IEEE Microwave Magazine - May 2016 - 77

To show the relationships among size,
gain, and EFoM, we made calculations
with different types of antennas.

and as small as possible in the remaining two dimensions, so as to achieve a good EFoM. First, we made
calculations with (very) small antennas and later with
microstrip patch antennas; finally, Yagi-Uda structures were investigated.
In general, electrically small antennas with length
l always have smaller gain and narrower bandwidth
for two reasons. First, bundling of the RF field is more
difficult due to a smaller aperture, leading to a smaller
directivity. Second, the quality factor Q of the antenna
increases with a smaller antenna size, which automatically reduces its bandwidth and efficiency. This results
from the fact that its radiation resistance also decreases
with the smaller size:
R + 12 for l 1 m .
8
l

factor of two, the gain and the EFoM will show a 3-dB
improvement:
G=

m
4r

(4)

A short lossless dipole, with total length l =
1.6 cm, theoretically shows at center frequency of
2.45 GHz, a radiation resistance of approximately
1 Ω, and a directivity of 1.8 dBi (see Table 1). Assuming only small ohmic losses of the same amount in
the matching network, this would decrease the efficiency down to 50%. A gain of only -1.2 dBi would
result, thus reducing the EFoM dramatically due
to the missing port power-consequently, reducing rectifier efficiency. This example clearly shows
that very small antennas do not satisfy the requirements. Therefore, further investigations with patch
antennas were made: a size-optimized square patch
antenna (6 × 6 × 0.5 cm), which shows a gain of
8.2 dBi, providing a EFoM of approximately 8.24 dB;
a 2 × 2 element patch array; and a 4 × 4 element
patch array. The results of these antenna investigations are displayed in Table 1.
The EFoM of the 4 × 4 patch array would be about
7 dB higher (6 dB because of higher gain and 1 dB
related to the higher rectifier efficiency) compared
to the EFoM of the 2 × 2 patch array, even if the 4 ×
4 patch array covers four times its size, as shown in
Table 1. It also has the highest EFoM of all the antennas investigated. Unfortunately, the contest's tight
weight limitation of 15 g could not be achieved with
patch arrays. Even the design of a single patch antenna
would have been a mechanical challenge. Again

(2)

To show the relationships among size, gain, and
EFoM, we made calculations with different types of
antennas. The ideal received power (PAnt in Table 1) is
calculated using (3) and is the available power at the
port of the antenna with gain GAnt, without taking
into account mismatch and antenna losses and under
an incident power density Pd of 1 nW/cm 2 of the field:
2
PAnt = Pd $ G Ant $ m .
4r

A eff

(3)

The approximate rectifier efficiency is based on
measurements of the rectifier with a network analyzer,
which was used as signal source. As shown in Figure 3, a load resistance of 2,250 Ω was attached to the
rectifier, which provided the best efficiency, assuming
ideal matching. Calculating the EFoM, it follows that
the antenna's gain is more important than the antenna's
size. It is clear that the power contributes quadratically
to the EFoM and that the area contributes only linearly.
When increasing the size of the antenna, its corresponding effective antenna area Aeff also increases and,
therefore, the gain G, as can be seen in (4). For example, by increasing the effective area of the antenna by a

Table 1. The antennas investigated for the harvester.

Ideal Received
Power (PAnt)/dBm

Approximated
Rectifier
Efficiency/%

EFoM/dB

Antenna

Length/cm

Width/cm

Antenna Gain
(GAnt)/dBi

Short dipole

1.6

0.5

1.8

-17.44

8.93

Optimized patch

8.2

-11.04

8.24

Patch array 2 x 2

13.3

-5.94

12.07

Patch array 4 x 4

19.3

0.06

19.03

Yagi-Uda four element

9.6

-9.64

11.33

Yagi-Uda six element

15.9

5.75

12.2

-7.04

13.83

Yagi-Uda array 2 x 6 element

15.9

15.15

14.3

-4.94

14.53

May 2016

Table of Contents for the Digital Edition of IEEE Microwave Magazine - May 2016