Low Power Wireless
λ2/4π. When these two factors are combined with gain factors
for the antennas, we have a fundamental RF communications
formula known as the General Friis Equation. An additional
issue which is more applicable to terrestrial communication than
intra-stellar communication is a phase loss factor related to multipath
from one unavoidable reflecting body—Earth (or ‘ground’).
Often referred to as flat-ground multipath or ground-bounce
(not to be confused with power supply noise), this loss tends to
become significant in low-cost, simple antenna systems found
in most SRD applications. The concept and mathematics behind
this effect are addressed in a Maxim application note4.
A paper describing the Voyager Telecommunications System,
published in 2002, provided a budget for the Voyager 2
down-link5. Using a distance of 7.273E+9km from Earth and
the down-link frequency of 8415 MHz, the free-space path loss
can be calculated with Maxim’s link budget tool2 and compared
to NASA’s result. As expected, NASA’s isotropic spreading and
aperture loss of -308.2 dB correlates with the results shown in
the example link budget calculation6. Because the Voyager
probes use circular polarized signals they do not suffer from the
flat-ground multipath problem common to our simple Earth
bound SRD applications. Likewise, there are no obstructions
between the ground-based radio telescope and space, as long
as southern California is facing towards Voyager 1 and the Earth
C
is not in the way. Combining the +89 dBm of TX power from
Voyager 1 and the -308 dB of channel loss from interstellar communication,
M
we are left with -219 dBm of receive signal strength
(RSS) seen here on Earth.
Unfortunately for the terrestrial radios, there are RF “penalties”
incurred in an SRD environment, so it is important to
include them in any link budget calculation. As a radio system
designer, we can use the same link-budget calculator on Voyager
CM
MY
CY
CMY
or an SRD system to determine several useful requirements
Y
K
such as receiver sensitivity or estimated range. If we use a
common ISM frequency of 433.92 MHz and a target distance of
100m for a home SRD application, we can use the tool to make
the calculations7.
Starting with the transmitter performance discussed earlier
(-7 dBm), we calculate a power loss of about 65 dB due to free
space propagation. Flat-ground multipath takes off another
18 dB of power and subtracting even more power by including
three common obstructions (-13 dB for one heavy and two light
walls in a home), we can calculate the signal strength at the
receiver antenna to be about -103 dBm. This value is a lot more
manageable for an average RF engineer compared to the miniscule
RSS at the Goldstone antenna.
THE RECEIVER
The last portion in the link budget which the SRD designer needs
to consider is the receiver block. The signal flow of the receiver
starts at the antenna and, just like on the transmitter, this antenna
can have gain or attenuation. Likewise, after accounting for interconnect
losses we reach the end goal of the link budget process
when we calculate the required sensitivity of the receiver itself.
For the Voyager system the receiver antenna is a towering
70m-wide radio dish known as DSS-14 or “Mars.” This system
provides an enormous 74 dBi of antenna gain with only a minute
0.2 dB of loss from pointing errors. The X-band receiver for
the down-link from Voyager can detect signals at an incredibly
low power of -185 dBm/Hz, but after adding in thermal noise
components, the effective receiver sensitivity threshold is around
-171 dBm (about 0.8E-20 W or 1.78 nVpp into 50 Ω). Subtracting
off the pointing, phase, and telemetry suppression losses
which takes away another 6.5 dB, the total SNR of the Voyager
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