5.5 FREE-SPACE SINGLE-PHOTON LIMIT FOR ENERGY IN EM
COMMUNICATION
First, a communication system operation in free space will be considered so that the effects of the
transmission medium such as absorption of radiation can be ignored. The minimum energy require-
ments in EM communication can be estimated based on the fact that the radiation can be emitted or
absorbed only in discrete increments – photons (see Box. 5.2). This means, among other things, that at
least one photon must be absorbed by a receiving device and the photon energy (Box 5.2) can be
viewed as the lower bound on the energy of EM communication.
BOX 5.3 ANTENNA
An antenna system provides a practical means of transmitting to a distant point in space energy (in the EM form) and
information. The antenna performance is characterized by the efficiency of transmission and the signal distortion.
(1)
In general, for an efficient antenna the antenna length should be comparable to the operational wavelength, L
ant
w
l
.
Some common simple antennas are the linear half-wave dipole (Fig. B5.3a) and the loop antenna (Fig. B5.3b).
Small loop antennas (i.e. the loop circumference 2
p
r <
l
/4) are often used in size-constrained applications.
(1) L.J. Chu, “Physical limitations of omni-directional antennas”, J. Appl. Phys. 19 (1948) 1163–1175.
r
/4
/4
(a)
(b)
FIGURE B5.3
Common simple antennas: (a) linear half-wave dipole and (b) loop antenna
R
loss
P
loss
=I
2
R
loss
P
in
I
R
rad
P
rad
=I
2
R
rad
FIGURE 5.4
Depiction of a typical antenna circuit model
5.5 Free-space single-photon limit for energy in EM communication 131
Consider the case of a uniformly radiated electromagnetic wave connecting a 10-
m
m nanomorphic
cell to an external device located at a distance, r, from the cell (Fig. 5.5). As was stated above in the
limit, at least one transmitted photon must be absorbed by the external detector for successful
communication. If the location of the external receiving device relative to the nanomorphic cell is
unknown, then in order to guarantee that at least one photo n will reach the detector, the entire sphere of
radius r must be ‘covered’ with photons. The area ‘covered’ by one photon of wavelength
l
isw
l
2
and
therefore the total number of photons needed to be emitted into the solid angle of 4
p
steradians (a
complete sphere) is
N
4p
w
4pr
2
l
2
(5.17)
Note that (5.17) is a variation of the Friis formula for signal strength attenuation with increased
distance [6,7].
The energy of each photon is
E
ph
¼ hn ¼
hc
l
(5.18)
Thus, the energy associated with one full ‘communication packet’, i.e. the minimum energy required
to transmit one bit of information such that it is equally accessible at all points on the sphere, is
approximately
E
com
¼ N
4p
,E
ph
w
4pr
2
l
2
,
hc
l
¼
4phcr
2
l
3
(5.19)
As was discussed in the previous section, the size of the transducer (e.g. the antenna) needs to be about
the same as the radiated wavelength,
l
(in order to maximize antenna efficiency). Let the antenna size
r
L
cell
~10 m
FIGURE 5.5
Illustration of communication between a nanomorphic cell and an external device
132 CHAPTER 5 Nanomorphic cell communication unit
be limited by the cell size, i.e.
l
wL
cell
w10
m
m. If the distance between the cell and the receiver r ¼ 1m,
Eq. (5.19) gives E
com
w2.510
–9
J/bit. Note that this energy estimate is a lower bound on commu-
nication and it does not consider, e.g., efficiencies of the transducer and detector, noise, etc.
The above result (5.19) reveals that the ubiquitous (i.e. omnidirectional) com munication by the
extreme microsystem is relatively costly from an energy point-of-view. For example, given a total
available energy of w10
–5
J , as was evaluated in Chapter 2, and E
com
w2.510
–9
J/bit, the maximum
number of bits the cell could send is
N
bit
¼
E
stored
E
com
w
10
5
J
2:5 10
9
J=bit
w4000 bits (5.20)
A comparison between the number of binary switching operations N
bit
obtained with 10
–5
J (see
Chapter 3) and the number of omnidirectional bits transmitted with the same amount of energy is given
below.
As can be seen, the communication is a very costly process compared to computation. The undirected
transmission of one bit of data is vastly more costly from an energy point of view than switching the state
of a single transistor. Note that the above derivation is very conservative since neither issues of noise nor
transmission losses have been taken into account. This will be considered in the following sections.
It is instructive to compare the result (5.19) to the existing radios under consideration for the
wireless sensor network applications [7,8]. Figure 5.6 displays the experimental data along with the
FIGURE 5.6
Energy to send a bit: a comparison of the single photon limit (5.13) with the energy per ‘useful bit’ data for
wireless sensor network communication [8]
Computation Communication
E
SW
w 10
–18
J E
com
w 10
–9
J
N
bit
w 10
13
N
bit
w 10
3
5.5 Free-space single-photon limit for energy in EM communication 133
Get Microsystems for Bioelectronics now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
