A STUDY ON THE MUTUAL COUPLING EFFECTS BETWEEN RECTANGULAR PATCH ANTENNAS AS A FUNCTION OF THEIR SEPARATION AND ANGLES OF ELEVATION SEOW THOMAS NATIONAL UNIVERSITY OF SINGAPORE 2003 A STUDY ON THE MUTUAL COUPLING EFFECTS BETWEEN RECTANGULAR PATCH ANTENNAS AS A FUNCTION OF THEIR SEPARATION AND ANGLES OF ELEVATION SEOW THOMAS (B.Eng (Hons), NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2003 Acknowledgement I would like to express my most heart-felt thanks to my supervisor, Prof. M S Leong whose support and advice go beyond the academic subject. The many lessons I have learnt while speaking to and discussing with him will I always carry as reminder and inspiration. I would also like to thank him for his patience and understanding while guiding me. Special thanks are also extended to Mr Sing and Mdm Lee of the Microwave laboratory whose help were invaluable in the antennas fabrication, experimental set-up and results verification of the project. i Table of Contents Acknowledgement i Table of Contents ii Summary iv List of Tables v List of Figures vi Chapter 1: Chapter 2: Chapter 3: Introduction 1.1 Introduction 1.2 Purpose of Research 1.3 Literature Survey 1.4 Objectives 1.5 Organization of Report The Rectangular Microstrip Patch 2.1 Microstrip Antenna Theory 2.2 The Transmission Line Model 10 2.3 The Cavity Model 14 2.4 Choice of Model to use for Study 19 2.5 Design Formulas for Rectangular Patch 20 2.6 Chapter Conclusion 29 Mutual Coupling Between Two Rectangular Patch Antennas 3.1 3.2 Mutual Coupling between two Rectangular Patches on the Same Plane Utilizing the Cavity Model 32 Discussion 41 ii 3.3 Chapter 4: Chapter Conclusion 55 Mutual Coupling Between Two Arbitrarily Oriented Rectangular Patch Antennas Chapter 5: Chapter 6: 4.1 Problem Formulation 57 4.2 Derivation 58 4.3 Analysis of Results 64 4.4 Chapter Conclusion 70 Experimental Verification 5.1 Design of Rectangular Patch 72 5.2 Antenna Fabrication 74 5.3 Measurement and Discussion 77 5.4 Chapter Conclusion 89 Conclusion 6.1 General Observations 90 6.2 Recommendation for Further Research 91 Bibliography 93 iii Summary A study of the mutual coupling between two rectangular patch antennas is presented. It developed formulation of arbitrarily oriented rectangular patches, including different heights and inclinations. This is an extension of traditional studies where the patch antennas under study are oriented in the same direction. The antennas are modeled as magnetic loops by the application of the cavity method. The mutual impedance is worked out using the reaction theorem. Theoretical results for the coupling coefficient are then compared with experimental results. Comparison between theory and experimental results was close especially when the assumptions used in our formulation were adhered to. iv List of Tables Table 1.1: The Advantages and Disadvantages of Microstrip Antennas v List of Figures Figure 2.1 - Top and cross-sectional view of a rectangular microstrip patch Figure 2.2 - Transmission Line Model (a) non-radiating edge feed, (b) radiating edge feed 11 Figure 2.3: The Principles of the Cavity Model 15 Figure 2.4: Coordinate System 19 Figure 2.5: The Rectangular Microstrip Patch Antenna 20 Figure 3.1: Problem Formulation for two Rectangular Microstrip Patch Antennas Lying on the Same Plane 32 Figure 3.2: Plot of Individual Integrals of Z12; where R1, R2 & R3 correspond to the 1st, 2nd & 3rd integral of Z12 – Eqn (3.34) 45 Figure 3.3: Plot of Individual Integrals of Z12; where R1, R2 & R3 correspond to the 1st, 2nd & 3rd integral of Z12 – Eqn (3.29) 46 Figure 3.4: Plot of Individual Integrals of Z12; where R1, R2 & R3 correspond to the 1st, 2nd & 3rd integral of Z12 using k0 instead of k for R3 47 Figure 3.5: Comparison between Cavity Model (Penard) and Transmission Line Model (Transm) for H-plane coupling between rectangular patches 48 vi Figure 3.6: Comparison between Cavity Model (Penard) and Transmission Line Model (Transm) for E-plane coupling between rectangular patches 49 Figure 3.7: Measured Mutual Coupling results according to [1]; values at 1410 MHz for 10.57 cm by 6.55 cm rectangular patches with 0.1575 cm substrate 51 Figure 3.8: Derived H-plane Mutual Coupling results according to Equation (3.2); values at 1410 MHz for 10.57 cm by 6.55 cm rectangular patches with 0.1575 cm substrate 52 Figure 3.9: Measured IS21|2 values at 1.41GHz for 10.57 (radiating edge) x 6.55 cm rectangular patches with 0.1575 cm substrate thickness [1] 53 Figure 3.10: Measured |S21|2 values at 1.44 GHz for circular patches with a 3.85 cm radius and a feed point location at 1.1 cm radius. The substrate thickness is 0.1575 cm [1] 54 Figure 4.1: Problem Formulation for the derivation of the general case of two arbitrarily placed rectangular patches 57 Figure 4.2: Figure showing the magnetic currents and the direction of the patches 58 Figure 5.1: Samples of antennas fabricated for measurements of Variation in the “d” parameters 75 Figure 5.2: One of the two antennas (Antenna A & B) fabricated for angular variation measurements Figure 5.3: HP 8510 Network Analyzer 75 77 vii Figure 5.4: Setup of Measurement for variation in the “d” direction 79 Figure 5.5: Theoretical and Experimental Result of Mutual Coupling Coefficient due to variation in the “d” parameters Figure 5.6: Setup of Measurement for variation in the “f” direction 83 85 Figure 5.7: Theoretical and Experimental Result of Mutual Coupling Coefficient due to variation in the “f” parameters Figure 5.8: Setup of Measurement for angular variation 86 87 Figure 5.9: Theoretical and Experimental Result of Mutual Coupling Coefficient due to Angular variations 88 viii “Infinite” Ground Plane Due to practical reasons, we would have to make use of a ground plane of several wavelengths to approximate an infinite ground plane. This may result in the possibility of unbalanced mode current flowing behind the plane. 5.3.1 S11 Measurement of the Single Rectangular Patch Antenna The S11 of both the single patch antennas (Antennas A & B) were measured to see if they conform to our design to resonant at 1.778 GHz. A sweep of frequencies from GHz to 2.2 GHz was carried out. Their results are as follows: 5.3.1.1 Antenna A The measured S11 is as shown below: Plot of Experimental S11 GHz 2.2GHz -2 S11 (dB) -4 -6 -8 -10 -12 -14 1.778 GHz Freq 1.780 GHz 79 5.3.1.2 Antenna B The measured S11 of Antenna B: Plot of Experimental S11 GHz 2.2GHz -2 S11 (dB) -4 -6 -8 -10 1.778 GHz -12 -14 Freq 5.3.1.2 1.772 GHz Observation From the measurements, we observe that the antennas resonate quite closely to our design frequency of 1.778 GHz (antenna A at 1.780 GHz & antenna B at 1.772 GHz). The slight shift from our design frequency is mostly likely due to the imperfect fabrication process. This is also the reason why they have shifted differently (Antenna A higher than the design frequency while Antenna B lower than the design frequency) from the design frequency of 1.778 GHz. Some factors in the fabrication process that could have affected this are: 80 • Different degree of etching; parts of one antenna could be etched away without notice if left too long in the etching solution, as the etching process is only controlled visually; • Uneven substrate thickness due to physically scratching away of the copper when etchant is unable to remove it. 5.3.2 Measurement of Mutual Coupling Coefficient due to variation in the “d” parameters With the verification that the antennas resonate close to our design, we can now move on to measure the mutual coupling between antennas with variation in the “d” parameters. Figure 5.4 shows the set up of the measurement. 81 Figure 5.4: Setup of Measurement for variation in the “d” direction; such antennas (with different “d”) were fabricated and their S12 measured 82 The measured mutual coupling coefficient together with the theoretical prediction is shown below. -16 20log|S12| -18 x -20 -22 x -24 - theoretical x experimental -26 x -28 x -30 x x -32 x -34 0.05 0.1 0.15 0.2 0.25 d/λ Figure 5.5: Theoretical and Experimental Result of Mutual Coupling Coefficient due to variation in the “d” parameters We can see from the comparison of the theoretical and measured results that the actual mutual coupling behavior between the rectangular microstrip patch antennas bears very close resemblance to theoretical prediction, especially when the distance of the antennas are further apart. The results began to diverge when the antennas are closer than 0.07λ (section 5.3.2). This compares quite closely with the result of Penard and Daniel [2] who showed that the results diverge when antennas are closer than 0.08 λ. This is 83 mainly due to the fact that the interior fields distribution of the patches are much affected when the antennas are too close together. The slight non-conformity in the results where some measurements seemed to deviate “widely” could be due to the fabrication process as each measurement of different “d” were made from a different set of antennas. 84 5.3.3 Measurement of Mutual Coupling Coefficient due to variation in the “f” parameters The setup for the measurement is shown below: Figure 5.6: Setup of Measurement for variation in the “f” direction; such antennas (with different “f”) were fabricated and their S12 measured 85 The measured mutual coupling coefficient together with the theoretical prediction is shown below. 20log|S12| -28 x -29 x x -30 - theoretical x experimental x -31 x -32 -33 x -34 x d/λ -35 0.05 0.1 0.15 0.2 0.25 Figure 5.7: Theoretical and Experimental Result of Mutual Coupling Coefficient due to variation in the “f” parameters Again we see close resemblance between the actual mutual coupling behavior and theoretical prediction of the rectangular microstrip patch antennas, and especially when the distance of the antennas is further apart. The level of coupling when the deviation is in the “f” parameter is much lower as compared to that of variation in only the “d” parameter. This conforms intuitively with the fact that coupling decreases as the antenna are placed further apart. 86 5.3.4 Measurement of Mutual Coupling Coefficient due to Angular variations For this set of measurements, the two single antennas are placed on a paper template with proper distance and angular demarcations, and held in place for the measurements by means of blu-tac. Antenna A is fixed at 45o, (ie. θ= 45o) while antenna B (ie. α) rotates through 0o, 15o, 30o, 45o, 60o, 75o & 90o. “d” is set at 0.03 m (> 0.07 λ), while “f” and “g” are both set to zero. The schematic diagram of the setup for the measurement is shown below: Paper Template with Distance & Angular Demarcation 90o θ Antenna A at fixed θ = 45o z 45o α Angular Demarcation Antenna B rotates through different α x Figure 5.8: Setup of Measurement for angular variation; Angle θ is fixed at 45o, while α is varied from 0o to 90o 87 The result of the measurement together with the theoretical prediction: -31.8 x -31.85 20log|S12| -31.9 x -31.95 x -32 -32.05 - theoretical x experimental x x x -32.1 x -32.15 10 20 30 40 50 60 70 80 90 α/deg Figure 5.9: Theoretical and Experimental Result of Mutual Coupling Coefficient due to Angular variations between Antennas A & B; Angle θ is fixed at 45o, while α is varied from 0o to 90o Here we see a general trend of the measured results when compared to the theoretical prediction. It does not conform as closely as that of the earlier two cases of variation in the “d” and “f” parameters. This is most likely due to the fact that a basic assumption used in our formulation was not adhered to, ie. there is no continuous ground plane and continuous substrate connecting the two antennas. Nevertheless we see that the general trend does follow that of our prediction. 88 Also of particular interest are: • level of variation of coupling when Antenna B is rotated through the angles is low ([...]... Microstrip Antenna” [1] and E Petard & J P Daniel, Mutual Coupling between Microstrip Antennas [2] They have shown both in theory and through experiments the gradual decline of the mutual coupling (S 12 values) between antennas as the distance between the antennas increase Their studies were, however, confined to a single directional variation of the distance between the antennas Emmanuel H Van Lila & Antoine... Antoine R Van De Capable, “Transmission Line Model for Mutual Coupling Between Microstrip Antennas ” [3], takes it a step further in the study of mutual coupling by introducing variation in another direction Expressions for the mutual coupling between antennas that are arbitrarily placed on the same plane were derived The basis of the derivation was on the Transmission line model of the patch antennas 1.4... oriented rectangular patches The antennas need no longer be confined to a singular directional variation It is also not necessary for the antennas to be on the same plane; (ii) to verify the formulation developed through the fabrication of the microstrip patch antennas and the measurement of their Sparameters with the use of a network analyzer 1.5 Organization of Report The report begins with a general study. .. broadly speaking, the objectives of this study are twofold: (I) to develop a mathematical model that can effectively predict the mutual coupling between two rectangular microstrip patch antennas We present the study and formulation of the mutual coupling between rectangular patch antennas that is yet another step 5 ahead of previous studies The formulation that was developed is for a pair of arbitrarily... that many researches have been carried out on the effects on mutual coupling on microstrip patch antennas 4 1.3 Literature Survey From literature survey, we have seen much work done on patch antennas and the mutual coupling between patch antennas that are placed close together Some of the more celebrated studies on mutual coupling were carried out by Wedlock, Poe & Carver “Measured Mutual Coupling Between. .. (ie patch and ground plane) • the current in the coaxial probe is independent of z With these assumptions, we can then solve the wave equations for the electromagnetic field distributions inside the cavity For the rectangular patch, the distribution is a function of the patch geometry [5] 21 2. 5.1 Fields Inside Cavity of the Rectangular Patch Solving the wave equation for the cavity of the rectangular. .. presents the main characteristics and assumptions made in the use of the cavity model to analyze the rectangular patch 7 2. 1 Microstrip Antenna Theory By analogy, the microstrip antenna may be seen as an open circuit element where radiation is caused by the fringing fields at the open circuit ends of the element This thus allows for far field radiated wave propagation The conducting patch may be of any arbitrary... every façade of antenna communications From the battle 2 field to commercial enterprises, the microstrip antenna is fast replacing many conventional antennas The advantages and disadvantages of the Microstrip Antenna are tabulated below: Advantages Disadvantages Thin Profile Low efficiency Lightweight Narrow Bandwidth (1-5%) Simple to manufacture Tolerance Problems Can be made conformal Good quality... quality Substrate required Low Cost Complex feed systems for arrays Compatible with Integrated Circuits Difficult to achieve polarization purity Simple arrays readily created Table 1.1: The Advantages and Disadvantages of Microstrip Antennas It is actually the last advantage in the list above that makes microstrip antennas so popular today Many characteristics of a single microstrip patch antenna can be modified... conductors resembles that of a capacitor with fringing fields For a rectangular patch excited in the dominant mode, the field variation along the patch length is about half of the dielectric wavelength with fringing fields at the edges of the patch length Figure 2. 1 shows a rectangular patch antenna and the radiating edges 8 Top View b Radiating Edges a Feed Point PATCH Side View PATCH Slot 1 Slot 2 . NATIONAL UNIVERSITY OF SINGAPORE 20 03 A STUDY ON THE MUTUAL COUPLING EFFECTS BETWEEN 2 RECTANGULAR PATCH ANTENNAS AS A FUNCTION OF THEIR SEPARATION AND ANGLES OF ELEVATION . A STUDY ON THE MUTUAL COUPLING EFFECTS BETWEEN 2 RECTANGULAR PATCH ANTENNAS AS A FUNCTION OF THEIR SEPARATION AND ANGLES OF ELEVATION SEOW THOMAS . 5.1: Samples of antennas fabricated for measurements of Variation in the “d” parameters 75 Figure 5 .2: One of the two antennas (Antenna A & B) fabricated for angular variation measurements