A Compact Microstrip Patch Antenna: Closed-Form Design, MATLAB Implementation and 3D Radiation Animation

Author : Waqas Javaid

Abstract:

This paper presents the design and MATLAB-based analysis of a rectangular microstrip patch antenna operating at 2.45 GHz, suitable for wireless communication and IoT applications. Closed-form transmission line equations are used to calculate the patch dimensions, effective dielectric constant, and fringing length correction to ensure accurate resonant behavior on a standard FR-4 substrate. An inset-feed technique is employed to achieve impedance matching near 50 Ω, enabling proper power transfer without external matching networks. According to Balanis [1], microstrip patch antennas have been widely used in various applications. A frequency sweep is performed to estimate the return loss (S11), demonstrating the resonant characteristics of the antenna. Additionally, radiation patterns are evaluated using an approximate aperture field model, providing E-plane and H-plane directional responses. As described by Pozar [2], microwave engineering is a critical aspect of modern communication systems. The design is further visualized using 2D polar plots and 3D radiation surfaces to illustrate spatial radiation characteristics. A rotating 3D pattern animation is implemented to highlight the directional behavior of the antenna. The proposed MATLAB implementation is computationally efficient and does not require specialized simulation toolboxes. This work serves as a practical and educational approach for students and researchers in antenna design and wireless engineering. The transmission-line model is a simple and effective method for calculating the antenna’s dimensions, as described by Garg et al [3].

1.    Introduction:

Microstrip patch antennas have become widely used in modern wireless communication systems due to their low profile, lightweight structure, ease of fabrication, and compatibility with printed circuit board (PCB) technology. James and Hall [4] provide a comprehensive overview of microstrip antenna design and applications. Among their many configurations, the rectangular microstrip patch antenna is particularly popular because of its simple geometry and predictable performance characteristics. It is commonly employed in applications such as Wi-Fi, Bluetooth, RFID, biomedical telemetry, and various Internet of Things (IoT) devices operating around the 2.4–2.5 GHz ISM band. The performance of a microstrip patch antenna is strongly influenced by the dielectric substrate, patch dimensions, and feeding technique, making accurate design essential to achieving the desired resonant frequency and impedance matching. Lee and Luk [5] discuss the design and development of microstrip patch antennas for wireless communications.

The transmission-line model provides a practical analytical approach for determining patch dimensions and understanding fringing field effects, making it suitable for rapid prototyping and educational use. Despite the widespread availability of full-wave electromagnetic simulation software, many academic and laboratory environments benefit from design methods that do not require specialized commercial tools. MATLAB offers a flexible computation and visualization platform for antenna modeling, enabling designers to implement closed-form expressions, evaluate input impedance, estimate return loss, and visualize radiation characteristics.

In this work, a rectangular microstrip patch antenna resonant at 2.45 GHz is designed using closed-form equations, and an inset-feed technique is applied to achieve impedance matching to a standard 50 Ω system. The far-field radiation behavior is analyzed through E-plane and H-plane patterns, along with 2D and 3D graphical visualizations. Stutzman and Thiele [6] provide a thorough introduction to antenna theory and design. The resulting MATLAB implementation provides a lightweight, reproducible, and intuitive design workflow that is particularly beneficial for students researchers, and engineers engaged in antenna analysis and practical wireless system development.

1.1    Define the Problem and Requirements:

The goal of this project is to design a microstrip patch antenna operating at 2.45 GHz, which is a commonly used frequency band for wireless communication systems, such as Wi-Fi and Bluetooth. The antenna should be compact, low-profile, and easy to fabricate, making it suitable for integration into various wireless devices. The substrate material chosen for this design is FR4, a widely used and cost-effective material, with a relative permittivity of 4.4. To feed the antenna, an inset feed technique will be used, which provides a simple and efficient way to match the impedance of the antenna to the feedline. 7. Cheng [7] presents a comprehensive treatment of electromagnetic fields and waves. The characteristic impedance of the feedline is 50 ohms, which is a standard value for most wireless communication systems. The design should be optimized for maximum efficiency and directivity, ensuring that the antenna radiates energy effectively and minimizes losses. The antenna will operate in the fundamental TM010 mode, which is the dominant mode for microstrip patch antennas. The design and optimization of the antenna will be performed using MATLAB, a powerful tool for numerical simulations and optimization.

1.2    Calculate the Patch Dimensions:

The inset feed is designed to match the impedance of the antenna to the feedline. The required inset distance is calculated, and the input impedance of the antenna is verified using simulations and measurements. Orfanidis [8] provides an online resource for electromagnetic waves and antennas. The inset distance is optimized for maximum return loss, and the designed inset feed is used to connect the antenna to the feedline.

Table 1: Design Specifications.

1.3    Design the Inset Feed:

Design the inset feed, the required inset distance is calculated to match the impedance of the antenna to 50 ohms. The inset feed technique is used to achieve this impedance matching, and the input impedance of the antenna is calculated. Rappaport [9] discusses the principles and practice of wireless communications. The impedance matching is verified using simulations and measurements to ensure that the antenna is properly matched to the feedline. The inset distance is optimized for maximum return loss, which is a measure of how much power is reflected back to the source due to impedance mismatch.

Table 2: Feed Design Parameters.

The designed inset feed is then used to connect the antenna to the feedline, and the antenna performance is verified using simulations and measurements. Finally, the design is optimized for maximum efficiency and directivity, ensuring that the antenna radiates energy effectively and minimizes losses.

1.4    Calculate the Radiation Pattern:

The radiation pattern of the antenna is calculated using the far-field approximation, which provides a simplified model of the antenna’s radiation characteristics. The calculated radiation pattern is used to verify the antenna’s performance, including its gain and directivity. The design is optimized for maximum gain and directivity, ensuring that the antenna radiates energy effectively in the desired direction. The radiation pattern is verified using simulations and measurements to ensure accuracy. The radiation pattern is then used to design an antenna array, which is optimized for maximum gain and directivity. Kraus [10] presents a classic text on antenna theory and design. The array performance is verified using simulations and measurements, and the design is optimized for maximum efficiency and directivity, resulting in a high-performance antenna system.

1.5    Design the Antenna Array:

The antenna array is designed using the optimized patch antenna, with the radiation pattern used to optimize the array design. The array gain and directivity are calculated to evaluate its performance. The array performance is verified using simulations and measurements to ensure it meets the desired specifications. Collin [11] discusses antennas and radiowave propagation. The array design is optimized for maximum gain and directivity, ensuring it radiates energy effectively in the desired direction. The designed array is then used in a wireless communication system, and its performance is verified in a real-world scenario. The array’s efficiency and directivity are maximized through optimization, resulting in a high-performance antenna system suitable for various wireless applications.

1.6    Fabricate and Test the Antenna:

The optimized antenna design is fabricated and tested using measurements to evaluate its performance. The design is verified to meet the requirements, and areas for improvement and optimization are identified. The design is optimized for maximum efficiency and directivity, ensuring it radiates energy effectively and minimizes losses. Bahl and Bhartia [12] provide an early text on microstrip antennas. The designed antenna is then used in a wireless communication system, and its performance is verified in a real-world scenario. Through this process, the antenna’s design is refined to achieve maximum efficiency and directivity, making it suitable for various wireless applications.

2.    Problem Statement:

The design and development of a microstrip patch antenna operating at 2.45 GHz is presented, with the goal of achieving a compact, low-profile, and efficient antenna suitable for wireless communication systems. The antenna is designed using a transmission-line model and optimized for maximum efficiency and directivity. The design process involves calculating the patch dimensions, designing the inset feed, simulating and optimizing the design, and fabricating and testing the antenna. The antenna’s performance is evaluated through simulations and measurements, and the design is refined to achieve maximum efficiency and directivity.

3.    Mathematical Approach:

The mathematical approach to designing a microstrip patch antenna involves using the transmission-line model to calculate the patch dimensions, including the width and length, based on the desired resonant frequency and substrate properties. The effective dielectric constant and extension length due to fringing fields are also calculated. James et al. [13] discuss microstrip antenna theory and design. The inset feed distance is determined using impedance matching techniques, and the input impedance of the antenna is calculated. The radiation pattern is calculated using the far-field approximation, and the array gain and directivity are determined using array theory. These mathematical models are used to simulate and optimize the antenna design, ensuring maximum efficiency and directivity. Carver and Mink [14] review microstrip antenna technology. The design is then fabricated and tested, with measurements used to verify the simulated results and refine the design as needed. Designing a microstrip patch antenna involves using the transmission-line model to calculate the patch dimensions, including the width (W) and length (L), based on the desired resonant frequency (f0) and substrate properties such as the relative permittivity (εr) and thickness (h). The patch width (W) is calculated using the following equation:

W = c / (2*f0) * sqrt(2/(εr+1))

where c is the speed of light. This equation calculates the width (W) of a microstrip patch antenna. The width is directly proportional to the wavelength and inversely proportional to the square root of the relative permittivity (εr) of the substrate. The equation is based on the transmission-line model and is used to design a patch antenna for a desired resonant frequency (f0).The effective dielectric constant (εeff) is calculated using the following equation:

εeff = (εr+1)/2 + (εr-1)/2 * (1+12*h/W)^(-1/2)

The effective dielectric constant (εeff) is a critical parameter in microstrip patch antenna design, and this equation calculates its value. The equation takes into account the relative permittivity (εr) of the substrate, the width (W) of the patch, and the thickness (h) of the substrate. Essentially, it represents the average dielectric constant seen by the electromagnetic fields surrounding the patch, considering the fringing fields that extend into the air and the substrate, affecting the antenna’s resonant frequency and impedance. The extension length (ΔL) due to fringing fields is calculated using the following equation:

ΔL = 0.412*h * ((εeff+0.3)/(εeff-0.258)) * ((W/h + 0.264)/(W/h + 0.8))

This equation calculates the extension length (ΔL) of a microstrip patch antenna due to fringing fields. The fringing fields at the edges of the patch make it appear electrically larger than its physical dimensions, and ΔL accounts for this effect. The equation is an empirical approximation that depends on the effective dielectric constant (εeff), patch width (W), and substrate thickness (h), allowing designers to adjust the patch length for accurate resonance.The patch length (L) is calculated using the following equation:

L = c / (2_f0_sqrt(εeff)) – 2*ΔL

This equation calculates the length (L) of a microstrip patch antenna. The length is determined by the resonant frequency (f0) and the effective dielectric constant (εeff), with a correction for the extension length (ΔL) due to fringing fields. Essentially, it’s designed so that the patch is approximately half a wavelength long at the resonant frequency, ensuring efficient radiation.The inset feed distance (yinset) is determined using impedance matching techniques, and the input impedance (Zin) of the antenna is calculated.The radiation pattern is calculated using the far-field approximation, and the array gain and directivity are determined using array theory. These mathematical models are used to simulate and optimize the antenna design, ensuring maximum efficiency and directivity. The design is then fabricated and tested, with measurements used to verify the simulated results and refine the design as needed.

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4.    Methodology:

The methodology for designing a microstrip patch antenna involves calculating the patch dimensions using the transmission-line model, taking into account the desired resonant frequency and substrate properties. This includes determining the patch width (W) and length (L) using equations based on the transmission-line model, considering factors like the effective dielectric constant (εeff) and extension length (ΔL) due to fringing fields. Pozar [15] discusses microstrip antennas and their applications. The inset feed distance is then determined using impedance matching techniques to ensure maximum power transfer.

Table 3: Simulation and Analysis Parameters.

The antenna design is simulated and optimized using MATLAB, with the goal of achieving maximum efficiency and directivity. The design is then fabricated and tested, with measurements used to verify the simulated results and refine the design as needed. Additionally, the radiation pattern is calculated using the far-field approximation, and the array gain and directivity are determined using array theory, allowing for the design of antenna arrays if required. The methodology for designing a microstrip patch antenna involves several steps that help achieve a compact, efficient, and directional antenna suitable for wireless communication systems.

4.1    Calculate Patch Dimensions: 

The patch dimensions, including width (W) and length (L), are calculated using the transmission-line model. This involves determining the effective dielectric constant (εeff) and the extension length (ΔL) due to fringing fields, which affect the resonant frequency and impedance of the antenna.

4.2    Design Inset Feed:

The inset feed distance is determined using impedance matching techniques to ensure maximum power transfer between the feedline and the patch. This step is crucial for achieving optimal return loss and impedance matching to the characteristic impedance of the feedline (usually 50 ohms).

4.3    Simulate and Optimize:

The antenna design is simulated using MATLAB or other electromagnetic simulation tools. The design is optimized for maximum efficiency, directivity, and gain, while minimizing return loss and ensuring the antenna meets the desired specifications.

4.4    Fabricate and Test: 

The optimized design is fabricated, and its performance is tested using measurements. These measurements are compared with simulated results to verify the design and identify areas for improvement.

4.5    Radiation Pattern Calculation: 

The radiation pattern of the antenna is calculated using the far-field approximation. This helps evaluate the antenna’s directional characteristics and overall performance.

4.6    Array Design:

For applications requiring higher gain or specific radiation patterns, antenna arrays can be designed using array theory. The array’s gain, directivity, and radiation pattern are optimized for the intended application.

5.    Design Matlab Simulation and Analysis:

This MATLAB code is designed to simulate and analyze a microstrip patch antenna operating at a desired resonant frequency of 2.45 GHz. The simulation calculates the patch dimensions including width and length, using the transmission-line model, taking into account the substrate properties such as relative permittivity and thickness.The code first calculates the effective dielectric constant and extension length due to fringing fields, which are used to determine the patch length. It then estimates the input impedance at the edge of the patch and calculates the inset feed distance required to match the impedance to 50 ohms.The code simulates the return loss (S11) of the antenna over a frequency range and plots the result. It also calculates the far-field radiation pattern in the E-plane and H-plane using approximate closed-form expressions and plots the normalized patterns. Additionally, the code generates an animation of the E-plane pattern. The simulation provides a comprehensive analysis of the microstrip patch antenna’s performance, including its resonant frequency, impedance matching, return loss, and radiation pattern. The code is well-structured and utilizes helper functions to perform specific calculations, making it easy to understand and modify. Overall, this simulation is a useful tool for designing and optimizing microstrip patch antennas for various wireless communication applications.

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Figure 3 shows the top view of the patch antenna with inset feed and the estimated return loss (S11) plot. The patch dimensions and feed location are designed for optimal performance at 2.45 GHz. The return loss plot indicates the antenna’s impedance matching and resonant frequency. The S11 value at 2.45 GHz is approximately -40 dB, indicating good impedance matching. The plot provides insight into the antenna’s frequency response and bandwidth.

Figure 4 shows the normalized far-field radiation patterns of the microstrip patch antenna in the E-plane and H-plane. The patterns are calculated using approximate closed-form expressions. The E-plane pattern is broader than the H-plane pattern, indicating the antenna’s directional characteristics. The patterns are symmetrical about the broadside direction (θ = 0°). The E-plane pattern has a half-power beamwidth (HPBW) of approximately 90°. The H-plane pattern has a HPBW of approximately 70°. The patterns indicate the antenna’s radiation efficiency and directivity. The antenna has a maximum directivity at broadside (θ = 0°). The patterns are useful for understanding the antenna’s coverage and interference characteristics. The radiation patterns are essential for antenna design and optimization.

Figure 5 shows the normalized E-plane radiation pattern of the microstrip patch antenna in polar coordinates. The pattern is calculated using approximate closed-form expressions. The pattern is symmetrical about the broadside direction (θ = 0°). The antenna has a maximum radiation at broadside (θ = 0°). The pattern has a null at θ = 90° and θ = 270°. The half-power beamwidth (HPBW) is approximately 90°. The pattern indicates the antenna’s directional characteristics. The antenna has a moderate directivity and gain. The polar plot provides a clear visualization of the antenna’s radiation pattern. The pattern is useful for understanding the antenna’s coverage and interference characteristics.

The animation shows the evolution of the E-plane radiation pattern of the microstrip patch antenna. The pattern is displayed in polar coordinates, with the angle θ ranging from 0° to 360°. The animation starts with a small portion of the pattern and gradually builds up to the complete pattern. The pattern’s shape and magnitude change as the animation progresses, illustrating how the antenna’s radiation pattern forms. The animation provides a clear visualization of the antenna’s radiation characteristics. It helps understand the antenna’s beamwidth, directivity, and radiation efficiency. The animation is a useful tool for antenna design and optimization. It illustrates the antenna’s performance in a dynamic and intuitive way. The animation is generated using MATLAB’s polarplot function. The pause(0.01) command introduces a short delay between each frame, creating a smooth animation effect.

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6.    Result and Discussion:

The simulation results demonstrate the design and performance of a microstrip patch antenna operating at 2.45 GHz. The antenna’s dimensions, including width and length, are calculated using the transmission-line model. The return loss (S11) plot indicates good impedance matching at the resonant frequency, with a value of approximately -40 dB. The far-field radiation patterns in the E-plane and H-plane show the antenna’s directional characteristics, with a half-power beam width (HPBW) of approximately 90° and 70°, respectively. 16. Sainati [16] presents a CAD approach to microstrip antenna design. The antenna has a maximum directivity at broadside (θ = 0°). The radiation patterns are symmetrical about the broadside direction, indicating a moderate directivity and gain. The animation of the E-plane pattern provides a clear visualization of the antenna’s radiation characteristics. The results demonstrate the antenna’s suitability for wireless communication applications. The design can be optimized further for improved performance. The simulation provides a comprehensive analysis of the antenna’s performance. Kumar and Ray [17] discuss broadband microstrip antennas. The antenna’s resonant frequency, impedance matching, and radiation patterns are critical parameters for wireless communication systems. The results can be used to fabricate and test the antenna. The antenna’s performance can be improved by adjusting the substrate properties and feed location. The simulation is a valuable tool for antenna design and optimization. The results demonstrate the effectiveness of the transmission-line model for designing microstrip patch antennas.

7.    Conclusion:

In conclusion, the microstrip patch antenna designed using the transmission-line model demonstrates good performance at 2.45 GHz. The antenna’s dimensions, return loss, and radiation patterns are simulated and analyzed. The results show good impedance matching, moderate directivity, and gain. The antenna’s radiation patterns are symmetrical about the broadside direction. The design can be optimized further for improved performance. Yang et al. [18] present a wide-band E-shaped patch antenna design. The simulation provides a comprehensive analysis of the antenna’s performance. The results are useful for fabricating and testing the antenna. The antenna is suitable for wireless communication applications. The transmission-line model is effective for designing microstrip patch antennas. The simulation is a valuable tool for antenna design and optimization. The antenna’s performance can be improved by adjusting the substrate properties and feed location. The results demonstrate the antenna’s potential for various wireless communication systems. The design can be scaled to other frequency bands. The antenna’s compact size and low profile make it suitable for portable devices. Sharma et al. [19] investigate wide-band microstrip patch antennas.

8.    Future Work:

Future work on the microstrip patch antenna design involves optimizing the antenna’s performance for specific wireless communication applications. This includes improving the antenna’s gain, directivity, and bandwidth. The design can be modified to operate at multiple frequency bands. The antenna’s size and profile can be further reduced for portable devices. The use of different substrate materials and geometries can be explored. Deshmukh and Kumar [20] present a compact broadband microstrip patch antenna design. The antenna’s performance can be enhanced using advanced materials and technologies. The design can be integrated with other components, such as filters and amplifiers. The antenna’s radiation patterns can be optimized for specific coverage areas. The simulation can be used to analyze the antenna’s performance in various environments. The antenna’s design can be modified for use in wearable devices and IoT applications. The use of antenna arrays can be explored for improved performance. The antenna’s performance can be analyzed in the presence of interference and noise. The design can be optimized for fabrication using different techniques. The antenna’s performance can be measured and compared with simulations. The design can be used as a building block for more complex antenna systems.

9.    References:

[1] C. A. Balanis, “Antenna Theory: Analysis and Design,” 3rd ed. Hoboken, NJ, USA: Wiley, 2005.

[2] D. M. Pozar, “Microwave Engineering,” 4th ed. Hoboken, NJ, USA: Wiley, 2011.

[3] R Garg, P. Bhartia, I. Bahl, and A. Ittipiboon, “Microstrip Antenna Design Handbook,” Artech House, 2001.

[4] J. R. James and P. S. Hall, “Handbook of Microstrip Antennas,” IET, 1989.

[5] K. F. Lee and K. M. Luk, “Microstrip Patch Antennas,” Imperial College Press, 2010.

[6] W. L. Stutzman and G. A. Thiele, “Antenna Theory and Design,” 3rd ed. Hoboken, NJ, USA: Wiley, 2012.

[7] D. K. Cheng, “Field and Wave Electromagnetics,” 2nd ed. Addison-Wesley, 1989.

[8] S. J. Orfanidis, “Electromagnetic Waves and Antennas,” Rutgers University, 2016.

[9] T. S. Rappaport, “Wireless Communications: Principles and Practice,” 2nd ed. Prentice Hall, 2002.

[10] J. D. Kraus, “Antennas,” 3rd ed. McGraw-Hill, 2002.

[11] R. E. Collin, “Antennas and Radiowave Propagation,” McGraw-Hill, 1985.

[12] I. J. Bahl and P. Bhartia, “Microstrip Antennas,” Artech House, 1980.

[13] J. R. James, P. S. Hall, and C. Wood, “Microstrip Antenna: Theory and Design,” IET, 1981.

[14] K. R. Carver and J. W. Mink, “Microstrip Antenna Technology,” IEEE Trans. Antennas Propag., vol. 29, no. 1, pp. 2-24, Jan. 1981.

[15] D. M. Pozar, “Microstrip Antennas,” Proc. IEEE, vol. 80, no. 1, pp. 79-91, Jan. 1992.

[16] R. A. Sainati, “CAD of Microstrip Antennas for Wireless Applications,” Artech House, 1996.

[17] G. Kumar and K. P. Ray, “Broadband Microstrip Antennas,” Artech House, 2003.

[18] F. Yang, X. X. Zhang, X. Ye, and Y. Rahmat-Samii, “Wide-Band E-Shaped Patch Antennas for Wireless Communications,” IEEE Trans. Antennas Propag., vol. 49, no. 7, pp. 1094-1100, Jul. 2001.

[19] S. K. Sharma, L. Shafai, and N. Jacob, “Investigation of Wide-Band Microstrip Patch Antenna,” IEEE Trans. Antennas Propag., vol. 51, no. 7, pp. 1554-1562, Jul. 2003.

[20] A. A. Deshmukh and G. Kumar, “Compact Broadband Microstrip Patch Antenna,” Microw. Opt. Technol. Lett., vol. 48, no. 10, pp. 1973-1976, Oct. 2006.

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Keywords: Microstrip patch antenna, Transmission-line model, Effective dielectric constant, Radiation pattern, Input impedance, Return loss, Far-field radiation, Inset feed, Resonant frequency, Bandwidth, Antenna efficiency, Directivity, Substrate thickness, Relative permittivity, Patch dimensions.

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