Tiny Tuned Loop Antennas

for the Minimum Mass Wireless Coupler

The basic Minimum Mass Wireless Coupler
technology is described and
links to other projects on this site that use the Minimum Mass Wireless
Coupler are located on the web page, Minimum Mass
Wireless Coupler.

Introduction

Loop Antennas are considered to be "samall" when their diameter drops below about 1/10 of the wavelength they are intended to be used at. In this case, I use the term "Tiny" because the antenna's diameter is about 1/30,000 the wavelength, and at 5.5 cm in diameter, they are quite small in human terms. Coils are one of the few components experimenters can easily do a good job of making for themselves, and the coil, with or without the core, is the major component in a resonant loop antenna.

The resonant loop antenna is fundamentally a parallel resonant LC circuit tuned to the carrier frequency. A coil, or in some cases coils, of wire form the antenna, which is usually mostly inductive, and a parallel capacitance is used to make the antenna resonant at the desired frequency. Time varying magnetic fields from the signal source that cross the coils of wire induce current in the loop, which results in a voltage across the output. The closer the incoming signal is to the loop's resonant frequency, the higher the output voltage.

Resonanting the Loop

Usually, I pick a capacitor with a practical impedance at the carrier frequency and then calculate the inductance needed to resonate with it. The formula for finding the target inductance is

,

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.

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.

V = K F N Q A B
cos(alpha), where

V is the voltage across the antenna coil in volts,

K is a constant for the antenna,

F is the carrier frequency in Hertz,

N is the number of turns in the loop,

Q is the quality factor of the tuned circuit (the ratio of XL to R),

A is the effective area of the antenna in meters,

B is the strength of the magnetic field fluctuations at the antenna, and

alpha is the angle of the receiving antenna with respect to that of the transmitter.

V is the voltage across the antenna coil in volts,

K is a constant for the antenna,

F is the carrier frequency in Hertz,

N is the number of turns in the loop,

Q is the quality factor of the tuned circuit (the ratio of XL to R),

A is the effective area of the antenna in meters,

B is the strength of the magnetic field fluctuations at the antenna, and

alpha is the angle of the receiving antenna with respect to that of the transmitter.

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.

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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.

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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.

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.