Handbook for Sound Engineers

Assistive Listening Systems 1549

impedance characteristic and falling loop current will
complement the rising sensitivity characteristic of the
T-coil, Fig. 33-7. Too high an impedance at high
frequencies will result in too low current, producing
poor response and degraded SNR.

A wire size that can handle the required current with
an acceptable heat rise is selected from Table 42-1. The
impedance is then calculated at several frequencies such
as 100 Hz, 1 kHz, and 10 kHz. The following equations
are useful:

(42-4)

where,
L is the inductance in henrys,
r is the radius of the loop in inches,
n is the number of turns,
d is the diameter of the conductor in inches
(this is a simplification of Wheeler’s equation);

and

(42-5)

where,
Z is the loop impedance,
R is the dc resistance of the length of the coil,
f is the frequency of interest,
L is the inductance of the loop from Eq. 42-4.

An example of the calculations required to determine
the impedance of a one turn 20 ft × 20 ft loop of AWG
#20 wire at 1 kHz is

If this is connected to a 1:4 autotransformer, the

amplifier will see 4.84:

Throughout this design procedure there is a certain

amount of approximation involved; for instance, Eq.

42-4 applies to round loops. Error is introduced in

calculating the inductance of a square or rectangular

loop, however, this error is not great enough to seriously

affect the results.

42.2.2.3 Electronic System

The power amplifier is selected that can supply the

required current to the loop. The power required is

determined with the basic equation

(42-6)

The adjustment of the output current is determined

by the equation

(42-7)

An autotransformer or other suitable impedance

matching device is used to match the amplifier to the

loop. In the absence of an impedance meter, the loop dc

resistance may be used for matching to the amplifier

because at the minimum impedance point (low frequen-

cies), the impedance is largely resistive.

A typical loop system diagram is shown in Fig. 42-8.

In very large halls, a delay unit may be required in the

more distant loops in order to avoid excessive time

delays between the loop signal and the acoustic signal.

Equalization is desirable to compensate for any

frequency response irregularities. The equalizer is

adjusted to provide a natural sound quality with a

typical receiver and to insure that power is not trans-

mitted outside the power bandwidth of the receiver.

A compressor is needed to insure that the system

does not produce excessive distortion at high signal

levels, either from clipping the amplifier or from over-

loading the hearing aid T-coil. The compressor should

Figure 42-7. Sensitivity of typical inductive coil. (From

Reference 1.)

Loaded with 2000 7

Open circuit

20

10

0

10

¾

 20

30

100 200 500 1 K 2 K 5 K 10 K

dB

Frequency

L

rn^2

13.5

---------- 2.8r

d

= log----------

ZR

2

2 SfL 10

6–

u

2

+=

L^ 10 ftu12 ft^1

2

u

13.5

--------------------------------------------- 2.8 10 ft^ u12 inches

0.03196

= log-----------------------------------------------------

=143 H

Z 80 10.15

1000

©¹§·u-------------

2

2 Su 103 143 uu 10 6–

2

= +

=1.21 :

PI=^2 Z

I E

Z

=---