Audio Induction Loop Theory  Theory of Operation
This page goes into the "nuts and bolts" of why and how an Induction Loop works and fully explains the subject using 3D trigonometry, vector diagrams and other complex terminology. Written by Leon Pieters the Managing Director of Ampetronic and someone who knows his subject inside out, from both a theoretical and practical perspective. Also has an input into setting the reference standards published by the BSI (British Standards Institute) to define how loop systems are to perform.
You will need pencil, paper and a strong Cappucino to understand this, but it IS worth studying if you want to really understand how Induction Loops work.


Audio Frequency Induction Loops  Fact or Imagination.
An exploration of the basic underlying theory and practice of complex loop systems.
Leon Pieters Ing. Tech., M.Inst.S.C.E. Ampetronic Ltd.
Audio Frequency Induction Loops, now sometimes known as AFILS carry with them a fair amount
of mythology. Many people claim to some extent that to design and install loop systems, especially
complex ones, we need the induction loop equivalent of the gardener's green fingers, combined with
an awareness of the mystical properties of loops. As a result, a sizeable amount of rubbish is talked
about this problem, and customers are misled (and taken for a financial ride) by those who are most
guilty.
An AFIL is actually a fairly simple system, whose behaviour can normally be fully described by
normal textbook physics. There are some unusual conditions where the presence of massive steel
structures render the systematic analysis extremely difficult, but even here, we can normally use
common sense to perceive the probable problem and solution.
In this paper I propose to deal with two major areas of (mis)understanding:
 Vectorial concept of magnetic fields.
 Amplifiers and loop specifications.
1. Electrical Current in a Wire  Magnetic Fields
We all know from our physics books that when we run an electrical current through a wire, a
magnetic field is established round this wire. The strength of this field is dependent upon the
distance from the wire, but this field retains the same strength, irrespective of direction, if we stay at
the same distance. As such, we can draw lines of equal field strength forming circles centred on the
wire. This is shown in Fig. 1, where a current I is causing magnetic field lines to pass throughout the space surrounding the wires. Because of this circular pattern, we can talk of magnetic vectors,
having a spatial orientation. Along line V1, the field orientation is horizontal (ignoring components
from other sections of the loop pattern), while along line Z1 the field vector is vertical. At all other
directions and positions, the field vector has a value that can be resolved in vertical and horizontal
components.
The actual magnitude of the field at any point in space can be calculated. The most common
formula for this found in reference textbooks is the wellknown Biot and Savard analysis, and this is
shown in Fig.2.
For a current I in wire A, we get a field strength at point P as given by the formula, where H is the vertical component of the field vector, x and h being the horizontal and vertical distances from point
P to wire A. For a full loop A B C D, we need to calculate the individual values for all the wires,
and adding them.

This Paper was presented to the May 1994 conference of the Institute of Sound and Communications Engineers. 
Ampetronic Ltd,
Northern Road, Newark, Nottinghamshire, NG24 2ET
United Kingdom
Telephone: +44 (0) 1636 610062
Fax: +44 (0) 01636 610063
ampetronic.com

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This is the fundamental formula used by Ampetronic in their computer program, where additional
calculations are made for allowing wires to be positioned anywhere in space at any angle (oh, what
lovely 3D trigonometry!), current ratios between loops, phase shift with RMS summing etc. Using
this tool, we can analyse the strength of the vertical magnetic component (the only one used in
hearing aids, though we can look at any vector angle). If we scan along line Z1 in Fig.1, we will get
a component of very high value close to the wire, and weakest in the middle. If we scan along line
Z2, we will find that now we meet a "null" in the field nearly above the wire. The actual point is
along a line shown as System Null Line, and this is caused by the component from the opposite
wire. We have plotted the field above a 10m x 15m rectangular loop, but with the height as a
percentage of the loop width. As the formula shows, only ratios matter, and this approach offers a
universal solution. In Fig. 3a and Fig. 3b we have plotted against the shown percentages and this
demonstrates that the worst loop position is at the hearing aid level. We normally recommend 14%
as an optimum value, but as the graphs show, there is a fairly wide latitude of displacements, and of
course the listening plane can be just as well above as below the loop plane.
Using the vector concept, we can now begin to analyse the behaviour of complex loop patterns. A
common problem is in theatres where we have loops round the stalls area and the circle (balcony)
area.
Fig. 4 shows the vectors due to current in both loops, which in this instance is the same phase
(vertical component in the middle of each loop). Here we see that underneath the balcony, the
vectors have the same orientation, and add together. However, in front of the balcony they are now
opposed, i.e. trying to cancel and the field at stalls level is attenuated.
This addition  subtraction problem is normally detrimental to obtaining a performance that satisfied
the field strength tolerance levels of BS6083 pt. 4.
An effective solution is shown in Fig. 5. The two loops are driven with signals that are phaseshifted
by 90º over the entire audio band. With maximum and equal values of A and B, changing the
magnitude and reversing phase, the signal sum in the receiver is the RMS sum S. This can vary by
3db when A and B are equal, and one of these components goes to null, and reverses phase.
Compare this to the inphase situation, where we can go from zero to double strength.
Fig. 6a, 6b and 6c show an actual theatre situation, with a typical curved balcony at a steeper angle
than the stalls area. Fig.6b is the scan from the rear to the front at stalls listening level, while Fig.6c
is the same, for the balcony.

Four sets of curves are shown: 

 both loops in phase  balcony is current reversed 

Y = 0 Y = 180º 
For both of these situations, the current magnitude is the same (loops in series). 

 balcony loop at current ratio to equaliseoptimise field strength Y = 180°
 phase shift of 90º between loops with optimum currents. 

The peaks at the rear and front are caused by the finite distance from loop plane to listening plane,
which is actually too small.
Another area where vector orientation matters is in crosstalk reduction between adjacent loops.
Outside a loop , in the same plane, the magnetic component is mainly vertical, and positioning
another loop there, fed by a weak audio signal from the main loop, does not work as the vector
angles from this correction signal do not line up with the spillover component of the first loop. It
should be noted that outside the loop, the components from the two sided of the loop are in opposite
phase, so that a significant attenuation exists. In general, the highest peak outside a loop is about 
12db down on the signal inside the loop, and then attenuates further.

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This same criteria exists where loops are stacked, and the heavily touted method of feeding a small
amount of signal into a loop to cancel an external interfering signal cannot ever work at the
crosstalk levels of 40db relative to normal signal used by Ampetronic in the design of lowspill
systems.
Another further area of concern is the installation of loops in a mosque, where the worshipper
bends over until the head is touching the floor, and the hearing aid axis is nearly horizontal. Special
solutions are needed for this.
In lecture theatres and conference rooms similar considerations can apply as the listener may bend
the head substantially while making notes, and the local magnetic orientation needs checking to
prevent undesirable null areas.
An analysis of magnetic vectors also shows that in multiloop systems, crossover areas, etc. as
shown in Fig. 7a, there is no need to keep the conductors close together. A magnetic "null" (vertical
component) exists on the centre line, as is shown in Fig. 7b. This method of creating a spatial null
away from the cable can sometimes be very desirable in the design of dedicated systems.
2. Amplifier Power and Loop Specification
A significant area of misapprehension exists on the specification of the loop driver and the cable to
use. Despite the design of specialised current driving amplifiers, design to drive singleturn loops,
we still find in various designs methodologies (such as published in “Public Address” recently
coming from the Millbank stable) references to using multiturn loops.
A length of wire positioned as a loop looks like a normal RL network as shown in Fig. 8. The
impedance rises by 3db at the frequency where R=Z . This also means that when driven by a
normal (voltage) amplifier, this will be the 3db response frequency in the absence of specialised
correction.

Cable Section in mm² 
Single Turn Loop 
2  Turn Loop 
3  Turn Loop 
0.50 
2864 
1432 
954 
0.75 
1910 
955 
637 
1.00 
1432 
716 
477 
1.50 
955 
477 
318 
2.50 
573 
286 
191 
Cable Section AWG 
Single Turn Loop 
2  Turn Loop 
3  Turn Loop 
22 
4052 
2026 
1350 
20 
2548 
1274 
849 
18 
1772 
884 
591 
16 
1091 
545 
364 
14 
697 
346 
231 
12 
436 
218 
145 
10 
275 
137 
92 
Table 1: 3db frequency in Hz versus copper size for loop cables. 
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It is accepted that the inductance of wire is very nearly 2µH/metre, for single cable in space. This
allows us to establish a frequency for each cable size where this 3db point falls. The data in table 1
is given for single, two and threeturn loops. As the inductance is little affected by the loop size, the
figures can be used with some measure of accuracy.
The reduction in corner frequency is due to the fundamental fact that while resistance increases
linearly with the number of turns, the inductance is increased by the square of the turns number.
Hence, for a 3turn loop, R increases 3 fold, Z increases 9 fold, hence the corner frequency is
reduced by a factor of 3. This is shown even more clearly in Fig. 9, which shows the impedance of
a 20m x 30m loop (100m perimeter) against frequency for different wire sizes in single and 3turn
configurations.
All amplifiers have a limiting output voltage, and operation into the clipping area generates RFI
which will become illegal. At the output current needed, this gives a limiting impedance for the
amplifier.
Analysis of the power distribution of speech indicates that the amplifier must be capable of
supplying the loop with the full required current at all frequencies up to at least 1.5KHz, beyond
which the drive capability can be allowed to drop at 6db/octave . Note that this is not the same as
frequency response, which I believe should be measured 20db below maximum current, to allow for
the peak limitation effect, and any signal processing to eliminate clipping.
Obtaining the loop impedance at 1.5KHz, and knowing the amplifier limiting impedance permits us
to estimate whether the loop  amplifier combination is acceptable.
Regrettably, most manufacturers do not publish the peak output voltage. Fig.9 indicates the
maximum fullpower impedance for the ILD9 loop driver, and it can be seen that this amplifier has
no difficulty satisfying the frequency requirements on this size loop. We do know of several
instances where this has been impossible, mainly because long, narrow loops can require a current
well inside the capability of the amplifier, yet the total cable length is such that the circuit
impedance is too high.
A further aspect of this is the need to choose a copper resistance which is less than this maximum,
so that there is headroom for the inductive component. Several suppliers seem to ignore this vital
aspect.
Fig. 9 demonstrates also clearly the nearimpossibility of driving multiturn loops in current mode.
In voltage mode, the frequency correction needed to meet the frequency response requirements of
BS6083 pt.4 is virtually nonpractical, while also needing a very powerful amplifier. This is due to
the need for full current capability when driving impedances of greater than 15. This equates to a
high power into a reactive load, for which normal amplifiers are not designed.
This paper has addressed two major areas of concern in AFILS, but there are many others that need
attention and guidance. Regrettably, very little of this exists anywhere in print.
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