Microstrip Patch Antennas

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EE-4382/5306 - Antenna Engineering Outline • Introduction – Basic Characteristics – Feeding Methods • Rectangular Patch – Transmission-Line Model – Conductance and Input Impedance – Matching Techniques – Fields – Directivity • Quality Factor, Bandwidth, and Efficiency • Antennas for Mobile Communications – Planar Inverted-F Antenna – Slot Antenna – Inverted-F Antenna

Microstrip Patch Antennas 2 Introduction

3 Microstrip Antennas - Introduction A microstrip patch antenna is a metallic strip or patch mounted on a dielectric layer (substrate) over a ground plane. Useful for high performance in extreme applications: aircraft, satellite, missiles, cellphones and electronic devices.

PROS: They are low profile, conformable, simple and inexpensive to manufacture, mechanically robust, and very versatile

CONS: Low efficiency, low power, high Q, poor polarization purity, poor scanning properties, spurious radiation, very narrow frequency bandwidth, still large dimensions at high frequencies

Microstrip Patch Antennas Slide 4 Microstrip Patch Antennas Slide 5 Basic characteristics

휆 휆 0 < L < 0 3 2 2.2 ≤ 휖푟 ≤ 12 W is tuned to get desired impedance

Microstrip Patch Antennas Slide 6 Basic characteristics

t ≪ 휆0 ℎ ≪ 휆0 (0.003휆0 ≤ ℎ ≤ 0.05휆0)

Microstrip Patch Antennas Slide 7 Basic Characteristics

Introduction to Antennas Slide 8 Basic Characteristics

http://antsim.elmag.org/patches/ Introduction to Antennas Slide 9 Basic Characteristics

Introduction to Antennas Slide 10 Basic characteristics

Microstrip Patch Antennas Slide 11 Feeding Methods

• Easy to fabricate • Simple to match • Low spurious radiation • Narrow bandwidth • Good for low h

Microstrip Patch Antennas Slide 12 Quarter Wave Transformer

푍1 = 푍0푅퐿

https://www.cst.com/academia/examples/qua rter-wave-transformer

Microstrip Patch Antennas Slide 13 Feeding Methods

• Easy to fabricate • Simple to match • Low spurious radiation • Matching is easily done by changing feed position • Narrow Bandwidth • Difficult to model & simulate

Microstrip Patch Antennas Slide 14 Feeding Methods

• Ground plane between substrates isolates the feed from the radiating element, minimizing interference • Simple to match • Moderate spurious radiation • Matching is easily done by changing feed position • Narrow Bandwidth • Easy to model & simulate • Most difficult to fabricate • Independent optimization of feed and radiating element

Microstrip Patch Antennas Slide 15 Feeding Methods

• Low Spurious Radiation • Largest Bandwidth • Easy to model & simulate • More difficult to fabricate • Length of feeding stub and width-to-line ratio of patch can control match

Microstrip Patch Antennas Slide 16 Rectangular Patch

17 Rectangular Patch Analysis

The rectangular patch is the most widely used configuration for microstrip patch antennas.

Transmission-Line Model It is the easiest approach to model and analyze the microstrip patch antenna. It is also less accurate, but gives a good physical insight.

EM Cavity Model It is more complex than the transmission line model, and it is more accurate. It also gives physical insight.

Full-Wave Model It is the most accurate, versatile, and easiest to simulate of all three models. It is also the most complex and has less physical insight.

Microstrip Patch Antennas Slide 18 Transmission-Line Model

The transmission-line model represents the microstrip antenna by two slots, separated by a low-impedance 푍푐 transmission line of length L. Looking at a cross section of the antenna (x-y plane), this is effectively a non- homogeneous transmission line. Fringing effects make the microstrip line look wider than it is. Effective dielectric constant is introduced to account for this.

Microstrip Patch Antennas Slide 19 Fringing Effects -Effective dielectric

1 휖 +1 휖 −1 ℎ − Static Values 휖 = 푟 + 푟 1 + 12 2 푟푒푓푓 2 2 푤 Microstrip Patch Antennas Slide 20 Effective Length, Resonant Frequency, and Effective Width Because of the fringing effects, the patch of the antenna is electrically longer than the physical dimensions. We take care of this by adding an electrical distance ΔL which is a function of the effective dielectric 푊 constant 휖 and width-to-height ratio 푟푒푓푓 ℎ

푊 Δ퐿 휖푟푒푓푓 + 0.3 + 0.264 = 0.412 ℎ 푊 ℎ 휖 − 0.258 + 0.8 푟푒푓푓 ℎ

퐿푒푓푓 = 퐿 + Δ퐿

Microstrip Patch Antennas Slide 21 Effective Length, Resonant Frequency, and Effective Width

Microstrip Patch Antennas Slide 22 Effective Length, Resonant Frequency, and Effective Width

The resonant frequency in the dominant TM010 mode is

1 푐0 푓푟010 = = 2퐿 휖푟 휇0휖0 2퐿 휖푟

Accounting for fringing effects,

1 1 푓푟푐010 = = 2퐿푒푓푓 휖푟푒푓푓 휇0휖0 2 퐿 + 2Δ퐿 휖푟푒푓푓 휇0휖0 1 푐 = 푞 = 푞 0 2퐿 휖푟 휇0휖0 2퐿 휖푟

푓푟푐 푞 = 010 푓푟010 Microstrip Patch Antennas Slide 23 Rectangular Antenna Design This procedure assumes we know the dielectric constant of the substrate 휖푟 , the resonant frequency 푓푟 , and the height of the substrate ℎ. 1. Determine 푊 1 2 푐 2 푊 = = 0 2푓푟 휇0휖0 휖푟 + 1 2푓푟 휖푟 + 1

2. Determine the effective dielectric constant 휖푟푒푓푓 3. Determine the extension of Δ퐿 4. Determine the actual length 퐿 of the patch 1 퐿 = − 2Δ퐿 2푓푟 휖푟푒푓푓 휇0휖0 휆 Approximate lengths of the microstrip vary between 0.47 − 0.49 0 휖푟

Microstrip Patch Antennas Slide 24 Rectangular Patch Design - Example

Design a rectangular microstrip antenna using a substrate (RT/Duroid 5880) with dielectric constant of 2.2, ℎ = 0.1588 cm and resonant frequency of 10 GHz.

Microstrip Patch Antennas Slide 25 Rectangular Antenna Conductance and Input Impedance

Microstrip Patch Antennas Slide 26 Conductance and Input Impedance

푌1 = 퐺1 + 푗퐵1

푊 1 2 ℎ 1 퐺1 = 1 − 푘0ℎ < 120휆0 24 휆0 10 푊 ℎ 1 퐵1 = 1 − 0.636 ln(푘0ℎ) < 120휆0 휆0 10

푌2 = 푌1, 퐺2 = 퐺1, 퐵2 = 퐵1

Microstrip Patch Antennas Slide 27 Conductance and Input Impedance At resonance 푌෨2 = 퐺෨2 + 푗퐵෨2 = 퐺1 − 푗퐵1

푌𝑖푛 = 푌1 + 푌෨2 = 2퐺1

1 1 푍𝑖푛 = 푅𝑖푛 = = 푌𝑖푛 2퐺1

This formula does not take into account mutual effects between the slots.

Introduction to Antennas Slide 28 Conductance and Input Impedance To take into account mutual effects between the slots, we introduce 퐺12 1 푅𝑖푛 = 2(퐺1±퐺12) where ‘+’ is used with odd (antisymmetric) resonant voltage distribution beneath the patch and between the slots and ‘–’ is used for modes with even (symmetric) resonant voltage distribution.

1 ∗ 퐺12 = 2 푅푒 ඵ 퐸1 × 퐻2 ∙ 푑푠 푉0 푆 퐸1 - E-field radiated by slot 1 퐻1 - H-field radiated by slot 2 푉0 - Voltage across the slot

Introduction to Antennas Slide 29 Conductance and Input Impedance

2 푘0푊 휋 sin cos 휃 1 2 3 퐺12 = 2 න 퐽0 푘0퐿 sin 휃 sin (휃) 푑휃 120휋 0 cos 휃

Where 퐽0 is the Bessel function of the first kind of order zero.

Introduction to Antennas Slide 30 Patch Input Impedance- Example

푊 A rectangular microstrip antenna has a width-to-height ratio of = 5, ℎ 휆 where the width has half-wave resonant dimensions 푊 = 0 . 2 Determine the input impedance of the antenna. Do not take into account mutual effects.

Microstrip Patch Antennas Slide 31 Matching Techniques – Inset feed

푅𝑖푛 푦=푦0 = 휋 푅 cos2 푦 𝑖푛(푦=0) 퐿 0

Microstrip Patch Antennas Slide 32 Antenna Patch Design - Example

A square patch has an input resistance at resonance of 260 Ω. Determine the inset feeding distance so that the input resistance is 50 Ω.

Now consider the feeding point to be 푦0 = 0.4퐿. Determine the input resistance.

Microstrip Patch Antennas Slide 33 Microstrip Line Characteristic Impedance

60 8ℎ 푊 푊 ln + 0 , 0 ≤ 1 휖푟푒푓푓 푊0 4ℎ ℎ 푍푐 = 120휋 푊 , 0 > 1 푊 푊 휖 0 + 1.393 + 0.667 ln 0 + 1.444 ℎ 푟푒푓푓 ℎ ℎ

Introduction to Antennas Slide 34 Matching Techniques – Inset feed

Microstrip Patch Antennas Slide 35 Rectangular Patch - Example

A microstrip antenna with overall dimensions of 퐿 = 0.906 cm and 푊 = 1.186 cm, substrate with height ℎ = 0.1588 cm and dielectric constant 휖푟 = 2.2, is operating at 10 GHz. Find:

(a) The input impedance. Do not take into account mutual effects between slots.

(b) The position of the inset feed point where the input impedance is 50 ohms.

(c) Taking into account mutual effects and new calculations, the −3 admittance between slots is calculated as G1 = 1.57 × 10 , 퐺12 = 6.1683 × 10−4. Calculate the input impedance and the distance of the inset feed point. Compare with parts (a) and (b)

Microstrip Patch Antennas Slide 36 Rectangular Patch - Fields

푘푊 sin sin 휃 sin 휙 2 푘퐿 푓 휃, 휙 = cos sin 휃 cos 휙 푘푊 sin 휃 sin 휙 2 2

푘퐿 퐹 휃 = cos sin 휃 , 휙 = 0° 퐸 2

푘푊 sin 2 sin 휃 퐹 휃 = cos(휃) , 휙 = 90° 퐻 푘푊 sin 휃 2

Introduction to Antennas Slide 37 Rectangular Patch - Fields Radiation Efficiency: 36.72%

Microstrip Patch Antennas Slide 38 Rectangular Patch - Fields

Introduction to Antennas Slide 39 Rectangular Patch Antenna Measurements & Simulation

Introduction to Antennas Slide 40 Rectangular Patch - Directivity

푈푚푎푥 4휋푈푚푎푥 퐷0 = = 푈0 푃푟푎푑

Single Slot 푘0ℎ ≪ 1 2 2 푉0 휋푊 푈푚푎푥 = 2 2휂0휋 휆0 2 푘0푊 2 휋 sin cos 휃 푉0 2 3 푃푟푎푑 = 2 න sin (휃) 푑휃 2휂0휋 0 cos 휃

Two Slots 푘0ℎ ≪ 1 2 2휋푊 휋 퐷2 = 휆0 퐼2 2 푘0푊 휋 휋 sin cos 휃 2 3 2 푘0퐿푒 퐼2 = න න sin (휃) cos sin 휃 sin 휙 푑휃푑휙 0 0 cos 휃 2

Microstrip Patch Antennas Slide 41 Quality Factor, Bandwidth, and Efficiency

42 Quality Factor The quality factor, bandwidth, and efficiency are interrelated figures-of-merit, and cannot be independently optimized. Stored Energy 푄 = 휔 푟 Dissipated Power

The quality factor is representative of the antenna losses. These are radiation, conduction (ohmic), dielectric, and surface-wave losses. 1 1 1 1 1 = + + + 푄푡 푄푟푎푑 푄푐 푄푑 푄푠푤 Where

푄푡 = Total Quality Factor 푄푟푎푑 = Quality Factor due to radiation (space-wave) losses. 푄푐 = Quality Factor due to conduction (ohmic) losses. 푄푑 = Quality Factor due to dielectric losses 푄푠푤 = Quality Factor due to surface waves (negligible for thin substrates)

Microstrip Patch Antennas Slide 43 Quality Factor

For very thin substrates (푘 ≪ ℎ0) of arbitrary shapes, there are approximate formulas to represent the quality factors.

푄푐 = ℎ 휋푓휇휎 1 푄 = 푑 tan(훿) 2휔휖푟 푄푟푎푑 = 퐾 ℎ 퐺푡/푙

׭ 퐸 2푑퐴 퐾 = 푎푟푒푎 2 ׯ푝푒푟𝑖푚푒푡푒푟 퐸 푑푙

푥 For rectangular aperture in the dominant 푇푀010 mode 퐿 퐾 = 4 퐺 퐺 푡 = 푟푎푑 conductance per unit length of radiating aperture 푙 푊

Microstrip Patch Antennas Slide 44 Quality Factor – Bandwidth The fractional bandwidth of the antenna is inversely proportional to the 푄푡 of the antenna Δ푓 1 = 푓0 푄푡

Δ푓 푓2−푓1 푓1+푓2 = Fractional Bandwidth , 푓0 = 푓0 푓0 2

Δ푓 푉푆푊푅 − 1 = 푓0 푄푡 푉푆푊푅 푓0 푓1 = , 푓2 = 푓0 1 + 1/푄푡 1 + 1/푄푡 1 An approximate expression of the bandwidth for VSWR ≤ 2, Γ ≤ , 3 휖 − 1 ℎ 푊 BW = 3.771 푟 휖 2 휆 퐿 Microstrip Patch Antennas 푟 0 Slide 45 Quality Factor – Dimensions and Bandwidth

Microstrip Patch Antennas Slide 46 Quality Factor, Bandwidth, and Efficiency – Example

The fractional bandwidth at a center frequency of 10 GHz of a rectangular patch antenna whose substrate is RT/Duroid 5880 휖푟 = 2.2 with height ℎ = 0.1588 cm is about 5% for a VSWR of 2: 1. Within that bandwidth, find resonant frequencies associated with the two lengths of the rectangular patch antenna, and relative ratio of the two lengths.