where L is the target inductance in henries,
is the constant 3.14..., F is the
carrier frequency in Hz, and C is
the resonating capacitor in farads.
I used .033 uf capacitors in all the 1818.818 kHz Minimum Mass RF
Couplers I have built, and this
resonates at 1818.818 KHz with and inductance of 23 micro henries.
There are several formulae available for calculating the number of
turns
to use in a coil once you decide how much space you have for it, but I
haven't found one that seems to get close enough to use without
trimming. To get a loop of the desired inductance, I wind a coil of
about the number of turns I expect to need, and then measure it.
Since
inductance is proportional to the square of the number of turns in a
coil,
I calculate an inductance factor for that size coil, and then I use
that
inductance factor to calculate the number of turns I will need. If I am
careful, this goes pretty quickly with only a couple of iterations
before the inductance is close enough to work with.
Inductance factor K,
where K is the inductance factor, L is
the inductance in
Henries, and N is the number of turns in the coil. For the
5.5 cm loop of #30 magnet wire used in some projects, the
constant came out as 1.11e-7 ( So the inductance is 111 nano henries
times the number of turns squared) and the number of turns to get 23
micro henries
came out to be 14.3 turns, so I just wound 14 turns and the measured
inductance came out to be 21.8 micro henries.
For convenience, here it is re-arranged to show the N, number of turns
once you know k.
The antenna's operation in transmit mode is analogous to its operation
in the receive mode, so let's take the receive mode first. The better
the receiving antenna, the larger the signal appearing across it, and a
lot
of factors affect the amplitude. Looking at how these factors relate to
one
another (See Formula 1) can be useful in understanding how to optimize
the
design for a particular application. At first glance the formula may
look
a little intimidating, but all it really means is that the higher the
carrier
frequency, the more turns on the antenna, the higher the antenna's Q,
the
larger the antenna's diameter, and the stronger the RF magnetic field
received
by the antenna, the larger the signal at its output - larger signals on
the
output correspond to greater sensitivity.
Besides the received signal strength, sensitivity increases as linear
function of the carrier frequency, the number of turns and the physical
size
of the loop and the Q (Quality factor) of the antenna.
Formula 1. This is simplified
expression that shows the major factors
that affect signal amplitude at the input to the receiver. Please take
note that the constant "K" in the formula immediately above is not the
inductance factor "K" used to assist in calculating the number of turns
to use in the loop.
In the case of Minimum Mass RF Couplers, the upper frequency limit is
set by
the response of the controllers' on-chip comparator and the speed at
which
controller can process the incoming interrupts, and the chosen carrier
frequency is 1818.818 KHz.
Antenna size, or effective area is one of the easier factors to
control. The initial prototype and some of the battery operated devices
I've built use 5.5 cm diameter circular air core loops because this is
a convenient size and they are easy to make. In the RS-232 base unit,
where space was
not such an issue, I used a larger square air core loop that took up
most
of the available space to extend the range a little bit.
In another application, where space is a premium, I retrofitted an
RS-232 LCD display board with the receiver circuit (only
a coil,
capacitor and two resistors + the firmware modifications). To get by
with
a small antenna footprint on the circuit board, I wound the coil
on
a 30 mm ferrite rod. This particular coil is made of 29 turns of #30
wire
on a 3 cm ferrite rod. The rod was covered with a layer of laser
printer paper to cushion the coil so its insulation would not be
scratched or nicked by the hard ferrite as it was being wound. The main
advantage of the ferrite rod is that
its
effective area is much larger than its physical size (A in formula 1 is
larger
for a given circuit board footprint) compared to the air core loop.
The Q of a
Tiny Loop
Another thing ferrite rods can do, and this could be good or bad,
depending upon a given situation, is raise the Q of the circuit. A
resonant circuit's Q, which means "Quality factor" is the ratio of its
reactance of its coil and capacitor to circuit resistance and is a
fundamental
measure of how well the circuit reuses energy stored in the reactive
components from cycle-to-cycle. For the Minimum Mass RF Link
receiver, increasing a circuit's Q increase the sensitivity, but at the
expense
of bandwidth. For the transmitter, increasing Q increases the amount of
current
in the antenna, and thus the strength of the radiation.
Although calculating Q is straightforward if the circuit resistance is
known, high frequency losses including skin effect, and the loading
effects of associated circuitry, calculating Q can give results
that
are off by a factor of two or more. Even though skin effect (the effect
in which a wire's own magnetic field reduces its effective conductive
cross-section) is well understood for straight wires, it is difficult
to predict in the case of several wires bunched together, as we have in
this loop because other losses, such as eddy currents induced in the
wire by adjacent turns or by changing flux gradient at the surface of a
ferrite core, or to a lesser extent, dialectric losses in the
insulating materials.
For the prototype coil design, 14 turns of #30 enameled copper wire
were wound to make a 5.5 centimeter diameter loop, which gives 21.8
micro henries and from a copper wire table, the resistance is estimated
to be 0.76 Ohms. Based on this data, Q was calculated with the formula:
Q = XL/R,
where XL is the reactance of the coil, XL = 2 pi f L, (pi
is
the constant 3.14..., f is the resonant frequency, and L is the coil
inductance
in micro henries. The calculated Q was 32. Remeber, it will be lower
because of the losses mentioned above.
Ringing test with prototype coil
-
14 turns of #30 heavy poly
on 5.5 cm
diam air core with polyester capacitor (21.8 uh).
To test a physical antenna, I measured the Q of a 5.5 cm prototype
coils and its resonating capacitor by pulsing a low voltage (1.25
volts) across it
with a
field effect transistor and then time constant of the decay of the
envelope,
then calculated the effective Q. The pulse generator was
set to a 1 kHz square wave adjusted to saturate
the 2N7000.
The initial flyback pulse rang from 1.25v to about + 13VDC, then
was damped at about -1v by the parasitic diode between the drain
and source of the FET.
The ringing interval was measured as 5.4 microseconds per
cycle (185.2 kHz). Decay to 62% occurred after almost six half-cylces,
or about 16 microseconds. The Q of the circuit is found by the formula:
Q = pi f t ), where pi and f are the same as in Formula 2, and t is the
time it takes
the envelope of the ringing to decay by 38%.
Plugging the time constant the formula gives a Q of only 9 at 182
kHz. About a third of what I estimated based on resistance. This is not
bad news, and it is to be expected given skin and eddy current effects.
The 3 db bandwidth of a resonant circuit can be found by BW =
Q/f (Formula 4), so in this case, the 3 db bandwidth would then be 182
kHz/9 = 20 kHz. Good - it means that the antennas can a little off
center frequency and still
work well with the 1200 baud data signal. Of course the downside will
be that the range will not be as great as it would have been with a
higher Q.
How would one obtain a higher Q? Some ideas are to parallel strands of
finer wire or use Litz wire to reduce skin effect and eddy and copper
resistance losses, or use a ferrite core. Use a high-Q (low loss)
capacitor.
Shielding
The Minimum Mass Wireless Couplers I built showed some sensitivity
toward some typical low frequency noise sources. Most notably, the LCD
backligh power supply on my notebook computer, and the deflection
circuits in my Trinitron CRT display. I was able to reduce the
sensitivity to the electrical part of these noise sources by forming a
grounded foil covering over the loop, being careful not to create a
shorted turn. Making a shorted turn reduced sensitivity to noise and
the desired signal.
Directionality
.
Magnetic loop antennas are directional. The best
arrangements is to place them so that they are parallel to one-another
as this will
give the greatest error-free range. Antennas that are positioned at 90
degrees to one-another will not be able to communicate as the signals
will
cancel. Some designs get around this problem by using two
orthogonal antennas together.
HOME (More Projects)
Contents ©2005, 2006 Richard Cappels All Rights Reserved.
http://www.projects.cappels.org/
First posted in March, 2005
You can send email to me at
projects(at)cappels.org. Replace
"(at)" with "@" before mailing.
Use of
information
presented on this page is for personal, nonprofit educational and
noncommercial
use only. This material (including object files) is copyrighted by
Richard
Cappels and may not be republished or used directly for commercial
purposes.
For commercial license, click
here.
Liability Disclaimer
and intellectual property notice (Summary:
No warranties, use these pages at your
own risk. You may use the information provided here for personal and
educational purposes but you may not republish or use this information
for any commercial purpose without explicit permission.) I neither
express nor imply any warranty for the quality, fitness for any
particular purpose or user, or freedom from patents or other
restrictions on the rights of use of any
software, firmware, hardware, design, service,information, or advice
provided,
mentioned,or made reference to in these pages. By utilizing or relying
on software, firmware, hardware, design, service,information, or advice
provided, mentioned, or made reference to in these pages, the user
takes responsibility to assume all risk and associated with said
activity and hold Richard Cappels harmless in the event of any loss or
expense associated with said activity. The contents of this web site,
unless otherwise noted, is copyrighted by Richard
Cappels. Use of information presented on this site for personal,
nonprofit
educational and noncommercial use is encouraged, but unless explicitly
stated
with respect to particular material, the material itself may not be
republished
or used directly for commercial purposes. For the purposes of this
notice,
copying binary data resulting from program files, including assembly
source
code and object (hex) files into semiconductor memories for personal,
nonprofit
educational or other noncommercial use is not considered republishing.
Entities
desiring to use any material published in this pages for commercial
purposes
should contact the respective copyright holder(s).