Power Consumption of Analog Circuits
Before embarking on the low-voltage endeavor, it is prudent
to consider the effects of low supply voltage on both analog and digital
circuits, and to identify fundamental limits.
After Vittoz,[69] the minimum possible power consumed by a pole of
analog filtering is
where
-
Pmin,a = the minimum
possible power consumed by a pole of analog filtering, W
-
f = the signal frequency bandwidth,
Hz
-
S = signal power, W
-
N = thermal noise power,
W
If an allowance is made for their voltage gain, Equation 6 also
applies to amplifier circuits. Note from Equation 6 that Pmin,a
varies directly with signal frequency and the S/N ratio in
the circuit. To minimize power consumption, one should, therefore, limit the
peak dynamic range requirement of the analog
circuit because its minimum power consumption increases directly with S/N ratio, an increasingly expensive trade as the required S/N ratio increases. In receivers, this means the aggressive
use of automatic gain control (AGC) and other "floating point analog" systems to
limit the instantaneous dynamic range required of analog circuits. The system
designer should distinguish between the instantaneous S/N
ratio required of analog circuits and the total dynamic range required of the
system.[70] In some
telecommunication systems, such as cellular telephone systems, the required
system dynamic range can be limited by regulatory means (e.g., by limiting the
allowable power present in a receiver's adjacent channel). This can be an
effective technique to reduce the minimum possible power consumption, and
minimum possible supply voltage, of receivers.[71] Unfortunately, in the unlicensed spectrum used by
wireless sensor networks, the receiver designer is not afforded that luxury. No
limits are placed on the size of signals that may be presented to the receiver's
filter circuits. If a specification is not otherwise set (by a standard, for
example) the designer must set one, by making a trade between power consumption
and the loss of system reliability that results from strong signal effects
(adjacent channel selectivity, blocking, etc.). An advantage in this regard held
by wireless sensor networks is that they usually do not support isochronous
communication and, therefore, permit the use of packet retransmissions (and
occasionally deletions). A temporary system failure due to a strong interferer,
therefore, is less of a concern than it might be in other types of networks, and
this flexibility can be traded for reduced receiver power consumption.
A second effect of Equation 6 on receivers is the sideband noise of
oscilators. If the sideband noise of a receiver local oscillator is too low,
reciprocal mixing can occur in the receiver mixers, resulting in poor
selectivity and spurious performance. (This is often a serious design concern in
receivers employing synthesized local oscillators, which may have sideband noise
several orders of magnitude above the thermal limit.) Equation 6 represents a lower bound on
power consumption of an oscillator for a given sideband noise specification
relatively far away in frequency from the desired output; sideband noise closer
to the carrier is dominated by nonthermal effects, including the effects of
flicker (1/f) noise in the active devices.
In transmitters, the effect of Equation 6 is to limit the attainable
transmitted spectral purity. With a fixed thermal noise floor, the level to
which the transmitted signal may rise above the floor is limited by the power
consumption of the transmitter circuits. Or, viewed differently, the minimum
attainable power consumption of the transmitter circuits is limited by the
minimum required transmitted S/N ratio. Regulatory limits
on transmitted spectral purity will usually set this requirement, although lower
limits may be desirable when the collocation
of transceivers from different services is contemplated because the transmitted
noise from the first service may desensitize the receiver of the second. This
can happen, for example, when a Wireless Personal Area Network (WPAN)
transceiver is placed in a cellular telephone handset — the noise transmitted by
the WPAN transmitter can raise the apparent noise floor of the cellular
telephone receiver. For cases such as these, when the noise affects a service in
a different frequency band, RF filtering at the transmitter output may be
employed to maintain the low transmitter power consumption, at the cost of
additional components. If desired receiving frequency of the affected service is
too close to the desired transmitter frequency of the WPAN, however, filtering
is impractical, and other means must be employed, including those that increase
the power consumed by the transmitter.
Note that Equation 6 is a lower bound, and does not take any
sources of noise, other than those due to thermal effects, into account. Nor
does it consider inefficiencies in the active devices, or the power consumption
of support circuitry, such as regulators or bias networks.
It is often stated that it is not possible to make useful systems
employing low voltage analog and RF circuits. Simply stated, this is not true.
Given the S/N limitations discussed, many examples of
transceivers operating at a 1-V supply exist. For example, most radio pagers
employ receivers operating from a single-cell supply, linearly regulated to 1
V.[72] These systems are
fully functional frequency-shift keying (FSK) receivers, employing low-noise
amplifiers, mixers, oscillators, intermediate-frequency (IF) amplifiers,
filters, and detection circuits, and have been sold by the tens of millions for
more than 15 years. The 930-MHz receivers employing a synthesized local
oscillator have a total active power drain of 7 mW or less; 150-MHz receivers
with a crystallized local oscillator can have active power drains below 3 mW.
The RF specifications of these receivers, which must perform in the land mobile
communication environment, far exceed those needed for wireless sensor networks.
(Manku, Beck, and Shin[73] have proposed a modified cascode RF amplifier
design that is suitable for supply voltages below 1 V.) The baseband analog
functions are often designed using current-mode techniques;[74] although there is no
fundamental reason why current-mode circuits should draw less power than
voltage-mode circuits, in practice it is often easier to employ current-mode
techniques when working with a 1-V supply.
A criticism of the previous examples can be that they are
composed largely of bipolar transistors, and do not integrate well with modern
very large scale integration (VLSI); however, the reduction of CMOS gate lengths
due to improved lithographic techniques has increased the maximum frequency of
operation of MOS devices far into the microwave region; submicron MOS is now
widely used for integrated RF circuits.[75][76][77][78] Abidi[79] describes many
CMOS RF circuits capable of operation from a 0.9-V supply. A transceiver
suitable for a wireless sensor network node that operates from a 1.2-V supply in
0.5 μm CMOS is presented in Porret et al.[80] The list is not limited to RF
circuits; for example, Serra-Graells and Huertas.[81] describes a CMOS proportional-to-absolute
temperature (PTAT) voltage and current reference operating from 0.9 V and
dissipating less than 5 μW.
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