Antenna 199

Figure 8.1: Operation diagram of leaky wave antenn a: (a) β > 0, (b)

β = 0, and (c) β < 0.

8.3 Circularly Polarized SIW Antenna

SIW structures have been recently explored for the design of high-quality fa c-

tor (Q) passive devices in b oth mm-wave and sub-THz regions [233, 234, 23 5].

SIW can be regarded as a dielectric-ﬁlled rectangular waveguide with sur-

rounding walls and metal layers on the top and bottom surfaces, which

leverages the advantages of both planar transmission line and non-planar

waveguide with lowe r loss and wide-band performance in a miniaturized cavity

for on-chip antenna design.

SIW antennas designs are proposed in both PCB scale [2 33] and chip

scale [234] with a wide bandwidth and a hig h gain. In [234], a 400GHz linear

polarized on-chip SIW antenna is demonstrated in SiGe process with -0.55dBi

gain and 7.8% relative bandwidth. However, its dimension has to satisfy an

equivalent electrical length of λ/2, which should be further miniaturized when

designed on-chip.

A compact circular-polarized SIW antenna design is designed in the CMOS

process with corner slots, of which the geometrical conﬁguration is illustrated

in Figure 8.2. The operating frequency of a SIW antenna is determined by

the cavity dimension. It can be approximated by the following equation by

considering the cavity resonance model [236].

f

mnp

=

c

2

√

µ

r

ε

r

s

(

m

L

eff

)

2

+ (

n

W

eff

)

2

+ (

k

h

)

2

(8.3)

where L

eff

= L and W

eff

= W are the eﬀective length and width of the

substrate integrated cavity, c is the speed of light in free space, µ

r

and ε

r

200 Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits

Figure 8.2: Geometrical conﬁguration of the proposed SIW antenna

with four corner slots.

are the relative permeability and permittivity of the dielectric material inside

the c avity and h is the cavity height. The resonance modes with lowest order

are used for a minimum antenna size, considering h is much smaller than the

wavelength when designed on-chip, the available resonance frequencies left are

f

210

and f

120

with

f

210

=

c

2

√

µ

r

ε

r

q

4

L

2

eff

+

1

W

2

eff

f

120

=

c

2

√

µ

r

ε

r

q

1

L

2

eff

+

4

W

2

eff

. (8.4)

After introducing co rner slots with 45

◦

to the edg e, both L

eff

and W

eff

can be approximated by the total eﬀective length of the center rectangular

cavity and two keystone cavities as shown in Figure 8.2:

L

eff

= L

rectangular

+ 2L

keystone

W

eff

= W

rectangular

+ 2W

keystone

(8.5)

where L

rectangular

= L −

√

2L

S

, W

rectangular

= W −

√

2L

S

, W

keystone

and

L

keystone

are the eﬀective lengths of each keystone cavity in the X and Y

directions, resp ectively. The eﬀective length of keystone cavity can be appr ox-

imated by the following equa tions [237]:

(

L

keystone

=

L

S

R

tl

1.152

W

keystone

=

L

S

R

tw

1.152

(8.6)

Antenna 201

with

R

tl

=

L

S

(2W −

√

2L

S

)

√

2W L

S

R

tw

=

L

S

(2L−

√

2L

S

)

√

2LL

S

. (8.7)

With (8.5), (8.6) and (8.7), L

eff

and W

eff

can be simpliﬁed as:

L

eff

= L + 1.042L

s

−

1.737L

2

s

W

W

eff

= W + 1.042L

s

−

1.737L

2

s

L

. (8.8)

As observed fro m (8.8), both the eﬀective width and length are extended

by a factor of L

eff

/L or W

eff

/W after introducing corner slots, which means

the antenna size can be re duced by the same ratio at a particular frequency.

However, the reduction radio is als o limited by higher-order eﬀects. As shown

in (8.8), L

eff

and W

eff

reach their maximums of 1.15L and 1.15W when

L

s

= 0.3W a nd 0.3L, respectively, which is equivalent to a 15% size reduction

in each dimension of SIW antenna.

Note that the lengths of center slots L1 and W 1 can be calculated by:

(

L1 =

1

2f

L1

√

µ

eff

ε

eff

W 1 =

1

2f

W 1

√

µ

eff

ε

eff

(8.9)

where f

L1

and f

W 1

are the resona nt frequencies of center slots, µ

eff

and ε

eff

are the e quivalent permeability and pe rmittivity in the center slots, respec-

tively. In a conventional SIW antenna design [233], to maximize radiation

eﬃciency, both center slots need to have the same resona nt frequencies as the

respective r esonance mode: f

L1

= f

120

and f

W 1

= f

210

. By properly adjusting

the cavity dimensions, f

120

and f

210

can be close to each other so tha t a cir-

cularly polarized radiation is generated at a frequency in between. However,

the antenna designed in such method has a narrow bandwidth, because only

two resonance modes exist. In this work, the radiation bandwidth is extended

by introducing additio nal resona nc e modes in the antenna design, whe re four

resonance modes are generated by designing f

L1

and f

W 1

slightly lower and

higher than f

120

and f

210

, respectively. Mor eover, the antenna perfo rmance

is further impr oved from the following two aspects. Firstly, the radiation eﬃ-

ciency is increased with the cavity heig ht, which could be achieved by selecting

a CMO S process option with a large number of sta cking layers. Secondly, the

metal loss of SIW walls is largely reduced by replacing metal vias with metal

bars. Note that vertical co nnection by metal bars is an option provided in the

standard CMOS process to connect many vias horizontally (Figure 8.3) if the

metal density is not critical in the particular area.

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