Overview of Microstrip Antennas

David R. Jackson Dept. of ECE University of Houston Overview of Microstrip Antennas

Also called “patch antennas”

• One of the most useful antennas at microwave frequencies (f > 1 GHz). • It consists of a metal “patch” on top of a grounded dielectric substrate. • The patch may be in a variety of shapes, but rectangular and circular are the most common. History of Microstrip Antennas

• Invented by Bob Munson in 1972. •Second Became Symp. popular on USAF starting Antenna Researchin the 1970s. and Development Program,

R. E. Munson, “Microstrip Phased Array Antennas,” Proc. of Twenty-

October 1972.

R. E. Munson, “Conformal Microstrip Antennas and Microstrip Phased Arrays,” IEEE Trans. Antennas Propagat., vol. AP-22, no. 1 (January 1974): 74–78. Typical Applications

single element array

(Photos courtesy of Dr. Rodney B. Waterhouse) Typical Applications (cont.)

MPA microstrip antenna filter DC supply Micro-D K-connector connector LNA PD fiber input with diplexer collimating lens

Microstrip Antenna Integrated into a System: HIC Antenna Base-Station for 28-43 GHz

(Photo courtesy of Dr. Rodney B. Waterhouse) Geometry of Rectangular Patch y

L x h

Note: L is the resonant dimension. The width W is usually chosen to be larger than L (to get higher bandwidth). However, usually W < 2 L. W = 1.5 L is typical. Geometry of Rectangular Patch (cont.)

view showing coaxial feed

y feed at (x0, y0) Feed along the centerline is the most common (minimizes W higher-order modes and cross-pol)

x L Advantages of Microstrip Antennas

• Low profile (can even be “conformal”). • Easy to fabricate (use etching and phototlithography). • Easy to feed (coaxial cable, microstrip line, etc.) . • Easy to use in an array or incorporate with other microstrip circuit elements. • Patterns are somewhat hemispherical, with a moderate directivity (about 6-8 dB is typical). Disadvantages of Microstrip Antennas

¾ Low bandwidth (but can be improved by a variety of techniques). Bandwidths of a few percent are typical. ¾ Efficiency may be lower than with other antennas. Efficiency is limited by conductor and dielectric losses*, and by surface-wave loss**.

* Conductor and dielectric losses become more severe for thinner substrates.

** Surface-wave losses become more severe for thicker substrates (unless air or foam is used). Basic Principles of Operation

The patch acts approximately as a resonant cavity (short circuit walls on top and bottom, open-circuit walls on the sides). In a cavity, only certain modes are allowed to exist, at different resonant frequencies. If the antenna is excited at a resonant frequency, a strong field is set up inside the cavity, and a strong current on the (bottom) surface of the patch. This produces significant radiation (a good antenna). Thin Substrate Approximation

On patch and ground plane, Et = 0 E = zEˆ z ( x, y)

Inside the patch cavity, because of the thin substrate, the electric field vector is approximately independent of z.

Hence E ≈ zEˆ z ( x, y)

Exyz ( , )

h Thin Substrate Approximation

Magnetic field inside patch cavity:

1 HE=− ∇× jωμ 1 =− ∇×()zEˆ z () x, y j ωμ 1 =−() −zExyˆ ×∇ (), j z ωμ Hence 1 Hxy(),,=×∇() zˆ E() xy jωμ z Thin Substrate Approximation (cont.)

1 Hxy(),,=×∇() zˆ E() xy jωμ z

Note: the magnetic field is purely horizontal.

(The mode is TMz.)

Exyz ( , ) h

H (xy, ) Magnetic Wall Approximation

On edges of patch, y

Jns ⋅=ˆ 0 J s W Also, on lower surface of tˆ nˆ patch conductor we have x L JzHs =−×()ˆ

J s nˆ Hence, h

Ht = 0 Magnetic Wall Approximation (cont.)

y Since the magnetic field is approximately independent of z, J we have an approximate PMC s condition on the edge. W tˆ nˆ

H = 0(PMC ) x t L

nˆ h

PMC Magnetic Wall Approximation (cont.)

nHxyˆ ×=(),0 y

1 Hxy(),,=×∇() zˆ E() xy J jωμ z s W tˆ nˆ Hence, x ˆ ˆ nz××∇() Exyz (),0 = L

znˆ ()ˆ ⋅∇ Ez () xy,0 = nˆ h ∂E z = 0 ∂n PMC Resonance Frequencies

22 y ∇+EkEzz =0

From separation of variables: (x0, y0) ⎛⎞⎛⎞mxππ ny W Ez = cos⎜⎟⎜⎟ cos ⎝⎠⎝⎠LW x (TMmn mode) L

⎡⎤22 ⎛⎞⎛⎞mnππ2 ⎢⎥−−+=⎜⎟⎜⎟kEz 0 ⎣⎦⎢⎥⎝⎠⎝⎠LW

⎡⎤22 ⎛⎞⎛⎞mnππ2 Hence ⎢⎥−⎜⎟⎜⎟−+=k 0 ⎣⎦⎢⎥⎝⎠⎝⎠LW Resonance Frequencies (cont.) y 22 2 ⎛⎞⎛⎞mnπ π k =+⎜⎟⎜⎟ ⎝⎠⎝⎠LW (x0, y0) W Recall that k = ω με ε x 00 r L ω = 2π f

Hence πε 22 cm⎛⎞⎛⎞π nπ f =+ ⎜⎟⎜⎟ c =1/ μ00ε 2 r ⎝⎠⎝⎠LW Resonance Frequencies (cont.) y

Hence f = fmn (x0, y0) W (resonance frequency of (m, n) mode) x L πε 22 cm⎛⎞⎛⎞π nπ fmn =+⎜⎟⎜⎟ 2 r ⎝⎠⎝⎠LW (1,0) Mode y current This mode is usually used because the radiation pattern has a broadside beam. W ⎛⎞π x Ez = cos⎜⎟ ⎝⎠L x L c ⎛⎞1 f10 = ⎜⎟ 2 ε ⎝⎠L This mode acts as a wide r microstrip line (width W) that has a resonant length ωμ ⎛⎞−1 ⎛⎞π ⎛π x ⎞ of 0.5 guided wavelengths Jx= ˆ sin s ⎜⎟⎜⎟ ⎜ ⎟ in the x direction. ⎝⎠jLL0 ⎝⎠ ⎝ ⎠ Basic Properties of Microstrip Antennas Resonance Frequency

The resonance frequency is controlled by the patch length L and the substrate permittivity. Approximately, Note: this is equivalent to saying that c ⎛⎞1 the length L is one-half of a f10 = ⎜⎟ wavelength in the dielectric: ε r ⎝⎠2L

λ0 /2 kL = π L ==λd /2 ε r Note: a higher substrate permittivity allows for a smaller antenna (miniaturization) – but lower bandwidth. Resonance Frequency (cont.)

The calculation can be improved by adding a “fringing length extension” ΔL to each edge of the patch to get an “effective length” Le .

y LLe =+Δ2 L

ΔL ΔL c ⎛⎞1 f10 = ⎜⎟ L L 2 ε r ⎝⎠e x

Le Resonance Frequency (cont.)

Hammerstad formula:

⎡ eff ⎛⎞W ⎤ ()ε r ++0.3⎜⎟ 0.264 ⎢ h ⎥ Δ=Lh/0.412⎢ ⎝⎠⎥ ⎢ eff ⎛⎞W ⎥ ()r ε −+0.258⎜⎟ 0.8 ⎣⎢ ⎝⎠h ⎦⎥

ε −1/2 eff εεrr+−11⎛⎞⎡ ⎛⎞h ⎤ r =+⎜⎟⎢112 +⎜⎟⎥ 22⎝⎠⎣ ⎝⎠W ⎦ Resonance Frequency (cont.)

Note: ΔL ≈ 0.5 h

This is a good “rule of thumb.” Results: resonance frequency

Hammerstad Y

C Measured

N 0.95

Q E

R 0.9

E Z

I 0.85

M R

O 0.8 N

0.75 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

h / λ0

The resonance frequency has been normalized εr = 2.2 by the zero-order value (without fringing):

W/ L = 1.5 fN = f / f0 Basic Properties of Microstrip Antennas Bandwidth: substrate effects

• The bandwidth is directly proportional to substrate thickness h.

• However, if h is greater than about 0.05 λ0 , the probe inductance becomes large enough so that matching is difficult.

• The bandwidth is inversely proportional to εr (a foam substrate gives a high bandwidth). Basic Properties of Microstrip Antennas Bandwidth: patch geometry

• The bandwidth is directly proportional to the width W.

Normally W < 2L because of geometry constraints:

W = 1.5 L is typical. Basic Properties of Microstrip Antennas

Bandwidth: typical results

• For a typical substrate thickness (h / λ0 = 0.02), and a typical substrate permittivity (εr = 2.2) the bandwidth is about 3%. • By using a thick foam substrate, bandwidth of about 10% can be achieved. • By using special feeding techniques (aperture coupling) and stacked patches, bandwidth of over 50% have been achieved. Results: bandwidth

) ε r = 10.8 %

( 20

T D

I 15

D N

A 10 B

5 2.2

0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

h / λ 0

The discrete data points are measured values. The solid curves are from a CAD formula. εr = 2.2 or 10.8 W/ L = 1.5 Basic Properties of Microstrip Antennas Resonant Input Resistance

• The resonant input resistance is almost independent of the substrate thickness h.

• The resonant input resistance is proportional to εr. • The resonant input resistance is directly controlled by the location of the fed point. (maximum at edges x = 0 or x = L, zero at center of patch.

(x0, y0) W

L L Resonant Input Resistance (cont.)

Note: patch is usually fed along the centerline (y = W / 2) to maintain symmetry and thus minimize excitation of undesirable modes.

(x0, y0) W

x L Resonant Input Resistance (cont.)

For a given mode, it can be shown that the resonant input resistance is proportional to the square of the cavity-mode field at the feed point.

2 RExyin∝ z ()00, y

(x , y ) For (1,0) mode: 0 0 W

2 ⎛⎞π x0 Rin ∝ cos ⎜⎟ ⎝⎠L x L Resonant Input Resistance (cont.)

Hence, for (1,0) mode: y 2 ⎛⎞π x0 RRin= edge cos ⎜⎟ ⎝⎠L (x0, y0) W

The value of depends strongly Redge x on the substrate permittivity. For a L typical patch, it may be about 100- 200 Ohms. Results: resonant input resistance

200 The discrete

data points are )

from a CAD

( 150

formula.

E εr = 10.8

A T

S 100

E R

2.2 T

U 50

N I y 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

h / λ0 (x0, y0) W εr = 2.2 or 10.8 W/L = 1.5 x = L/4, y = W/2 0 0 L x Basic Properties of Microstrip Antennas Radiation Efficiency

• Radiation efficiency is the ratio of power radiated into space, to the total input power.

Pr er = Ptot

• The radiation efficiency is less than 100% due to ¾ conductor loss ¾ dielectric loss ¾ surface-wave power Radiation Efficiency (cont.)

TM0 surface wave

cos (φ) pattern Radiation Efficiency (cont.)

Hence,

PPrr er == PtotPPPP r+++() c d sw

Pr = radiated power Pc = power dissipated by conductors P = power dissipated by dielectric Ptot = total input power d

Psw = power launched into surface wave Radiation Efficiency (cont.)

• Conductor and dielectric loss is more important for thinner substrates. • Conductor loss increases with frequency (proportional to f ½) due to the skin effect. Conductor loss is usually more important than dielectric loss.

1 2 Rs is the surface resistance Rs = δ = of the metal. The skin depth σδ ωμσ of the metal is δ. Radiation Efficiency (cont.)

• Surface-wave power is more important for thicker substrates or for higher substrate permittivities. (The surface-wave power can be minimized by using a foam substrate.) Radiation Efficiency (cont.)

•For a foam substrate, higher radiation efficiency is obtained by making the substrate thicker (minimizing the conductor and dielectric losses). The thicker the better!

•For a typical substrate such as εr = 2.2, the radiation efficiency is maximum for h / λ0 ≈ 0.02. 0.1 0.09 0.08 2.2 0.07 10.8 Note: CAD plot uses Pozar formulas 0.06 0 λ 0.05 h / 0.04 = 1.5 L exact CAD / 0.03 W 0.02 0.01 10.8 or 0 0

80 60 40 20

100 E F F I C I E N C Y

( % ) = 2.2 r

Results: conductor and dielectric losses are neglected ε Results: accounting for all losses

100 2.2

)

% (

exact

Y 60

C CAD

N E

I εr = 10.8 C

I 40

F E

0 0 0.02 0.04 0.06 0.08 0.1

h / λ0

εr = 2.2 or 10.8 W/L = 1.5 Note: CAD plot uses Pozar formulas Basic Properties of Microstrip Antenna Radiation Patterns

• The E-plane pattern is typically broader than the H- plane pattern. • The truncation of the ground plane will cause edge diffraction, which tends to degrade the pattern by introducing: ¾ rippling in the forward direction ¾ back-radiation

Note: pattern distortion is more severe in the E-plane, due to the angle dependence of the vertical polarization Eθ and the SW pattern. Both vary as cos (φ). Radiation Patterns (cont.)

E-plane pattern

Red: infinite substrate and ground plane Blue: 1 meter ground plane

30 -30

-10

60 -20 -60

-30

-40 -30 -20 -10 90 -90

120 240

150 210

180 Radiation Patterns (cont.)

H-plane pattern

Red: infinite substrate and ground plane Blue: 1 meter ground plane

45 -10 -45

-20

-30

-40 -30 -20 -10 90 -90

135 225

180 Basic Properties of Microstrip Antennas Directivity

• The directivity is fairly insensitive to the substrate thickness. • The directivity is higher for lower permittivity, because the patch is larger. Results: Directivity

10 ε r = 2.2

)

B d

( 10.8

Y 6

I T

C 4

E exact

R I

D CAD 2

0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

h / λ 0

εr = 2.2 or 10.8 W/ L = 1.5 Approximate CAD Model for Zin

• Near the resonance frequency, the patch cavity can be approximately modeled as an RLC circuit.

• A probe inductance Lp is added in series, to account for the “probe inductance”.

probe patch cavity

L Lp R C Zin Approximate CAD Model (cont.) R ZjLin≈+ω p 12+ jQ() f / f0 − 1

R 1 Q = BW = BW is defined here by ω L 0 2 Q SWR < 2.0. 1 ωπ==2 f 00LC

L Lp R C Approximate CAD Model (cont.)

RR= in max

Rin max is the input resistance at the resonance of the patch cavity (the frequency that maximizes Rin).

L Lp R C Results : input resistance vs. frequency

60 CAD

) 50 exact

(

n i frequency where the R 30 input resistance is maximum 20

0 4 4.5 5 5.5 6 FREQUENCY (GHz)

εr = 2.2 W/L = 1.5 L = 3.0 cm Results: input reactance vs. frequency frequency where the input resistance is maximum 80

60 CAD exact

)

( 20

i X 0

-20 shift due to probe reactance

-40 4 4.5 5 5.5 6 FREQUENCY (GHz) frequency where the input impedance is real

εr = 2.2 W/L = 1.5 L = 3.0 cm Approximate CAD Model (cont.) Approximate CAD formula for feed (probe) reactance (in Ohms)

a = probe radius h = probe height

η ⎡ ⎛⎞2 ⎤ Xkh=⎢−+⎥0 ()ln ⎜⎟ f 2 0 ⎜⎟ka π ⎣⎢ ⎝⎠r ()0 ⎦⎥ γ XL= ω f p ε

γ 0.577216 (Euler’s constant)

ημε000==Ω/376.73 Approximate CAD Model (cont.)

• Feed (probe) reactance increases proportionally with substrate thickness h. • Feed reactance increases for smaller probe radius.

η ⎡ ⎛⎞2 ⎤ Xkh=⎢−+⎥0 ()ln⎜⎟ f 2 0 ⎜⎟ π ⎢ r ()ka0 ⎥ ⎣ γ ⎝⎠⎦

ε Results: probe reactance (Xf =Xp= ωLp)

εr = 2.2 35 CAD exact 30 W/L = 1.5

)

Ω (

20 h = 0.0254 λ

f X 15 a = 0.5 mm 10

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Xr

xr is zero at the center of the patch, and is xr = 2 ( x0 / L) - 1 1.0 at the patch edge. CAD Formulas

In the following viewgraphs, CAD formulas for the important properties of the rectangular microstrip antenna will be shown. CAD Formula: Radiation Efficiency

ηλλ πη λ ehed e = r r ⎡⎤⎡⎤ hed ⎛⎞⎛⎞Rs 13⎛⎞⎛⎞ε r ⎛⎞L ⎛⎞ 1 1 ++erd⎢⎥⎢⎥ ⎜⎟⎜⎟⎜⎟⎜⎟ ⎜⎟ ⎜⎟ ⎣⎦⎣⎦⎝⎠⎝⎠00hpcWh/16/⎝⎠⎝⎠ 1 ⎝⎠ ⎝⎠ 0

where

d ==tanδ loss tangent of substrate 1 ωμ R ===surface resistance of metal s σδσ2 CAD Formula: Radiation Efficiency (cont.)

hed hed Psp 1 er ==hed hed hed PPsp+ sw Psw 1 + hed Psp where λ hed 1 2 2 Pkhcsp = 2 ()01()80π 0 λε⎡ 3 ⎤ hed 113 3 ⎛⎞ Pkhcsw =−2 ()01⎢60π ⎜⎟ 1 ⎥ 0 ⎣⎢ ⎝⎠r ⎦⎥

Note: “hed” refers to a unit-amplitude horizontal electric dipole. CAD Formula: Radiation Efficiency (cont.)

Hence we have

hed 1 er = 3 311⎛⎞⎛ ⎞ 11+−π ()kh0 ⎜⎟⎜ ⎟ 4 ⎝⎠⎝c1 r ⎠

ε (Physically, this term is the radiation efficiency of a horizontal electric dipole (hed) on top of the substrate.) CAD Formula: Radiation Efficiency (cont.)

The constants are defined as

12/5 c1 =−1 + 2 ε rrε

a2 2422 ⎛⎞31 ⎛⎞ pkWaakWckL=+12()024020 +() +⎜⎟() + ⎜⎟() 10⎝⎠ 560 ⎝⎠ 5

⎛⎞1 22 + ac22⎜⎟()() kW 0 kL 0 ⎝⎠70

c2 =−0.0914153

a2 =−0.16605

a4 = 0.00761 CAD Formula: Radiation Efficiency (cont.)

Improved formula (due to Pozar)

hed 1 er = 1λ 2 Phed Pkhched = ()80π 2 1 + sw sp 2 01() Phed 0 η sp 3/2 2 2 k ε r (x0 −1) Phed = 00 εε sw 4 22 rr()1()11++xkhx100 −+() x 1

x2 −1 222 0 −+ε rrrαα01 ε ε+ αα α −2 01 + 0 x1 = 2 x =+1 ε − x 0 22 r 0 r − 1 εα CAD Formula: Radiation Efficiency (cont.)

Improved formula (cont.)

α00= skhstan ⎣⎡( ) ⎦⎤

⎡⎤ 1 kh0 () s α =−⎢⎥tan ⎡⎤()kh s + 10s ⎣⎦cos2 ⎡ kh() s⎤ ⎣⎦⎢⎥⎣ 0 ⎦

s =−ε r 1 CAD Formula: Bandwidth

⎡⎤⎛⎞ 11161Rs ⎛⎞⎛⎞⎛⎞pc1 ⎛⎞hW ⎛⎞ ⎛⎞ BW =+⎢⎥ d ⎜⎟⎜⎟ +⎜⎟⎜⎟ ⎜⎟ ⎜⎟ ⎜⎟hed ⎜⎟ λ ε πη λ hLe/3 2 ⎣⎦⎢⎥⎝⎠00⎝⎠⎝⎠⎝⎠rr ⎝⎠ 0 ⎝⎠ ⎝⎠

BW is defined from the frequency limits f1 and f2 at which SWR = 2.0:

ff− BW = 21 (multiply by 100 if you want to get %) f0 CAD Formula: Resonant Input Resistance

(probe-feed)

2 ⎛⎞π x0 RR= edge cos ⎜⎟ ⎝⎠L

⎛⎞4 ⎛Lh ⎞⎛⎞ ⎜⎟πλ()η0 ⎜ ⎟⎜⎟ ⎝⎠ ⎝W ⎠ R = ⎝⎠0 edge λ ε πη λ ⎛⎞⎛⎞Rs 116⎛⎞⎛⎞pc1 ⎛⎞Wh ⎛⎞ ⎛⎞ 1 d ++⎜⎟⎜⎟⎜⎟⎜⎟ ⎜⎟ ⎜⎟ ⎜⎟hed ⎝⎠⎝⎠00hLe/3⎝⎠⎝⎠rr ⎝⎠ ⎝⎠ 0 ⎝⎠ CAD Formula: Directivity

⎡⎤ ⎛⎞3 ε r 2 Dkh= ⎜⎟⎢⎥ε 2 ()tanc ()1 ⎝⎠pc11⎣⎦r + tan () k h

where tanc(xxx)≡ tan( ) / CAD Formula: Directivity (cont.)

For thin substrates:

3 D ≈ p c1

(The directivity is essentially independent of the substrate thickness.) CAD Formula: Radiation Patterns (based on electric current model)

L x

h εr

infinite GP and substrate

The origin is at the H-plane center of the patch. y

⎛⎞ W E-plane ⎜πx⎟ Jxs = ˆ cos⎜ ⎟ ⎝⎠⎜ L ⎟ x The probe is on the x axis. L CAD Formula: Radiation Patterns (cont.)

The far-field pattern can be determined by reciprocity. θφ θφ ⎡⎤⎛⎞kWy ⎡ ⎛⎞kL ⎤ ⎢⎥sin ⎜⎟⎢ cos x ⎥ 2 ⎜⎟ hex ⎛⎞πWL ⎢⎥⎝⎠⎢ ⎝⎠2 ⎥ Erii(, , )= E() r , , ⎜⎟ 2 2 2 ⎢⎥kW ⎢ ⎥ ⎝⎠y ⎛⎞ ⎛⎞kLx ⎢⎥⎢⎜⎟− ⎥ 2 22⎜⎟ i =θ or φ ⎣⎦⎣⎝⎠ ⎝⎠⎦ π

kkx = 0 sinθ cosφ

kky = 0 sinθ sinφ

The “hex” pattern is for a horizontal electric dipole in the x direction, sitting on top of the substrate. CAD Formula: Radiation Patterns (cont.)

hex Erφ ( ,,θ φφθ)=− E0 sin F( )

hex Erθ ( ,,θ φφθ)()= E0 cos G

⎛⎞− jωμ θθwhere 0 − jkr0 Ee0 = ⎜⎟ ⎝⎠4 πr

θθ θ 2tan(khN0 (θ )) F ()=+Γ1 TE = () tan()khN0 ()θ − jN()θθ sec

2 tan(khN0 (θθ)) cos G ()=+Γ=cos() 1 TM () tan()khN()θ − j εrθ cosθ 0 N ()

2 N ()θ =−εθr sin () Circular Polarization

Three main techniques:

1) Single feed with “nearly degenerate” eigenmodes. 2) Dual feed with delay line or 90o hybrid phase shifter. 3) Synchronous subarray technique. Circular Polarization: Single Feed

The feed is on the diagonal. The patch is nearly (but not W exactly) square.

Basic principle: the two modes are excited with equal amplitude, but with a ±45o phase. Circular Polarization: Single Feed

y Design equations: 1 BW = Resonant frequency 2Q ff0 = CP is the optimum CP frequency (SWR < 2 ) W

x00= y ⎛⎞1 ffx = 0 ⎜⎟1∓ ⎫ 2Q ⎝⎠⎪ Top sign for LHCP, L x ⎬ bottom sign for RHCP. ⎛⎞1 ⎪ ffy =±0 ⎜⎟1 ⎭ ⎝⎠2Q

and are the resonant input resistances of the two LP ( and ) R ==RRx y Rx Ry x y modes, for the same feed position as in the CP patch. Circular Polarization: Single Feed (cont.)

Other variations

Note: diagonal modes are used as degenerate modes y y

L L

L x L x

Patch with slot Patch with truncated corners Circular Polarization: Dual Feed

y Phase shift realized with delay line L

P L

LHCP P+λg/4 Circular Polarization: Dual Feed

Phase shift realized with 90o hybrid (branchline coupler)

L Z0 /2 Z Z0 0 feed

λg/4 Z0

50 Ohm load L λg/4

x LHCP Circular Polarization: Synchronous Rotation

Elements are rotated in space and fed with phase shifts

-180o

-90o

-270o

Because of symmetry, radiation from higher-order modes tends to be reduced, resulting in good cross-pol. Circular Patch

a x h Circular Patch: Resonance Frequency

From separation of variables: a PMC

Ezm= cos()mJkφ ( ρ )

Jm = Bessel function of first kind, order m.

∂Ez = 0 Jkam′ ( )= 0 ∂ρ ρ =a Circular Patch: Resonance Frequency (cont.)

ka= xmn′ a PMC ′ (nth root of Jm Bessel function) c fmn= x mn′ 2πεr

Dominant mode: TM11 c f = x′ 11 11 x11′ ≈1.842 2πεa r Circular Patch: Resonance Frequency (cont.)

Fringing extension: a = a + Δa e a PMC c f = x′ 112πεa 11 er a + Δa

“Long/Shen Formula” :

πε2ha⎡⎤⎛⎞π πεha⎡ ⎛⎞π ⎤ aae =+1 ln⎜⎟ + 1.7726 or Δ=a ln + 1.7726 ah⎢⎥2 ⎢ ⎜⎟ ⎥ r ⎣⎦⎝⎠ r ⎣ ⎝⎠2h ⎦ Circular Patch: Patterns (based on magnetic current model) 2a x

h εr kk= 0 εr

infinite GP and substrate H-plane

The origin is at the y center of the patch. x E-plane

a The probe is on the x axis.

In patch cavity: ⎛⎞ ⎜ Jk1 ( ρ)⎟⎛⎞1 E ()ρ,φφ= cos ⎜ ⎟⎜ ⎟ z ⎜ ⎟⎜ ⎟ ⎝⎠⎜ Jkah1 ( )⎟⎝⎠ (The edge voltage has a maximum of one volt.) Circular Patch: Patterns (cont.)

R E0 Er,θ ()θ,φπ= 2tanccossinakh()z110φ J' k (a θ Q θ )() η0 E ⎛⎞Jka( sinθ) Er,R ()θ,φπ=−2tancsinakh0 ()φ ⎜ 10 ⎟P()θ φ z1 ⎜ ⎟ η00⎝⎠⎜ kasinθ

where tanc(xx/x)= tan( )

⎡ ⎤ TE ⎢ −2 jN ()θ ⎥ P()θθΓθθ=−cos() 1 () = cos ⎢ ⎥ tankhN()θ − jN ()θθ sec ⎣⎢ ()0 ⎦⎥ ⎛⎞ε ⎜ r ⎟ −2cosj⎜ ⎟ θ ⎝⎠⎜ N θ ⎟ () Q()θΓθ=−1 TM () = ε tan()khN()θ − j r cosθ 0 N (θ) 2 N ()θ =−εθr sin () Circular Patch: Input Resistance

ρ0

⎡ Jk2 ( ρ )⎤ RR≈ 10 in edge ⎢ ()2 ⎥ ⎣⎢ Jka1 ⎦⎥ Circular Patch: Input Resistance (cont.)

⎡ 1 ⎤ Redge= ⎢ ⎥ e r ⎣⎢2Psp ⎦⎥ er = radiation efficiency where

π /2 π 2 PkakhN= tanc2 sp ()00∫ () () 8 η0 0 22 ⋅+⎡⎤QJkaPJka()θ ′ 22()()sinθθ θθθ() sin sin d ⎣⎦⎢⎥10θ inc 0

JxJxxinc ( )= 1 ( )/

Psp = power radiated into space by circular patch with maximum edge voltage of one volt. Circular Patch: Input Resistance (cont.)

CAD Formula:

π 2 PkaIspc= ()0 8η0

6 e =1 4 2k 0 Ip= pkaeck= ∑()02 e =−0.400000 cc 2 3 k =0 e4 = 0.0785710 −3 e6 =−7.27509 × 10 −4 e8 =×3.81786 10 −5 e10 =−1.09839 × 10 −7 e12 =×1.47731 10 Feeding Methods

Some of the more common methods for feeding microstrip antennas are shown. Feeding Methods: Coaxial Feed

Advantages: ¾ simple ¾ easy to obtain input match 2 ⎛⎞π x0 RR= edge cos ⎜⎟ ⎝⎠L

Disadvantages: ¾ difficult to obtain input match for thicker substrates, due to probe inductance. ¾ significant probe radiation for thicker substrates Feeding Methods: Inset-Feed

Advantages: ¾ simple ¾ allows for planar feeding ¾ easy to obtain input match

Disadvantages: ¾ significant line radiation for thicker substrates ¾ for deep notches, pattern may shown distortion. Feeding Methods: Proximity (EMC) Coupling

Advantages: ¾ allows for planar feeding ¾ less line radiation compared to microstrip feed patch

microstrip line Disadvantages: ¾ requires multilayer fabrication ¾ alignment is important for input match Feeding Methods: Aperture Coupled Patch (ACP)

Advantages: ¾ allows for planar feeding ¾ feed radiation is isolated from patch radiation ¾ higher bandwidth, since probe inductance problem restriction is eliminated and a double-resonance can be created. ¾ allows for use of different substrates to optimize antenna and feed-circuit performance patch

Disadvantages: slot ¾ requires multilayer fabrication microstrip line ¾ alignment is important for input match Improving Bandwidth

Some of the techniques that has been successfully developed are illustrated here.

(The literature may be consulted for additional designs and modifications.) Improving Bandwidth: Probe Compensation

L-shaped probe:

capacitive “top hat” on probe: Improving Bandwidth: SSFIP

SSFIP: Strip Slot Foam Inverted Patch (a version of the ACP).

• Bandwidths greater than 25% have been achieved. • Increased bandwidth is due to the thick foam substrate and also a dual-tuned resonance (patch+slot). patch substrate patch

foam microstrip substrate microstrip line slot Improving Bandwidth: Stacked Patches

• Bandwidth increase is due to thick low-permittivity antenna substrates and a dual or triple-tuned resonance. • Bandwidths of 25% have been achieved using a probe feed. • Bandwidths of 100% have been achieved using an ACP feed.

patch substrates driven patch parasitic patch microstrip substrate

microstrip line slot Improving Bandwidth: Stacked Patches (cont.)

-5

) -10

d (

-15

s s

o Measured

-20 L

Computed n

r -25

t e

R -30

-35

-40 3 4 5 6 7 8 9 10 11 12 stacked patch with ACP feed Frequency (GHz)

-10 dB S11 bandwidth is about 100% Improving Bandwidth: Parasitic Patches

Radiating Edges Gap Coupled Microstrip Antennas (REGCOMA).

Non-Radiating Edges Gap Coupled Microstrip Antennas (NEGCOMA)

Four-Edges Gap Coupled Microstrip Antennas (FEGCOMA)

Bandwidth improvement factor: REGCOMA: 3.0, NEGCOMA: 3.0, FEGCOMA: 5.0? Improving Bandwidth: Direct-Coupled Patches

Radiating Edges Direct Coupled Microstrip Antennas (REDCOMA).

Non-Radiating Edges Direct Coupled Microstrip Antennas (NEDCOMA)

Four-Edges Direct Coupled Microstrip Antennas (FEDCOMA)

Bandwidth improvement factor: REDCOMA: 5.0, NEDCOMA: 5.0, FEDCOMA: 7.0 Improving Bandwidth: U-shaped slot

The introduction of a U-shaped slot can give a significant bandwidth (10%-40%).

(This is partly due to a double resonance effect.)

“Single Layer Single Patch Wideband Microstrip Antenna,” T. Huynh and K. F. Lee, Electronics Letters, Vol. 31, No. 16, pp. 1310-1312, 1986. Improving Bandwidth: Double U-Slot

A 44% bandwidth was achieved.

“Double U-Slot Rectangular Patch Antenna,” Y. X. Guo, K. M. Luk, and Y. L. Chow, Electronics Letters, Vol. 34, No. 19, pp. 1805-1806, 1998. Improving Bandwidth: E-Patch

A modification of the U-slot patch.

A bandwidth of 34% was achieved (40% using a capacitive “washer” to compensate for the probe inductance).

“A Novel E-shaped Broadband Microstrip Patch Antenna,” B. L. Ooi and Q. Shen, Microwave and Optical Technology Letters, Vol. 27, No. 5, pp. 348-352, 2000. Multi-Band Antennas

A multi-band antenna is often more desirable than a broad-band antenna, if multiple narrow-band channels are to be covered.

General Principle:

Introduce multiple resonance paths into the antenna. (The same technique can be used to increase bandwidth via multiple resonances, if the resonances are closely spaced.) Multi-Band Antennas: Examples

low-band

low-band feed high-band feed

low-band

high-band

Dual-Band E patch Dual-Band Patch with Parasitic Strip Miniaturization

• High Permittivity • Quarter-Wave Patch •PIFA • Capacitive Loading •Slots • Meandering

Note: miniaturization usually comes at a price of reduced bandwidth.

General rule: maximum obtainable bandwidth is proportional to the volume of the patch (based on the Chu limit.) Miniaturization: High Permittivity

H-plane

ε r =1 ε r = 4 W E-plane W´=W/2

L´=L/2 L

It has about one-fourth the bandwidth of the regular patch.

(Bandwidth is inversely proportional to the permittivity.) Miniaturization: Quarter-Wave Patch

H-plane H-plane

short-circuit Ez = 0 vias

W E-plane W E-plane

L L´=L/2

It has about one-half the bandwidth of the regular patch. Miniaturization: Planar Inverted F Antenna (PIFA)

L < λd /4

shorting plate feed or via top view

side view

A single shorting plate or via is used.

This antenna can be viewed as a limiting case of the quarter-wave patch, or as an LC resonator. PIFA with Capacitive Loading

shorting plate feed top view

side view

The capacitive loading allows for the length of the PIFA to be reduced. Miniaturization: Slotted Patch

top view

0o ±90o

linear CP

The slot forces the current to flow through a longer path, increasing the effective dimensions of the patch. Miniaturization: Meandering

via via

feed feed

meandered quarter-wave patch meandered PIFA

Meandering forces the current to flow through a longer path, increasing the effective dimensions of the patch. Improving Performance: Reducing Surface-Wave Excitation and Lateral Radiation

z feed b ρ shorted annular ring 0 ρ a o x a b h

ground plane feed

SIDE VIEW TOP VIEW

Reduced Surface Wave (RSW) Antenna

D. R. Jackson, J. T. Williams, A. K. Bhattacharyya, R. Smith, S. J. Buchheit, and S. A. Long, “Microstrip Patch Designs that do Not Excite Surface Waves,” IEEE Trans. Antennas Propagat., vol. 41, No 8, pp. 1026-1037, August 1993. RSW: Improved Patterns

Reducing surface-wave excitation and lateral radiation reduces edge diffraction.

space-wave radiation (desired)

lateral radiation (undesired)

diffracted field at edge

surface waves (undesired) RSW: E-plane Radiation Patterns Measurements were taken on a 1 m diameter circular ground plane at 1.575 GHz. Measurement

0 Theory 0

30 -30 30 -30

-10 -10

60 -20 -60 60 -20 -60

-30 -30

-40 -30 -20 -10 -40 -30 -20 -10 90 -90 90 -90

120 240 120 240

150 210 150 210

180 180

conventionalconventional RSWRSW RSW: Mutual Coupling

Reducing surface-wave excitation and lateral radiation reduces mutual coupling.

space-wave radiation

lateral radiation

surface waves RSW: Mutual Coupling (cont.)

Reducing surface-wave excitation and lateral radiation reduces mutual coupling.

0 RSW - Measured -10 RSW - Theory -20 Conv - Measured Conv - Theory -30

-40

[dB] -50 12 S -60

-70

-80

-90

-100 012345678910 Separation [Wavelengths]

“Mutual Coupling Between Reduced Surface-Wave Microstrip Antennas,” M. A. Khayat, J. T. Williams, D. R. Jackson, and S. A. Long, IEEE Trans. Antennas and Propagation, Vol. 48, pp. 1581-1593, Oct. 2000. References

General references about microstrip antennas:

Microstrip and Printed Antenna Design, Randy Bancroft, Noble Publishers, 2004.

Microstrip Patch Antennas: A Designer’s Guide, Rodney B. Waterhouse, Kluwer Academic Publishers, 2003.

Microstrip Antenna Design Handbook, R. Garg, P. Bhartia, I. J. Bahl, and A. Ittipiboon, Editors, Artech House, 2001.

Advances in Microstrip and Printed Antennas, K. F. Lee, Editor, John Wiley, 1997.

Microstrip Antennas: The Analysis and Design of Microstrip Antennas and Arrays, David M. Pozar and Daniel H. Schaubert, Editors, Wiley/IEEE Press, 1995. References (cont.)

General references about microstrip antennas (cont.):

Millimeter-Wave Microstrip and Printed Circuit Antennas, P. Bhartia, Artech House, 1991.

The Handbook of Microstrip Antennas (two volume set), J. R. James and P. S. Hall, INSPEC, 1989.

Microstrip Antenna Theory and Design, J. R. James, P. S. Hall, and C. Wood, INSPEC/IEE, 1981. References (cont.)

More information about the CAD formulas presented here for the rectangular patch may be found in:

Computer-Aided Design of Rectangular Microstrip Antennas, D. R. Jackson, S. A. Long, J. T. Williams, and V. B. Davis, Ch. 5 of Advances in Microstrip and Printed Antennas, K. F. Lee, Editor, John Wiley, 1997. References (cont.)

References devoted to broadband microstrip antennas:

Compact and Broadband Microstrip Antennas, Kin-Lu Wong, John Wiley, 2003.

Broadband Microstrip Antennas, Girish Kumar and K. P. Ray, Artech House, 2002.

Broadband Patch Antennas, Jean-Francois Zurcher and Fred E. Gardiol, Artech House, 1995.