Undergraduate Microwave Engineering

Microstrip Antennas Study Guide

Comprehensive study guide covering patch antenna theory, design equations, radiation patterns, and practical implementations for modern wireless systems.

Study Guide Contents

1. Introduction to Microstrip Antennas

A microstrip antenna (also known as a patch antenna) consists of a metallic patch placed above a ground plane with a dielectric substrate in between. First proposed by Deschamps in 1953 and practically developed by Howell and Munson in the early 1970s, these antennas have become ubiquitous in modern wireless communication.

The patch is typically made of conducting material such as copper or gold and can take various shapes, though rectangular and circular configurations are most common due to their ease of analysis and fabrication.

Key Advantages

  • Low Profile: Conformal to surfaces, lightweight, and compact
  • Low Cost: Simple fabrication using PCB techniques
  • Versatile: Easy integration with microwave circuits
  • Dual/Triple Frequency: Multiple resonant modes possible

Limitations

  • Narrow bandwidth (typically 1-5%)
  • Low gain (6-8 dBi for single element)
  • Low power handling capacity
  • Surface wave excitation in thick substrates

Rectangular Microstrip Patch Configuration

Patch Substrate Ground

2. Antenna Structure & Configurations

Rectangular Patch

Most common shape. Length L ≈ λ/2, Width W controls input impedance and bandwidth.

L = c/(2f√εeff)
W = c/(2f) × √[2/(εr+1)]

Circular Patch

Symmetric radiation pattern. Radius a determined by TM11 mode resonance.

a = F / {1 + 2h/(πεrF) × [ln(πF/2h) + 1.7726]}^(1/2)
where F = 8.791×10^9/(fr√εr)

Triangular Patch

Compact size compared to rectangular. Useful for dual-frequency operation.

Side length: s = 2c/(3fr√εr)
TM10 mode operation

Feeding Techniques

Microstrip Line Feed

Conducting strip connects directly to patch edge. Easy to fabricate but narrow bandwidth due to surface wave excitation.

Coaxial Probe Feed

Inner conductor extends through substrate to patch. Low spurious radiation but narrow bandwidth and difficult to model.

Aperture Coupled Feed

Non-contact feeding through slot in ground plane. Higher bandwidth (~10-20%) but multi-layer fabrication.

Proximity (Electromagnetically) Coupled

Two dielectric layers with feed line on bottom and patch on top. Very high bandwidth up to 13%.

3. Theory of Operation

Transmission Line Model

The rectangular patch is viewed as two radiating slots separated by a low-impedance transmission line of length L. Each slot radiates with equivalent admittance:

G = W/(120λ₀) × [1 - (1/24)(k₀h)²] for h << λ₀

B = W/(120λ₀) × [1 - 0.636ln(k₀h)]

where k₀ = 2π/λ₀ is the free-space wavenumber

Cavity Model

The region between patch and ground plane is treated as a cavity bounded by magnetic walls (open circuits) at the edges and electric walls (conductors) top and bottom.

Resonant Frequency (TM₁₀₀ mode):

fᵣ = c/(2L√εᵣₑff)

εᵣₑff = (εᵣ + 1)/2 + (εᵣ - 1)/2 × [1 + 12h/W]^(-1/2)

Fringing Effects

Electric fields fringe at the patch edges, effectively increasing the electrical length. This is accounted for by the effective length:

Lₑff = L + 2ΔL

where ΔL/h = 0.412 × (εᵣₑff + 0.3)(W/h + 0.264) / [(εᵣₑff - 0.258)(W/h + 0.8)]

Radiation Mechanism

The two radiating slots act as radiating apertures with fields perpendicular to the ground plane. The far-field pattern is the vector sum of fields from both slots separated by distance L.

Key Parameters

Directivity ~6-8 dBi
Beamwidth (E-plane) ~100°-120°
Beamwidth (H-plane) ~70°-80°
Input Resistance 150-300 Ω (edge)
Bandwidth (VSWR < 2) 1-5%

4. Design Procedure

1

Specify Parameters

  • Operating frequency (fᵣ)
  • Dielectric constant (εᵣ) and height (h) of substrate
  • Desired input impedance (typically 50Ω or 75Ω)
2

Calculate Width (W)

W = c/(2fᵣ) × √[2/(εᵣ + 1)]

For efficient radiation, W should be slightly less than λ/2 in the dielectric. Wider patches provide better bandwidth but excite higher order modes.

3

Calculate Effective Dielectric Constant (εᵣₑff)

εᵣₑff = (εᵣ + 1)/2 + (εᵣ - 1)/2 × [1 + 12h/W]^(-1/2)

Accounts for fringing fields extending into air above the patch.

4

Calculate Length Extension (ΔL)

ΔL/h = 0.412 × (εᵣₑff + 0.3)(W/h + 0.264) / [(εᵣₑff - 0.258)(W/h + 0.8)]
5

Calculate Physical Length (L)

L = c/(2fᵣ√εᵣₑff) - 2ΔL

The actual resonant length is shorter than λ/2 due to fringing.

6

Determine Feed Point

For 50Ω impedance match, the inset feed position y₀ is:

Rᵢₙ(y=y₀) = Rᵢₙ(y=0) × cos²(πy₀/L)
y₀ = (L/π) × arccos√(50/Rᵢₙₑdge)

Design Example

Frequency 2.4 GHz
Substrate (FR4) εᵣ = 4.4, h = 1.6mm
Calculated W 38.03 mm
εᵣₑff 4.08
ΔL 0.74 mm
Final L 29.4 mm

Patch Geometry:

5. Interactive Design Calculator

Input Parameters

Calculated Dimensions

Patch Width (W)

--

mm

Patch Length (L)

--

mm

εᵣₑff

--

ΔL Extension

--

mm

Scale: Not to scale

6. Microstrip Arrays & Beam Steering

Array Factor & Directivity

Single microstrip elements provide modest gain (6-8 dBi). To achieve higher gains for radar and communication systems, multiple patches are arranged in arrays. The total field is the product of the element pattern and the array factor.

Array Factor (N elements, uniform spacing d)

AF(θ) = sin[N/2 × (k₀d sinθ + β)] / sin[1/2 × (k₀d sinθ + β)]

where β = phase shift between elements. For broadside: β = 0, For scanning: β = -k₀d sinθ₀

Broadside Array: Maximum radiation perpendicular to array axis (θ = 0°)
End-fire Array: Maximum radiation along array axis (θ = 90°)
Phased Array: Electronic beam steering via phase shifters

4-Element Array Pattern

Linear Arrays

Patches arranged along a line. Simple feeding network but limited to one-dimensional scanning.

Gain ≈ 6 dBi + 10log₁₀(N)
Beamwidth ≈ 100°/N

Planar Arrays

Two-dimensional matrix of patches. Allows scanning in both azimuth and elevation.

N × M elements
Gain ≈ 6 dBi + 10log₁₀(N×M)

Corporate Feed

Parallel feed network using quarter-wave transformers. Wide bandwidth but physically large.

T-junction power dividers
Equal path lengths

7. Applications & Advanced Topics

📱

Mobile Communications

Smartphones, WiFi routers (2.4/5 GHz), Bluetooth devices, and wearable technology.

🛰️

Satellite Systems

GPS receivers, satellite radio (SDARS), and direct broadcast satellite (DBS) systems.

🚗

Automotive Radar

77 GHz collision avoidance systems, adaptive cruise control, and parking sensors.

🏥

Medical Applications

Microwave imaging, hyperthermia treatment, and wireless capsule endoscopy.

Bandwidth Enhancement Techniques

Stacked Patches

Electromagnetically coupled parasitic patches above driven element. Bandwidth: 10-20%.

Slot Loading

U-slots, L-slots, or E-shaped patches create multiple resonant modes. Bandwidth: 20-40%.

Thick Substrates

Low dielectric constant foam substrates reduce Q factor. Bandwidth: 10-15%.

Meta-materials

Mushroom-like EBG structures or metamaterial loading. Bandwidth: Ultra-wideband possible.

Dual-Band & Multi-Band Designs

  • Stacked patches: Different sizes resonate at different frequencies
  • Slot loading: Slots perturb current distribution creating new resonances
  • Reactively loaded: Shorting pins or varactor diodes for tunable operation
  • Fractal geometries: Self-similar structures for multi-band behavior

Circular Polarization

Required for satellite communications to mitigate Faraday rotation and polarization mismatch.

Single Feed: Truncated corners or diagonal slot creates orthogonal modes with 90° phase shift.
Dual Feed: Two orthogonal feeds with quadrature hybrid providing equal amplitude, 90° phase difference.
Sequential Rotation: Array technique using rotation and phase progression for wideband CP.

Study Summary

Microstrip antennas are essential components in modern microwave engineering, offering low-profile, conformal solutions for wireless systems. Key design considerations include substrate selection (balancing bandwidth vs. size), feeding technique (matching and efficiency), and array configuration (gain and beam steering requirements).

Key Formula

L = λ/2√εᵣₑff - 2ΔL

Typical Gain

6-8 dBi (single)

Bandwidth

1-5% (standard)