Microstrip Patch Antennas
Study Guide

Comprehensive guide to the theory, design, and analysis of microstrip antennas for undergraduate microwave engineering students.

Microwave Engineering Antenna Theory RF Design
01

Introduction to Microstrip Antennas

A microstrip patch antenna (MSA) is a type of radio antenna with a low profile, which can be mounted on a flat surface. It consists of a rectangular (or other shaped) metallic patch placed on one side of a dielectric substrate, with a ground plane on the other side [^2^].

Key Characteristics

  • Low profile and conformal structure
  • Lightweight and compact size
  • Compatible with integrated circuits
  • Moderate bandwidth (typically 1-5%)
  • Easy to fabricate using PCB technology

Microstrip antennas operate as open resonant cavities. The field confinement between the patch and ground plane determines the eigenmodes, with the antenna typically operating in the fundamental mode [^3^].

Applications

Satellite Communications
GPS, Satellite TV
Mobile Communications
Cell phones, WiFi
Radar Systems
Automotive radar
Biomedical
Implantable devices

Frequency Range

Microstrip antennas are most useful at microwave frequencies (f > 1 GHz) where their electrical size becomes practical [^2^].

02

Structure and Geometry

The basic microstrip antenna consists of three layers: the ground plane, dielectric substrate, and radiating patch. The patch is typically made of copper or gold and can take various shapes, though rectangular and circular are most common [^2^].

Geometric Parameters

L (Length) Resonant dimension
W (Width) W ≈ 1.5L (typical)
h (Height) Substrate thickness
εr Dielectric constant
t Patch thickness
x₀ Feed position

Cavity Model Concept

The patch acts approximately as a resonant cavity with Perfect Electric Conductor (PEC) walls on top and bottom, and Perfect Magnetic Conductor (PMC) walls on the edges [^2^]. Radiation is accounted for by using an effective loss tangent for the substrate.

Key Insight: As the substrate gets thinner, the patch current radiates less due to image cancellation. However, the Q of the resonant cavity increases, making patch currents stronger at resonance. These two effects cancel, allowing the patch to radiate well even for thin substrates [^2^].

Figure 1: Rectangular Microstrip Patch Antenna Structure

Radiating Patch
Dielectric Substrate
Ground Plane
03

Design Equations and Formulas

The design of a microstrip patch antenna follows a systematic procedure using transmission line model and cavity model approximations [^3^][^4^].

Design Procedure

1

Select Operating Frequency (f₀)

Determine target resonance frequency based on application requirements.

2

Calculate Patch Width (W)

W = c / (2f₀√((εr+1)/2))
3

Calculate Effective Dielectric Constant (εeff)

εeff = (εr+1)/2 + (εr-1)/2 × [1+12h/W]^(-1/2)
4

Calculate Length Extension (ΔL)

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

Calculate Patch Length (L)

L = c/(2f₀√εeff) - 2ΔL

Key Parameters

Speed of Light (c) 2.998 × 10⁸ m/s
Free-space wavelength λ₀ = c/f₀
Guide wavelength λg = λ₀/√εeff
Wavenumber k₀ = 2π/λ₀
Intrinsic impedance η₀ ≈ 377 Ω

Design Note

The width W is usually chosen to be larger than L to obtain higher bandwidth. However, typically W < 2L to avoid excitation of higher order modes [^2^].

Field Distribution (TM₁₀ Mode)

Figure 2: Electric Field Distribution in Microstrip Patch Antenna (Side View)

The electric field is maximum at the radiating edges (x = 0 and x = L) due to the open-circuit boundary condition. The fringing fields at these edges are responsible for radiation [^7^].

04

Feeding Techniques

The performance of microstrip antennas depends significantly on the feeding technique. Methods are classified as contacting (direct connection) and non-contacting (electromagnetic coupling) [^1^][^5^].

Microstrip Line Feed

Contacting

Figure 3: Microstrip Line Feed Configuration

  • Easy to fabricate (planar structure)
  • Simple etching process
  • Spurious feed radiation
  • Bandwidth limited to 2-5%

Coaxial (Probe) Feed

Contacting

Figure 4: Coaxial Feed Configuration

  • Easy impedance matching
  • Low spurious radiation
  • Requires drilling hole
  • Probe inductance limits bandwidth

Aperture Coupled Feed

Non-contacting

Figure 5: Aperture Coupled Feed Configuration

  • High bandwidth possible
  • Isolates feed from patch radiation
  • Requires multilayer fabrication
  • Alignment critical

Proximity Coupled Feed

Non-contacting

Figure 6: Proximity Coupled Feed Configuration

  • Very low spurious radiation
  • Bandwidth up to 13%
  • Multilayer fabrication required
  • Poor polarization purity

Inset Feed for Impedance Matching

An inset cut is integrated into the patch to achieve impedance matching without additional matching elements. The input impedance varies with inset depth [^3^]:

Rin(y) = Rin(0) × cos⁴(πy/L)

where y is the inset distance from the edge, and Rin(0) is the input resistance at the edge.

Figure 7: Inset Feed Configuration

05

Radiation Characteristics

The radiation from a microstrip antenna can be modeled using either the electric current model (physical currents on the patch) or the magnetic current model (equivalent currents at the edges) [^2^].

E-Plane and H-Plane Patterns

Figure 8: Radiation Pattern (Linear Scale)

E-Plane (φ = 0°): Contains the electric field vector and direction of maximum radiation. Pattern is broader.

H-Plane (φ = 90°): Contains the magnetic field vector. Pattern is typically narrower.

Radiation Parameters

Directivity

For thin substrates, directivity is essentially independent of substrate thickness [^2^].

D ≈ (2/15) × (W/λ₀)² × (k₀h)² × εr

Beamwidth

The half-power beamwidth (HPBW) depends on the patch dimensions and frequency. Typical values range from 50° to 100°.

Bandwidth

The fractional bandwidth is inversely proportional to the quality factor Q [^2^]:

BW = 1/(√2 × Q) (for SWR < 2)

Efficiency

Radiation efficiency depends on conductor losses, dielectric losses, and surface wave excitation. Typical values: 80-95%.

Surface Wave Effects

As substrate thickness increases, surface wave excitation becomes significant, degrading pattern performance and causing mutual coupling in arrays. Techniques to reduce surface waves include using photonic bandgap structures or Reduced Surface Wave (RSW) antenna designs [^2^].

06

Interactive Design Calculator

Input Parameters

1 GHz 2.4 GHz 10 GHz
2.0 4.4 12.0
0.5 mm 1.6 mm 5.0 mm

Common Substrates

Calculated Dimensions

Patch Width (W) --
Patch Length (L) --
Effective εr --
Length Extension (ΔL) --
W/L Ratio --

Figure 9: Patch Geometry Visualization (Scale Approximate)

Quick Reference Table

Parameter Symbol Formula/Value Units
Speed of Light c 2.998 × 10⁸ m/s
Free-space Wavelength λ₀ c/f₀ m
Patch Width W c/(2f₀√((εr+1)/2)) m
Effective Dielectric Constant εeff (εr+1)/2 + (εr-1)/2(1+12h/W)^(-1/2) --
Length Extension ΔL 0.412h(εeff+0.3)(W/h+0.264)/(εeff-0.258)(W/h+0.8) m
Patch Length L c/(2f₀√εeff) - 2ΔL m
Input Resistance (edge) Rin 90(λ₀/W)² (typical) Ω