, this can be easily modified if a more accurate representation of the current flowing through the feed and load pins is required. Therefore the first mode, namely an attachment mode, has a distribution on the feed and the pat& and no distribution through the load. The second mode, another attachment mode, has a distribution on the load pin and the patch, and no distribution on the feed. In addition to these modes, a series of entire domain basis functions (typically six) based on the cavity model solution (with only a distribution on the patch) are used (the form of these is given in References 16 and 17).

The short-circuit port impedances [17] can be determined once eqn. 5 has been solved for the current coeff- cients. Using these results, the input impedance can be expressed as

where Z D is the impedance of the varactor diode. To determine the far fields radiated from the probe-fed

loaded patch, the current distribution on the antenna is required. The current distribution can be obtained from the superposition of the currents due to each port source of the multiport system, with the proper weighting of the port current associated with the load [18]. Using the expressions derived in Reference 19 the far fields can then be calculated.

The efficiency of the varactor-tuned microstrip patch can be defined as [ 12,201 :

(7)

where Pin is the total input power to the antenna (which includes radiated power, power lost to surface waves, and

I E E Proc.-Microw. Antennas Propag., Vol. 141, No. 5, October I994

power dissipated in the lossy substrate and in the diode) and P , is the power dissipated in the diode. As will be shown below, the amount of power dissipated in the diode is very important, particularly if large tuning ranges are required.

The radar cross-section (RCS) of a diode-loaded microstrip patch can be determined by modifying the for- mulation of RCS for an unloaded patch (as given in Ref- erences 19 and 21) to account for the loading effect of the diode impedance. This is achieved by including the diode equivalent impedance in the impedance matrix equation (eqn. 9) for the component associated with the self- impedance of the attachment mode at the load port. This is the same technique as used in Reference 21 to account for the 50 R termination at the probe feed, and thus can be considered an extension to a two-port case.

3 Results

To investigate the performance of a single probe-fed rectangular patch loaded with a varactor diode, a 13.6 mm x 16.4 mm microstrip patch was etched using the substrate Arlon LX (thickness, d = 0.7874 mm and relative dielectric constant E, = 2.17). For reasons of symmetry the probe feed and diode load were positioned at x p , = 3 mm and x p 2 = -3 mm, respectively, along the x-axis (see Fig. 1). To position the diode a small hole was drilled through the substrate and the diode was soldered into place. The diode used to load the patch was an Alpha Schottky barrier detector diode, model DMF 3078. The circuit parameters of the diode were obtained from the manufacturer's data sheet and are: CJO) = 0.8 pF, RJO) = 1 MR, R, = 7 R, L, = 0.5 nH and C, = 0.06 pF. All impedance measurements were carried out using a HP 8510 network analyser. Eight basis functions, including two attachment modes, were used for the simu- lations.

Fig. 3 shows the variation in resonant frequency of the diode-loaded microstrip patch with applied reverse bias

6.41 I

0 0 0.5 1.0 1.5 20 2 5 30 bias,-V

Fig. 3 Measured and calculted resonant jiequency against bias level for single probe-fed rectangular patch loaded with diode ~,=2.17, d=0.7874mm, L=13.6mm. W=16.4mm, x P , = - x , , = 3 . 0 m m ,

C Expenmen1 Theory

Y,, = Y,2 = 0

levels in the range 0 to -3 V. Also shown is a comparison with the theoretical predictions, and (as is clearly evident) very good agreement between theory and experi-

I E E Proc.-Microw. Antennas Propag., Vol. 141, No. 5, October 1994

ment was obtained. The error in the resonant frequency (less than 1%) is well within the tolerances of the substrate's material parameters, as are the small errors in the positioning of the diode. A tuning range of approximately 350 MHz was obtained, which may be interpreted as an effective 10 dB return loss bandwidth of approximately 10%. It should be pointed out that a broader range could have been achieved by using a more suitable diode, namely one with a larger tuning capacitance.

Fig. 4 shows the impedance behaviour of the loaded patch when the diode is biased at -3 V (the maximum

0'71

- $ 0.3 o'L t 0.0

6 6

/

frequency, GHz

Fig. 4 loaded probe-fed patch at bias leuel -3 V ~ Experiment

Theory

Experimental and theoretical reflection c m c i e n t s of diode-

bias level that can be applied to the diode). As can be seen from the graph, excellent agreement between theory and experiment was obtained. The measured and predicted instantaneous 10 dB bandwidths were 225 and 220 MHz, respectively (approximately 3.3%). It is interesting to compare these values with the instantaneous bandwidth of the unloaded rectangular microstrip patch antenna. The measured unloaded bandwidth was approximately 160 MHz or 2.25%. The increase in instantaneous bandwidth can be attribute6 to the power dissipated in the diode (a consequence of the real component of the equivalent diode impedance), which in simplistic terms lowers the instantaneous Q-factor of the resonating element, thereby giving an increase in the bandwidth. There are at the same time, however, some disadvantages related to this effect, and these will be referred to below.

The measured return loss of the loaded patch when the diode is biased at 0 V is shown in Fig. 5. The minimum return loss occurs at 6.5GHz and the 10dB bandwidth is approximately 3.08%. Also shown in this Figure is the predicted return loss, which once again shows good agreement with the experimental data. The error in the frequency location of the minimum return loss is -0.38% and the predicted bandwidth of the loaded patch at 0 V bias is 3.5%. The explanation given earlier for the increase in instantaneous bandwidth is also applicable here.

A comparison of the measured and predicted E-plane far-field radiation patterns of the loaded patch when the diode is biased to - 3 V (corresponding to a resonance of approximately 6.85 GHz) is shown in Fig. 6. Good agreement was achieved between the results given by the

369

theory derived in Section 2 and measurements; however, at scan angles greater than 45" an error between experiment and theory to within 2.5 dB was present. Originally

at the particular 0. Therefore a direct comparison of the copolarised and the cross-polarised patterns cannot be made from this graph. The unloaded patch calculations

-201 6 2 6-4 6.6 6.8

f requency.GHz

Fig. 5 fed patch at bias level 0 0 Experiment

Theory

Experimental and theoretical return loss oJdiode-loaded probe-

-201 -80 -60 -LO -20 0 20 40 60 80

Q.deg

Fig. 8 with diode biased at - 3 V ~ Theory

E-plane Jar-field radiation pattern of probelfed patch loaded

...... Experiment

this error was thought to be associated with the finite ground plane of the patch resonator; however, it was later shown to be directly related to the poor dynamic range and resolution of the six-port receiver system in the anechoic chamber [22].

Unfortunately, as a result of the limited dynamic range of the receiver used in the anechoic chamber [22], no measurements of cross-polarisation could be made. To illustrate the effect of the diode on this quantity, the theoretical unloaded and loaded H-plane copolarisation and cross-polarisation (using Ludwig's third definition [23]) radiation patterns for the patch were calculated, and a comparison of the unloaded and loaded quantities are presented in Fig. 7. It should be noted that the copolarised field pattern at a particular angle 0 is normalised with respect to the maximum field value (occurring at 0 = 0), and the cross-polarised pattern is a ratio of EJE,

370

8.deg

Fig. 7 Comparison of H-plane Jar-field copolar and cross-polar radiation pattern o/ probelfed patch when unloaded and loaded with diode biased at - 3 V ~ Capolar (unloaded, 7.125 GHz) . . . . . . . Copolar (loaded, 6.85 GHz) _ _ _ _ Cross-polar (unloaded, 7.125 GHz)

Cross-polar (loaded, 6.85 GHz)

were made at 7.125 GHz (the resonant frequency of the unloaded patch) and the loaded calculations were made at 6.85 GHz. As can be seen in Fig. 7, the copolarisation levels are very similar; however, there is a significant variation in the cross-polarisation of the two structures. The predicted increase in cross-polarisation level when the patch is loaded can be attributed to two mechanisms, the first of which is related to the physical positioning of the varactor diode, and the other of which is due to the loading effect of the diode. In general, owing to the discontinuity associated with the placement of the diode, the generation of cross-polarisation currents (in this case y- directed, as in Fig. 1) is likely to increase. However, if the diode is placed symmetrically opposite the feed position with respect to the centre of the patch, then cancellation of these cross-polarisation currents should occur (similarly to a balanced feed configuration). This is indeed the case, and the effect of the diode position on the patch on the cross-polarisation level will be fully investigated below.

The observed increase in cross-polarisation in Fig. 7 can therefore be attributed to the loading effect of the diode on the resonator. As the diode draws more current the symmetry of the radiating structure is lost, and thus there is an increase in the cross-polarisation currents and the resulting cross-polarisation level. This is evident from an examination of Fig. 8, which shows a comparison of the H-plane copolarisation and the cross-polarisation levels of the loaded patch at two bias levels (- 3 and 0 V). Once again, a direct comparison of the copolarised and the cross-polarised patterns cannot be made from Fig. 8, owing to the reasons outlined in the preceding para- graph. As the bias level applied to the diode is decreased, the diode draws more current, and thus the symmetry is reduced, which leads to an increase in the cross- polarisation level. Two conclusions can be drawn from the results presented in Fig. 8. First, at the extremes of the tuning range (when the bias level to the diode is small), the cross-polarisation level is significantly increased. Secondly, the level of cross-polarisation generated will depend on the characteristics of the diode. It

I E E Proc.-Microw. Antennas Propag., Vol. 141, No. 5 , October 1994

was shown in Reference 20 for infinite arrays of probe-fed microstrip patches loaded with varactor diodes, that not only can the cross-polarisation levels be minimised using

e.deg

Fig. 8 Comparison of H-plane farrfield copolar and cross-polar radiation pattern ofprobe-jed patch when loaded with diode biased at 0 and - 3 v _ _ Copolar (bias = 0)

_ _ _ ~ Cross-polar (bias = 0) . . Copolar (bias = - 3 V)

Cross-polar (bias = - 3 V)

a symmetrical configuration, but also the level can actually be reduced (with respect to an unloaded patch at particular biases).

Another interesting observation can be made from Fig. 8 regarding the copolarisation far-field radiation pattern. The 3 dB beamwidth is reduced as the bias to the diode is decreased. From Fig. 8, the H-plane 3dB beamwidth when the diode is biased at -3 V is approximately 75", compared with 55" when there is no bias applied to the diode. This phenomenon can be attributed to the reduced efficiency of the radiator as the bias level to the diode decreases. From eqn. 7 the efficiency of the diode-loaded microstrip patch can be determined once the current through the diode is known. The results for the particular configuration under analysis are displayed in Table 1. As these results indicate, the efficiency is sig-

Table 1 : Radiation efficiency of diode-loaded probe-fed Datch at several bias levels

Bias Efficiencv

V Yo -3.0 78.34 -1.0 67.33 0.0 49.05

nificantly reduced when the applied bias level to the diode is decreased: from 78.34% at -3 V to less than 50% at 0 V. Of course, this efficiency is dependent on the characteristics of the diode used, as well as on the parameters of the microstrip patch. As was shown in References 12 and 20, high efficiencies (greater than 90%) can be obtained, operating at a broader range of frequencies, if appropriate choices of varactor diode and patch are made. It should be noted that a similar reduction in beamwidth to that shown in Fig. 8 was observed in Ref- erence 7, where tuning stubs were used to vary the resonant frequency.

Perhaps the best means of summarising the above results is to investigate the radar cross-section (RCS) of the antenna structure. Using the technique outlined in

IEE Proc.-Microw. Antennas Propag., Vol. 141, No. 5, October 1994

Reference 21, Fig. 9 gives a comparison of the RCS for the unloaded patch and the loaded case when the diode is biased at -3 and 0 V. As can be seen from Fig. 9, the

-401 6.2 6.L 6 6 6.8 7 0 7.2 7.4 7 6

frequency,GHz

Fig. 9 Comparison of radar cross-section of single probe-jed patch when unloaded and loaded with diode biased at 0 and - 3 V (0 = 0, 4 = 0) 0 Unloaded + Loaded (bias = ~ 3 V) A Loaded (bias = 0)

peak in RCS shifts according to the change in resonant frequency when the patch is loaded. This phenomenon is in agreement with the results presented in Reference 12 for a loaded circular patch. For the situation when a 0 V bias level is applied to the diode, the RCS peaks at the resonant frequency of 6.475 GHz and is significantly lower than the unloaded peak (approximately 7.125 GHz). From this result an application of the loaded patch resonator, other than an effectively broadband radiator, can be found. By simply decreasing the applied bias to the varactor diode, the RCS of the antenna can be reduced; this presents an ideal technique to avoid threat frequencies. The frequency of operation of the antenna is designed at a high varactor diode bias level, and when a reduction in the RCS is required the bias to the diode is simply switched off.

The effect of the location of the varactor diode on the microstrip patch antenna will now be investigated. It was stated in References 11 and 12 that if the diode were to be positioned closer to the radiating edge, a stronger coupling between the patch fields and the varactor diode would exist, and therefore a greater tuning range could be expected. This was verified in Reference 11 with an example of an edge-fed patch loaded with two diodes. Consider the probe-fed patch previously analysed, now loaded with the same varactor diode; however, the varactor diode is now located at xpz = -5.5 mm. Using the analysis derived in Section 2, the amount of junction capacitance required to achieve resonance at 6.475 GHz is 0.42 pF. This is considerably less than the capacitance required when the varactor diode is positioned symmetrically opposite the probe feed ( C j = 0.8 pF). Thus it can be concluded that a greater tuning range of the loaded patch can be achieved if the same varactor diode is located near one of the radiating edges.

Owing to the reduced loading effect of the varactor diode on the patch when the diode is located closer to a radiating edge, the efficiency is also expected to be higher, which is indeed the case. For a resonance at 6.85 GHz the efficiency when the diode is positioned at xp2 =

371

I -5.5mm is 85.43%, compared with 78.34% when the diode and feed are. symmetrically positioned. However, the drawback associated with placing the diode close to a radiating edge is the increased level of cross-polarised fields generated. Fig. 10 shows a comparison of the

4 0 1 I

-75 -50 -25 0 25 50 75 e.deg

Fig. 10 londed probe-jed patch with diode located at xP2 = -3.0 mm and xp2 = -5.5 mm - x,, = -3.Omm

Comparison of calculated H-plane cross-polarisation levels for

x,, = -5.5 mm _ - - -

H-plane cross-polarisation level for the two varactor diode positions when each loaded patch is operating at 6.475 GHz. The level of cross-polarisation is considerably greater when the varactor diode is located closer to the radiating edge, even though less current is drawn by the diode. The rigorous analysis used to generate the results in Fig. 10 confirms the expectation that an unsymmetri- cal configuration will increase the likelihood of cross- polarisation generation in a diode-loaded microstrip patch.

Finally, it is interesting to compare the directive gain of an unloaded patch to that of a loaded patch. Since the operating frequency of a loaded patch is lowered when the diode is biased, the effective area of the antenna is smaller than that of an unloaded patch antenna radiating at the same frequency. Consider an unloaded patch designed to resonate at 2.5 GHz. Using the definition of directive gain given in Reference 23 the gain of this element is 7.1 dBi. If we now consider a patch loaded with a hypothetical lossless diode, and if this radiating structure is also designed to resonate at the same frequency, the diode-loaded patch has a directive gain at 6.5 dBi. Therefore the reduction in area that occurs for a loaded patch also results in a decrease in the directive gain.

4 Conclusions

In this paper probe-fed rectangular microstrip patches loaded with varactor diodes have been thoroughly investigated. A multiport full-wave analysis which incorporates an equivalent circuit model of the diode has been derived for a single probe-fed patch loaded with a varactor diode, and a rigorous technique was developed to model accurately the current through the diode and coaxial feed. This was achieved by using special attachment modes, which also account for the discontinuity between the feed and the patch and between the varactor diode and the

372

patch. Very good agreement between experiment and theory for the resonant frequency, input impedance behaviour and far-field patterns of the loaded patch was achieved. An investigation of the effect of the position of the varactor diodes on the tuning range for the radiating structures has been presented. A thorough examination of the efficiency, cross-polarisation level generation and radar cross-section for the probe-fed patch loaded with a varactor diode has also been given, and from this investigation a novel technique was proposed to reduce the detectability of a microstrip patch antenna.

It is clear that varactor diodes can be used to provide broad effective bandwidth operation for microstrip patches. Some precautions are necessary, however espe- cially at low bias levels when the power dissipated in the diode can become significant, and can thus reduce the efficiency of the radiator and increase the generation of cross-polarised fields. The incorporation of symmetrical configurations can lower the level of cross-polarisation if the loading by the varactor diode is not too great.

5 References

1 JAMES, J.R., and HALL, P.S.: ‘Handbook of microstrip antennas’ (Peter Peregrinus, London, UK, 1989)

2 ZURCHER, J.-F.: “The SSFIP: a global concept for high performance broadband planar antennas’, Electron. Lett., 1988, 24, pp. 1433-1435

3 KUMAR, G., and GUPTA, K.C.: ‘Broadband microstrip antennas using additional resonators gap coupled to the radiating edges’, IEEE Trans. Antennns Propng., 1984.32, pp. 1375-1379

4 SMITH, H.K., and MAYES, P.E.: ‘Stacking resonators to increase the bandwidth of low profile antennas’, IEEE Trans. Antennns Propng., 1987,35, pp. 1473-1476

5 POZAR, D.M., and KAUFMAN, B.: ‘Increasing the bandwidth of a microstrip antenna by proximity coupling’, Electron. Lett., 1987, 23, pp. 366369

6 PUES, H.F., and VAN DE CAPELLE, A.R.: ‘An impedance matching technique for increasing the bandwidth of microstrip antennas’, IEEE Trans. Antennas Propag., 1989,31, pp. 1345-1354

7 ALI-KHAN, A., RICHARDS, W.F., and LONG, S.A.: ‘Impedance control of microstrip antennas using reactive loading’, IEEE Trans. Antennas Propng., 1989,37, pp. 247-251

8 BHARTIA, P., and BAHL, 1.J.: ‘Frequency agile microstrip antennas’, Microwave J., 1982,25, pp. 67-70

9 HASKINS, P.M., HALL, P.S., and DAHELE, J.S.: ‘Active patch antenna element with diode tuning’, Electron. Lett., 1991, 21, pp. 1846-1848

10 WATERHOUSE, R.B., and SHULEY, N.V.: ‘Dual frequency microstrip patches’, Electron. Lett., 1992.28, pp. 606-607

11 WATERHOUSE, R.B., and SHULEY, N.V.: ‘Analysis of microstrip patch antennas with broad bandwidth and frequency agility using Schottky-barrier diodes’. Proc. 3rd Int. Symp. Recent Advances in Microwave Technology, Reno, USA, 1991, pp. 277-230

12 ABERLE, J.T., CHU, M., and BIRTCHER, C.R.: ‘Scattering and radiation properties of varactor tuned microstrip antennas’. Proc. IEEE Symp. on Antennas Propagation, Chicago, USA, 1992, pp. 2229-2232

13 WATERHOUSE, R.B., and SHULEY, N.V.: ‘Frequency agile microstrip rectangular patches using varactor diodes’. Proc. IEEE Symp. Antennas Propagation, Chicago, USA, 1992, pp. 21862191

14 WATERHOUSE, R.B., and SHULEY, N.V.: ‘Tunable probe-fed microstrip rectangular patch antennas using Schottky-barrier diodes’. Proc. URSI Symp. Electromagnetic Theory, Sydney, Aus- tralia, 1992, pp. 427-429

15 WATSON, H.A.: ‘Microwave semiconductor devices and their circuit application’ (Maraw-Hill, New York, 1969)

16 ABERLE, J.T., and POZAR, D.M.: ‘Accurate and versatile solu- tions for probe fed microstrip patch antennas and arrays’, Electro- mngn., 1991, 11, pp. 1-19

17 ABERLE, J.T., and POZAR, D:M.: ‘Analysis of infinite arrays of probe fed rectangular microstrip patches using a rigorous feed model’, IEE Proc. H, 1989,136, pp. 110-119

18 HARRINGTON, R.F.: ‘Field computation by moment methods’ (MacMillan, New York, 1968)

19 POZAR, D.M.: ‘Radiation and scattering from a microstrip patch on a uniaxial substrate’, IEEE Trans. Antennns Propng., 1987, 35, pp. 613-621

IEE Proc.-Microw. Antennas Propng.. Vol. 141, No. 5, October 1994

20 WATERHOUSE, R.B., and SHULEY, N.V.: ‘Scan performance of infinite arrays of mirostrip patch elements loaded with varactor diodes’, IEEE Trans. Antennas Propag., 1993,41, pp. 2173-2180

21 ABERLE, J.T., POZAR, D.M., and BIRTCHER, C.R.: ‘Evaluation of input impedance and radar cross section of probe fed microstrip

Antennas Propug., 1991.39, pp. 1691-1697

22 DIMITRIOS, A.: ‘Antenna testing facility for small radiators’. Masters of Engineering Science Thesis, Department of Electrical and Computer Engineering, University of Queensland, 1993

23 RUDGE, A.W., MILNE, K., OLVER, A.D., and KNIGHT, P.: ‘The handbook of antenna design’ (Peter Peregrinus, New York, 1982),

patch elements using an accurate feed model’, IEEE Trans. Vol. 1

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full characterisation of varactor-loaded, probe-fed, rectangular, microstrip patch antennas

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