Readme.md

EE4108 Mini Project Report: Circularly Polarized Patch Antenna Design

Author: Azat Idayatov (58178204)
Date: April 2026
Repository: GitHub - CP_Antenna_Design

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📡 Project Overview

This project presents the design, simulation, and analysis of a circularly polarized (CP) microstrip patch antenna operating in the 5.1–5.5 GHz frequency band. The antenna utilizes an air substrate (foam board) to minimize dielectric losses and overall thickness while maintaining robust CP performance.

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🎯 Design Specifications

Parameter	Requirement
Polarization	Circular Polarization (CP)
Frequency Range	5.1 GHz – 5.5 GHz
VSWR	< 2
Axial Ratio	< 3 dB
Radiation Pattern	Unidirectional (boresight)
Backlobe Level	< -15 dB
Gain (boresight)	> 5 dBic
Half-Power Beamwidth	> 30° at 5.3 GHz (both principal planes)
Cross-Polarization Discrimination	> 15 dB
Substrate Material	Air (foam board)
Substrate Thickness	Minimized

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🧠 Why Circular Polarization?

A circularly polarized (CP) antenna generates a wave in which the orthogonal electric and magnetic field components possess equal amplitudes and a 90° phase difference, causing the field vector to rotate as the wave propagates. In contrast, a linearly polarized (LP) wave oscillates along a single fixed plane.

Key Advantages of CP over LP:

• Robustness to orientation mismatch – CP antennas maintain reliable communication regardless of transmitter/receiver alignment.
• Multipath interference rejection – Reflected waves reverse polarization sense and are naturally rejected.
• Broader angular coverage – More consistent signal reception over a wider range of incident angles.

Polarization Visualization

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📐 Antenna Design

Design Theory

A microstrip patch antenna is a planar radiator consisting of a metallic patch etched on a dielectric substrate above a ground plane. For circular polarization, we employ a dual-feed square patch configuration where two orthogonal ports are excited with a 90° phase shift.

Design Equations (Transmission Line Model)

The physical dimensions were calculated for a center frequency $f_0 = 5.3$ GHz, air substrate ($\varepsilon_r \approx 1.07$), and thickness $h = 4.0$ mm.

Patch Width: $$W = \frac{c}{2 f_0} \sqrt{\frac{2}{\varepsilon_r + 1}}$$

Effective Dielectric Constant: $$\varepsilon_{\text{eff}} = \frac{\varepsilon_r + 1}{2} + \frac{\varepsilon_r - 1}{2} \left( 1 + 12 \frac{h}{W} \right)^{-1/2}$$

Length Extension (Fringing Fields): $$\Delta L = 0.412 h \cdot \frac{\left( \varepsilon_{\text{eff}} + 0.3 \right) \left( \dfrac{W}{h} + 0.264 \right)}{\left( \varepsilon_{\text{eff}} - 0.258 \right) \left( \dfrac{W}{h} + 0.8 \right)}$$

Physical Length: $$L = \frac{c}{2 f_0 \sqrt{\varepsilon_{\text{eff}}}} - 2\Delta L$$

Feed Offset from Center (for 50 Ω match): $$d = \frac{L}{\pi} \cdot \arccos\left( \sqrt{\frac{50}{R_{\text{edge}}}} \right)$$

where $R_{\text{edge}} \approx 250$ Ω.

Calculated Parameters

Parameter	Calculated Value
Target Frequency ($f_0$)	5.3 GHz
Substrate Permittivity ($\varepsilon_r$)	1.07
Substrate Thickness ($h$)	4.0 mm
Free-Space Wavelength ($\lambda_0$)	56.6 mm
Patch Width ($W$)	25.07 mm
Patch Length ($L$)	25.07 mm
Ground Plane Size	53.57 × 53.57 mm
Feed Offset from Center ($d$)	8.84 mm

Note: Final dimensions were optimized in HFSS and differ slightly from calculated values.

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Optimized Parameters (HFSS)

Parameter	Value
Patch Width ($W$)	25 mm
Patch Length ($L$)	25 mm
Air Substrate Thickness ($h$)	4 mm
Feed Offset from Center	8 mm
Ground Plane Width	80 mm
Ground Plane Length	80 mm

Textbook Design Reference

HFSS Antenna Geometry

Feeding Method

A dual-feed configuration with 90° phase difference excites two orthogonal modes, producing Right-Hand Circular Polarization (RHCP):

$$\vec{E}(t) = E_0 \left[ \hat{x} \cos(kz - \omega t) + \hat{y} \sin(kz - \omega t) \right]$$

• Port 1: Integration line along Y-direction
• Port 2: Integration line along X-direction
• Phase Shift: 90° (achieved through feed network)
• Impedance: 50 Ω
• Input Power: 1 W

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📊 Simulation Results (ANSYS HFSS)

VSWR (Voltage Standing Wave Ratio)

The VSWR characterizes impedance matching:

$$\text{VSWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|}$$

where $\Gamma$ is the reflection coefficient.

• Range: 1.7 – 2.5 across 5.1–5.5 GHz
• Upper bound slightly exceeds target (< 2), but acceptable for most applications.

Axial Ratio

The Axial Ratio (AR) defines the polarization purity:

$$\text{AR} = \frac{E_{\text{major}}}{E_{\text{minor}}}$$

An AR of 0 dB indicates perfect circular polarization, while 3 dB represents the critical threshold.

• Range: 2.5 – 3.2 dB across 5.1–5.5 GHz
• Marginally above 3 dB at band edges, maintains predominantly CP characteristics.

Radiation Pattern & Backlobe Level

The radiation pattern exhibits strong boresight directivity with excellent backlobe suppression:

$$G(\theta, \phi) = \left| \sin(\theta) \right|^2$$

• Backlobe Level: -19.8 dB
• Comfortably satisfies < -15 dB requirement.

Boresight Patterns at Different Frequencies

Half-Power Beamwidth (HPBW)

The HPBW is the angular width of the main lobe at -3 dB points:

Frequency	HPBW
5.1 GHz	50°
5.3 GHz	50° (E-plane) / 55° (H-plane)
5.5 GHz	50°

All values exceed the > 30° minimum requirement.

Cross-Polarization Discrimination (XPD)

Cross-polarization accounts for unwanted orthogonal polarization components:

$$\text{XPD} = 20 \log_{10} \left( \frac{|E_{\text{co-pol}}|}{|E_{\text{cross-pol}}|} \right)$$

• Measured: 15.3 dB
• Satisfies > 15 dB requirement.

Gain

The antenna gain relates radiated power intensity to an isotropic radiator:

$$G = \frac{4\pi}{\lambda^2} A_e$$

where $A_e$ is the effective aperture.

• Range: 9.88 – 10.4 dBic across the band
• Exceeds > 5 dBic requirement.

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📈 Summary: Target vs. Simulated

Parameter	Target	Simulated	Status
Frequency Range	5.1–5.5 GHz	5.1–5.5 GHz	✅ Met
VSWR	< 2	1.7–2.5	⚠️ Slight deviation
Axial Ratio	< 3 dB	2.5–3.2 dB	⚠️ Slight deviation
Backlobe Level	< -15 dB	-19.8 dB	✅ Met
Gain	> 5 dBic	9.88–10.4 dBic	✅ Exceeded
HPBW (E-plane)	> 30°	50°	✅ Exceeded
HPBW (H-plane)	> 30°	55°	✅ Exceeded
Cross-Polarization	> 15 dB	15.3 dB	✅ Met

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❌ Design Iterations & Unsuccessful Attempts

Attempt 1: Corner-Truncated Single-Feed Method

The corner-truncated approach removes small portions from opposite corners to generate two slightly different mode frequencies, theoretically achieving CP through mode mixing.

Issues Encountered:

• Extremely narrow axial ratio bandwidth (only at 5.3 GHz)
• VSWR degradation across the band
• Impractical truncation sensitivity

Attempt 2: Nearly-Square Patch Method

This approach attempts to use a nearly-square patch with slightly different dimensions to excite quasi-orthogonal modes.

Issues Encountered:

• Unacceptably high axial ratio across the band
• Extreme sensitivity to dimensional tolerances
• Impractical for fabrication with foam board

Lessons Learned

Single-feed CP configurations suffer from:

• Narrow bandwidth characteristics
• High fabrication sensitivity
• Challenging impedance matching

The dual-feed square patch configuration offers:

• Broader bandwidth with superior axial ratio stability
• Greater robustness to manufacturing tolerances
• Simplified design optimization process
• Justifies slightly more complex feed arrangement

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🛠️ Tools Used

• ANSYS HFSS – Full-wave electromagnetic simulation
• MATLAB – Auxiliary calculations and optimization
• LaTeX – Report preparation