PATCH antennas formed with high-dielectric-constant (epsilon) thick su
bstrates are being used to satisfy the size requirements of portable s
ystems such as radio pagers and cellular handsets. The use of a thick
substrate reduces the patch dimensions by increasing the effective wid
th. However, high-E material also reduces the operating bandwidth whil
e the use of thick substrates increases surface-wave effects, which de
grades performance. An alternative is to employ a patch antenna that i
s short-circuited at one end. This approach results in a patch size th
at is half that of an open-ended antenna at the same resonant frequenc
y. A simple closed-form equation can be used to calculate the input im
pedance of these compact antennas.