Free This Energy: Resistor Power
In circuit theory any real world electronic device can be reduced into a
simple circuit consisting of four idealized electronic circuit elements,
namely a capacitor, an inductor, a resistor, and a power source
supplying both current and voltage. Even a single electronic component
contains all four of these idealized elements. Most engineers only think
of a component as having only one of these elements when they design a
circuit. But even the lowly resistor posses all four ideal circuit
elements.
More than a load to sink current into... but a current source!
Not just a mere voltage drop... a voltage rise!
Instead of a place where power is lost... a source of power!
How is this possible?
In a conductor electrons are loosely bound to atoms. Indeed they move
from atom to atom in a conduction band. The tiniest bit of energy sends
an electron flying throughout the matrix. Ambient heat creates many
currents within a conductor. The higher the temperature or the smaller
the resistance of the conductor, the greater the currents flowing thru a
conductor.
In a resistor the electrons tightly held by atom and can only move when
hit by a large amount of energy. Instead, ambient heat causes atoms to
vibrate randomly within the matrix. When atoms move together they move
electrons in orbit around them closer together generating regions of
higher voltage. When atoms move away from each other they move electrons
away from each
other generating a region of lower voltage. Ambient heat fills the
resistor with potential differences. The higher temperature or the
greater the resistance, the higher the potential differences within the
resistor.
Why no voltage then when you connect a D.C. meter across a resistor?
The currents and voltages exist as random fluctuations. Just as much
current flows in one direction as flows in the opposite direction. Just
as much of voltage rise appears in one region of a resistor as a voltage
drop appears in another region of the resistor. And random fluctuations
are very very fast, but that doesn't mean you cannot find them. They
exist as random A.C. frequencies and you can hear them as "white noise"
when you crank up an amplifier-speaker combo with no other source of
sound connected.
The current is defined by the equation I=SQRT(4KTB/R) and the voltage is
defined by the equation V=SQRT(4KTBR); where SQRT is the square root, B
equals the bandwidth in hertz, I equals the current in amps, K equals
Boltzmann's constant of 1.380622E-23 joules per degree Kelvin, R equals
the resistance in ohms, T equals the temperature in Kelvins, and V
equals the
voltage in volts.
Now how do you get power from a this?
Simple. If I wanted to extract current from a conductor I'd use a
precision rectifier. But I don't want to bother with the precise biasing
of a double op amp circuit. Instead, I extract voltage from a single
resistor connected across a diode bridge in much the same way as one
connects a voltage source. Ordinary silicon diodes will not do because
their recovery times in the
millisecond range are just too slow. In their place will be high speed
Schottky Barrier diodes with nice picosecond recovery times. The special
diodes will rectify signals in the ten gigahertz range - as the equation
shows the higher the frequency rectified, the higher the output voltage.
Also, as the equation shows the higher the resistance the higher the
output voltage - I'll select a common ten gigaohm resistor.
So how much power do you get out of this circuit?
Given a room temperature of about twenty degree Celsius or 293.15
Kelvins, the output voltage would be about 1.27 volts - not half bad -
and the output current would be about 127 picoamps - not so good - for
an output power of 162 picowatts. Okay it's a small source of power. But
some small electronic devices like LCD watches run off of very small
power sources. If you think
about it, over the past fifty years of the electronics revolution there
has been ado about making circuits ever smaller - miniaturization.
Imagine a trillion of these circuits on a chip - a million columns by a
million rows - all connected together producing enough power for a
portable radio with the added benefit practically no A.C. ripple.
Ah, but there must be a catch?
Yes, the energy as you remember comes from the ambient background heat
around the circuit. As you draw power from the circuit it cools down,
chilling the immediate environment. But on the plus side, this effect
can be put to good use. A freezer oven combo unit becomes possible -
turn on the stove and your freezer cools down. If international
agreements could be worked out allowing power to be sent around the
world, a person in the northern hemisphere in summer cools his house
with these circuits, sends the power to the southern hemisphere where in
wintery cold another person uses the power to heat his house. Half a
year later the seasons switch hemispheres and power flows in the
opposite direction.
But this circuit cannot solve every energy problem. For example, a car
driven from Houston to Fort Worth during a nice sunny August day
consumes so much power - thousands of watts - that the driver would
suffer sever frost bite before ending his journey.