Audio-Frequency Induction Loops (IEC 60118-4)

A hearing aid switched to its telecoil picks up a magnetic field instead of sound: the voice of a talker, fed to an amplifier that drives a current round a loop of wire laid in the floor, reaches the listener without the reverberation and the noise of the room in between. Two IEC standards divide the work. IEC 60118-4 says what field the installed system has to produce, where, and with how little noise, and how an installer shows that it does. IEC 62489-1 says how the manufacturer of each component, the amplifier, the loop as a load and the neck loop, measures and states what it does. This guide follows both: the reference level and its units, the field a loop produces, the loop as the load an amplifier drives, the test signals and the meter, the verdicts on a room, a refuge and a counter, the overload test of Amendment 1, and the amplifier and the neck loop.

Every level in the standard is referred to a magnetic field strength of 400 mA/m, 0 dB: $L=20\lg (H/0.4A/m)$. The reference is chosen so that a long-term average of −12 dB, 100 mA/m, gives the hearing aid the same acoustic output as a sound pressure level of 70 dB at its microphone (4.3), while 0 dB itself is the maximum field strength of 8.2.7, read with a 1 kHz sine or the combi signal on the true-RMS meter. The field strength is in amperes per metre because it is proportional to the current in the loop and falls with distance from the conductor; in air the flux density is $B={\mu }_{0}H$, so 400 mA/m is about 0.5 µT (E.6).

A telecoil is a small coil on a ferrite rod, and it responds to the component of the field along its axis: $20\lg |\cos \theta |$, 3 dB down at 45° and 9.3 dB down at 70° (E.2, Figure E.6). A telecoil in a hearing aid worn upright is vertical, which is why every measurement of IEC 60118-4 is made with the pick-up coil vertical unless the users kneel or lie (8.1), and why the horizontal loop in the floor is the usual design.

import numpy as np
from phonometry import electroacoustics

print(electroacoustics.field_strength_level([0.4, 0.1]).round(2))    # [  0.   -12.04]
print(electroacoustics.field_strength([-3.0, 3.0]).round(3))         # [0.283 0.565] A/m
print(round(float(electroacoustics.magnetic_flux_density(0.4)) * 1e6, 3))  # 0.503 µT
print(electroacoustics.telecoil_response([45.0, 70.0]).round(2))     # [-3.01 -9.32]

The ±3 dB window of 10.2 as amended is printed as “283 mA/m to 566 mA/m”: those are $400/\sqrt{2}$ and $400\sqrt{2}$, a factor of $\sqrt{2}$ read as 3 dB; exactly ±3 dB is 283 mA/m to 565 mA/m. E.6 prints the flux density of 1 A/m as 1.256 µT where $4\pi \times 10^{-7}$ rounds to 1.257 µT, a slip the errata register records.

A current $I$ round a loop of $N$ turns produces a field proportional to $NI$ everywhere. IEC 60118-4 E.1 gives the one closed form it uses, the field at the centre of a single-turn square loop of side $d$, in its plane:

and extends it to a rectangle: “Provided that the sides $d_1$, $d_2$ of a rectangular loop are not extremely different”, $d$ is taken as $\sqrt{d_1{d}_2}$. Everything else about the field is a figure in the standard. rectangular_loop_field computes it instead: each of the four sides is a straight filament whose Biot-Savart field closes exactly, so the field at any point, in any component, carries no discretisation. At the centre of a square it is the E.1 formula to machine precision; for a rectangle, the $\sqrt{d_1{d}_2}$ approximation reads low by $\sqrt{(d_1^2+d_2^2)/(2d_1{d}_2)}$, 0.35 dB at an aspect ratio of 1.5.

IEC 62489-1 5.4.10.2 fixes where an amplifier’s field is stated: 1.4 m above the centre of a horizontal square loop whose resistance and inductance equal the rated load. loop_current inverts the exact on-axis field for the current a loop needs, and loop_dimensions answers 5.4.11 the other way round: the largest square loop, and loop of aspect ratio 3:1, whose centre reaches 400 mA/m at 1.4 m with the amplifier’s current.

current = electroacoustics.loop_current(10.0, 14.0, height_m=1.2)
print(round(current, 2))                      # 5.41 A for 400 mA/m above the centre
x = np.linspace(-8.0, 8.0, 641)               # a traverse across the 10 m side, y = 0
field = electroacoustics.rectangular_loop_field(current, 10.0, 14.0, x, 0.0, 1.2)
level = field.level_db("z")
print(x[np.abs(level) <= 3.0][[0, -1]])       # [-4.75  4.75] m within ±3 dB

print(round(electroacoustics.loop_centre_field(1.0, 10.0, width_m=14.0), 4))  # 0.0761 A/m (E.1)
exact = electroacoustics.rectangular_loop_field(1.0, 10.0, 14.0, 0.0, 0.0, 0.0)
print(round(float(exact.h_z_a_per_m), 4))                                   # 0.0782 A/m

print([round(v, 1) for v in electroacoustics.loop_dimensions(5.0)])                    # [10.3, 10.3] m
print([round(v, 1) for v in electroacoustics.loop_dimensions(5.0, aspect_ratio=3.0)])  # [7.4, 22.1] m

print([round(electroacoustics.loop_current(10.0 * r, 10.0), 2) for r in (1, 1.5, 2, 3, 5)])
# [4.88, 5.63, 6.04, 6.41, 6.64] A: Figure H.1 at a 10 m shorter side

Two of the standard’s figures are reproduced point for point. The currents of Figure H.1, for 400 mA/m 1.4 m above the centre of a loop against its shorter side and aspect ratio, come back within the width of the printed line, about 0.01 A at the 10 m end of each curve. The two curves of Figure E.2 b), the vertical and horizontal components 1.2 units above a 15 by 10 loop, come back within about half a decibel across the loop’s 10-unit width, which is the traverse E.1 describes (“the distribution of the vertical component across a loop”). The figure’s own panel a) draws the vertical-field line along the 15-unit length instead, where the vertical component would read about 2 dB higher near the conductor; the errata register records it.

The vertical field across the loop at listening height. Inside, it stays within ±3 dB out to 4.75 m of the 5 m half-width; just above each conductor the field turns horizontal and the vertical component a telecoil reads vanishes, and outside the loop it comes back with the opposite sign. That is the spill a neighbouring room hears, and the reason the useful volume stops short of the walls.

import matplotlib.pyplot as plt

x = np.linspace(-8.0, 8.0, 641)
field = electroacoustics.rectangular_loop_field(current, 10.0, 14.0, x, 0.0, 1.2)
ax = field.plot()
ax.set_ylim(-30.0, 8.0)
plt.show()

The loop is a resistance in series with an inductance (IEC 62489-1 5.4.3.2, B.2). The resistance is $R=\rho Nl/a$ for a conductor of length $l$ and area $a$, with the resistivity of standard annealed copper, 1/58 Ω·mm²/m at 20 °C and 0.00393 per degree (IEC 60028). The inductance of a rectangle of round wire is Grover’s Formula (58); for $N$ turns it is multiplied by $N^2$, the perfect coupling Table B.1 assumes. The magnitude of the impedance, $|Z|=\sqrt{R^2+(2\pi fL{)}^2}$, is $\sqrt{2}$ times the resistance at the corner frequency $R/(2\pi L)$, “1.4 times” in IEC 60118-4 E.3, and the voltage the amplifier has to deliver for a current $I$ is $U=I|Z|$.

Table B.1 of IEC 62489-1 is the oracle. Its resistances all come out of the 20 °C resistivity with the perimeter of each loop, and four of its six inductances out of Formula (58) without the term for the flux inside the wire:

The impedances are computed from the printed $R$ and $L$. The counter loop’s resistance needs the 1.6 m its sides give, not the 1.5 m the table prints for its perimeter, which is an erratum. Table B.1 does not say which formula it used for the inductance, and no reading of the wire size reaches the neck loop’s 85 µH or the large loop’s 218 µH, so those two are not claimed. rectangular_loop_inductance keeps the internal term by default, 2.7 % to 4.2 % more on these four loops, because at audio frequencies the skin depth in copper (2 mm at 1 kHz) exceeds the radius of every conductor in the table: pass internal_inductance=False to reproduce Table B.1. IEC 60118-4 E.3 offers a rule of thumb for a single-turn square loop of side $d$ over a square metre, $L=8d$ µH, and it reads high: for 1.5 mm² wire Formula (58) gives $6.7d$ µH for a 5 m square and $7.8d$ µH for a 20 m one.

r = electroacoustics.loop_resistance(60.0, 1.5)                  # typical place of worship
l = electroacoustics.rectangular_loop_inductance(10.0, 20.0, 1.5, internal_inductance=False)
z = electroacoustics.loop_impedance(r, l)
print(round(r, 3), round(l * 1e6, 1))            # 0.69 ohm 109.2 µH
print(round(z.corner_frequency_hz))              # 1005 Hz
print(z.at([2000.0, 5000.0]).round(2))           # [1.54 3.5 ] ohm
print(round(electroacoustics.rectangular_loop_inductance(10.0, 20.0, 1.5) * 1e6, 1))  # 112.2 µH
print(round(electroacoustics.loop_resistance(60.0, 1.5, conductor_temperature_c=40.0), 3))  # 0.744 ohm

Above its corner frequency the loop’s impedance rises 6 dB per octave, so a voltage-driven loop loses its treble. The usual cure is a current-drive amplifier, whose output resistance, some ten times the loop’s, keeps the current constant while the impedance varies (E.3); the price is voltage, and the overload test of section 7 is where it is paid.

The field strength meter is a sound level meter with a magnetic pick-up coil in place of the microphone, equalized flat within ±1 dB from 50 Hz to 10 kHz, with a true-RMS detector and the 125 ms averaging of its “F” mode (6.1.3); the peak programme meter of 6.1.4 is the alternative, and in case of doubt the true-RMS reading is definitive (6.1.1). field_strength_meter reads a record flat or A-weighted, the latter for the noise measurements of clause 7 and 10.4.

The pink noise of 6.4 is band-limited by third-order Butterworth filters at 75 Hz and 6.5 kHz and has a peak-to-peak to RMS ratio of at least 18 dB, a crest factor of 4; IEC 62489-1 5.4.8.2 b) asks the same signal for 18 dB ±2 dB. Gaussian noise reaches about 5.5 times its RMS in a minute at 48 kHz, 21 dB peak to peak, which meets the first and fails the second, so loop_test_noise clips at 4 times the RMS and rescales, which meets both. The combi signal of 6.6 and Table 2 interleaves 1 kHz tone bursts of at least 1 s, with 5 ms ramps, with at least four times as much of that noise 6 dB lower: the sine’s peaks sit 3 dB below the noise’s, and the amplifier runs cooler than on a steady sine while the level can still be read on the bursts.

fs = 48000
print(electroacoustics.band_limit_response([100.0, 5000.0]).round(2))  # [-0.71 -0.82] dB
noise = electroacoustics.loop_test_noise(fs, 30.0, seed=7)
print(round(20 * np.log10(np.ptp(noise) / np.sqrt(np.mean(noise**2))), 2))  # 18.06 dB

combi = 0.4 * electroacoustics.combi_signal(fs, cycles=2, seed=7)  # sine bursts at 400 mA/m
reading = electroacoustics.field_strength_meter(combi, fs)
print(round(reading.maximum_db, 2), round(reading.equivalent_db, 2))  # 0.0 -3.98 dB

6.4 NOTE 2, and NOTE 3 to 5.4.8.2 of IEC 62489-1, print the theoretical responses of the band-limiting filters as −0.8 dB at 100 Hz and −0.7 dB at 5 kHz. The two filters give −0.71 dB and −0.82 dB, the other way round; the ±1 dB flatness the note explains holds either way. The clause itself asks for “at least one-third-order” filters, a slip for the third order its B.2.3, its own NOTE 2 and IEC 62489-1 all name; both are in the errata register.

The meter on the combi signal. The bursts read 0 dB, the noise 6 dB less, and the maximum indication, which 8.2.7 reads, is the sine’s; the level of the whole record is 4 dB down, which is what spares the amplifier.

ax = reading.plot()
ax.set_ylim(-16.0, 4.0)
plt.show()

1. The site first, loop off (7.1). Everything else normally in use is on and dimmable lighting half-dimmed; the magnetic background noise is read A-weighted at enough points of the intended volume, at 1.2 m for seated and 1.7 m for standing listeners, and it is worth listening to as well, because its spectrum decides how disturbing it is.
2. Set the level (8.2). With a 1 kHz sine, or the combi signal, and the true-RMS meter, the amplifier’s controls are set so that the field reaches 400 mA/m; with speech or pink noise the target is the reading the manufacturer states for 400 mA/m (Table 3 gives −6 dB for pink noise on the RMS meter). A warm-up of 10 min comes first, and the AGC’s release time is waited out after every change of input level.
3. Survey the field and the response (8.3, 8.4). The level at the selected points of the useful volume, and the frequency response at 100 Hz, 1 kHz and 5 kHz at least, starting with 5 kHz, where metal in the building shows first.
4. The noise with the system on (10.4), all inputs muted, A-weighted at the same points as the background noise, so the two can be compared point by point.
5. The overload test (10.3) at the frequency Table 4 gives for the programme, then the commissioning with sound sources in their normal places and, where possible, a few hearing-aid users present (10.1).

The difference between the 0 dB reference and the A-weighted background noise is the reference signal-to-noise ratio of 7.2. Above 47 dB is the ideal, for theatres and wherever the aesthetic value of speech matters; 32 dB is the recommended minimum, and a lower ratio “shall be reported and agreed with the system operator”; as low as 22 dB may be tolerable for short periods, where the noise “has no significant undesirable tonal quality or is mostly at low frequencies”. These are recommendations, and assess_background_noise classes the site at its noisiest point without folding the class into a verdict; noise_is_tonal=True, there and in verify_induction_loop_system, withholds the 22 dB relaxation from a noise with an undesirable tonal quality.

The requirements of the installed system are four. The maximum field is 400 mA/m at one point at least of the useful volume (8.2.1, 8.2.7), and every selected point is within ±3 dB of that specified level (8.4.3); the frequency response is within ±3 dB of the response at 1 kHz from 100 Hz to 5 kHz at every point (8.3.7); and the noise with the system switched on is below −47 dB where the site’s ratio is above 47 dB, otherwise no more than 1 dB above the loop-off level at the same point (10.4.7 as amended, which was 10.2.7). The two sentences of 10.4.7 say “greater than 47 dB” and “less than 47 dB”, so a ratio of exactly 47 dB falls in neither; the 1 dB rule is applied there, and the gap is in the errata register. verify_induction_loop_system judges each requirement it is given on every value it covers, and returns one verdict object.

current = electroacoustics.loop_current(10.0, 20.0, height_m=1.2)   # the typical place of worship
x, y = np.meshgrid([-3.5, 0.0, 3.5], [-8.0, -4.0, 0.0, 4.0, 8.0])     # fifteen seats
levels = np.stack([
    electroacoustics.rectangular_loop_field(current, 10.0, 20.0, x, y, height).level_db("z")
    for height in (1.2, 1.7)
])
first = electroacoustics.verify_induction_loop_system(levels)
print(first.passes, first.failed)                                     # False ('field_strength',)
print(round(first.requirement("field_strength").worst_margin_db, 2))  # -1.41 dB, +4.41 at the corners

levels = levels - 2.0          # turned down 2 dB, so the spread straddles 0 dB
off = [-38.5, -36.0, -40.2, -37.1, -35.4]   # loop off, A-weighted, dB re 400 mA/m
on = [-38.1, -35.6, -39.9, -36.6, -35.0]    # system on, inputs muted
verdict = electroacoustics.verify_induction_loop_system(
    levels,
    frequencies_hz=[100.0, 1000.0, 5000.0],
    response_db=[[-0.4, 0.0, -1.8], [-0.3, 0.0, -2.4], [-0.6, 0.0, -3.4]],
    background_noise_levels_db=off,
    system_noise_levels_db=on,
)
site = verdict.background_noise
print(round(site.reference_signal_to_noise_ratio_db, 1), site.category)  # 35.4 acceptable
print(verdict.passes, verdict.failed)                                    # False ('frequency_response',)
for requirement in verdict.requirements:
    print(requirement.name, round(requirement.worst_margin_db, 2))
# field_strength 0.56 / field_strength_reached 2.41
# frequency_response -0.4 / system_noise 0.5

The first verdict is the lesson of section 2 again: with 400 mA/m set above the centre, the seats near the conductors run 4.4 dB hot, and the cure is to set the level on the spread, not on one point. Turned down 2 dB, the hottest seat still reads 2.4 dB above the reference, which is what 8.2.7 asks: the maximum field reaches 400 mA/m somewhere in the volume. A spread set wholly below the reference, every seat between −3 dB and −0.1 dB, would pass the window of 8.4.3 and fail 8.2.7. The second fails on the far seat at 5 kHz, 3.4 dB down: the loss to metal of Annex F, which the standard gives no model for. Its correction is the response the installer measures and equalizes, and the overload test of section 7 is what checks that the amplifier can afford the lift.

The site is acceptable but not ideal, so the system-on noise is judged on the 1 dB rule, which it meets by half a decibel. The field meets its window once the level is set on the spread; the response does not, at one seat and one frequency, and that is enough to fail the system.

fig, (ax_site, ax_verdict) = plt.subplots(1, 2, figsize=(13.5, 5.6))
verdict.background_noise.plot(ax_site)
verdict.plot(ax_verdict)
plt.show()

A small system is judged at fixed points instead of over a useful volume. Amendment 1 rewrites clause 9: six points for a disabled refuge or call point, along the perpendicular and ±45° at 300 mm and 500 mm from the reference point (Figure 2 a), or on two rows 424 mm and 700 mm wide for a larger source (Figure 2 b), at 1.2 m and 1.7 m; three points for a counter, on a semicircle of 300 mm radius at its bottom and 150 mm either side (Figure 3), at 1.2 m, 1.45 m and 1.7 m, the middle height because a poorly designed installation may have a null there. At every point the level is within ±6 dB of 400 mA/m and meets 8.3.7, at one point at least it reaches 0 dB, and nowhere where people are expected to stand, which Figure 3 puts outside the semicircle of points, is it above +8 dB (9.5).

points = electroacoustics.small_volume_measurement_points("counter")
print(points.shape, points[0, :, :2].round(3).tolist())
# (3, 3, 3) [[-0.15, 0.26], [0.0, 0.3], [0.15, 0.26]]  x, y in m; z the height

counter = electroacoustics.verify_small_volume_system(
    [[5.1, 4.2, 5.3], [2.0, 1.1, 2.2], [-2.9, -3.8, -2.7]],   # rows at 1.2 m, 1.45 m, 1.7 m
    layout="counter",
    standing_area_levels_db=[6.5, 7.9, 9.2],   # the standing area beside the semicircle
)
print(counter.passes, counter.failed)                                    # False ('standing_area',)
print(round(counter.requirement("standing_area").worst_margin_db, 2))    # -1.2 dB

The rows of field_strength_levels_db follow the heights of small_volume_measurement_points, lowest first, so the counter above is strongest at 1.2 m and weakest at 1.7 m. The informative Annex A.4 allows “up to, but not greater than, +12 dB” at 1.45 m for a counter and calls the counter’s requirement less stringent than a refuge’s; 9.5 applies the same limits to both at every height, and 9.5 is what is applied. Amendment 1 also corrects the key of Figure 2 a), whose outer radius the 2014 print gave as 200 mm.

By contract, a useful magnetic field volume with representative points of the installer’s choosing may replace the points of 9.2 or 9.3 (9.4). The same limits of 9.5 hold at every point, and as a minimum the volume has to meet them at one position at least at each height of the clause it replaces: 1.2 m and 1.7 m for a refuge, 1.2 m, 1.45 m and 1.7 m for a counter. The layouts "refuge_useful_volume" and "counter_useful_volume" take the height of each point, and refuse a set of points that leaves one of those heights out.

volume = electroacoustics.verify_small_volume_system(
    [4.6, 3.9, 1.8, 0.7, -2.4, -3.1],
    layout="counter_useful_volume",
    heights_m=[1.2, 1.2, 1.45, 1.45, 1.7, 1.7],
)
print(volume.passes)                  # True

A counter loop that meets its window at all nine points and still fails, because a customer standing beside the semicircle, close to the counter face, reads 9.2 dB. A vertical loop in the counter face makes a strong field close to it by construction, which is what the +8 dB cap and 9.5 NOTE 1 are about.

fig, (ax_area, ax_verdict) = plt.subplots(1, 2, figsize=(13.5, 5.6))
counter.requirement("standing_area").plot(ax_area)
counter.plot(ax_verdict)
plt.show()

Amendment 1 replaces the 1.6 kHz overload test with one tied to the programme. With a 1 kHz sine set 7 dB below the field required at a point, the voltage across the loop is measured and the frequency raised at the same input until that voltage doubles, or the frequency of Table 4 is reached, whichever is the higher frequency (10.3.2), and no clipping may appear at the frequency of Table 4 and that level (10.3.3):

The test frequency is about twice the upper limit because a sine at the limit itself would draw an unrealistically high current from the power supply; the reduced level at twice the frequency loads it the way real programme does (10.3.1). Of the three ways the amendment lists to detect clipping, the second compares the loop voltage with the amplifier’s compliance voltage of IEC 62489-1, and that one is computable from the loop’s impedance and the current the amplifier puts into it. The verdict is taken at the Table 4 frequency, where 10.3.3 puts the requirement; when the voltage doubles only above that frequency, the sweep runs on to the doubling, and the rest of it is drawn and its highest voltage kept as max_voltage_v, but not judged. Here the amplifier lifts its current above 1 kHz to make up the metal loss of section 6:

lift = electroacoustics.amplifier_frequency_response(
    [100.0, 1000.0, 2000.0, 3150.0, 4000.0, 5000.0, 8000.0],
    [2.0, 2.0, 2.4, 2.9, 3.2, 3.5, 3.6],       # output current, A
)
print(lift.response_db.round(2))                # [0.   0.   1.58 3.23 4.08 4.86 5.11] dB re 1 kHz
speech = electroacoustics.verify_amplifier_overload(current, z, 11.0, current_response=lift)
print(round(speech.test_current_a, 2), round(speech.doubling_frequency_hz))  # 2.65 A 2091 Hz
print(round(speech.end_frequency_hz), round(speech.test_frequency_voltage_v, 2), speech.passes)  # 3150 8.71 True
music = electroacoustics.verify_amplifier_overload(
    current, z, 11.0, programme="music", current_response=lift
)
print(round(music.test_frequency_voltage_v, 2), round(music.headroom_db, 2), music.passes)  # 11.99 -0.75 False

The voltage doubles at 2.1 kHz, below the Table 4 frequency in both cases, so the sweep runs on to 3.15 kHz for speech and to 4 kHz for music. The amplifier that serves speech with 2 dB to spare clips on music: at 4 kHz the loop wants 12 V and the amplifier has 11 V. That is the trade the equalization of section 6 made, and it is why a correction for metal loss is decided together with the amplifier and not after it.

The loop as a load, and the overload sweep for music. The rise of the impedance above the corner and the lift of the current multiply, and the crossing with the compliance voltage lies just inside the sweep.

fig, (ax_z, ax_sweep) = plt.subplots(1, 2, figsize=(13.5, 5.6))
z.plot(ax_z)
music.plot(ax_sweep)
plt.show()

IEC 62489-1 lists what an amplifier’s specification states. The rated conditions (5.4.1 to 5.4.6) are declared, not measured; standard measuring conditions put the output current 10 dB below the rated one (5.2.2). The measured characteristics that are computations are these:

• Maximum (distortion-limited) output current (5.4.7): from standard measuring conditions the 1 kHz load current is raised until the total harmonic distortion across the resistive part of the load reaches the rated value, and the current is the total voltage across that resistance over its value. It has to be deliverable for at least 10 s, a condition on the measurement rather than a computation.
• Compliance voltage (5.4.8): the maximum positive-going and negative-going peak voltages across the rated load, over at least 60 s of the specified pink noise with the AGC fully in operation, averaged and divided by $\sqrt{2}$: the RMS voltage of the sine with the same peaks.
• Noise (5.4.9): the equivalent input noise voltage $U_{\mathrm{n}}=U{I}_{\mathrm{n}}/I$, the 1 kHz input that gives the same current as the noise, or the signal-to-noise ratio $S=10\lg (I_{\mathrm{r}}^2/I_{\mathrm{n}}^2)$ dB.
• Frequency response (5.4.12): the load current at one-third-octave centres from at least 50 Hz to 8 kHz, 0 dB at 1 kHz.
• Automatic gain control (5.4.13): the steady-state output current against the source e.m.f.; Amendment 1 adds the recommendation of an input range of at least 32 dB for an output change of at most 3 dB (5.4.13.4).
• Quadrature phase error (5.4.14): two adjacent loops fed about 90° apart make a rotating field instead of nulls; the characteristic is the maximum deviation from 90° over 100 Hz to 5 kHz.

steps = electroacoustics.maximum_output_current(
    [2.0, 3.0, 4.0, 4.5, 5.0],            # V across the 0.69 ohm of the rated load
    [0.05, 0.08, 0.3, 1.2, 4.0],          # THD there, %
    load_resistance_ohm=0.69,
    rated_thd_percent=1.0,
)
print(round(steps.maximum_current_a, 2))  # 6.36 A where the THD reaches 1 %

load = np.clip(4.5 * electroacoustics.loop_test_noise(fs, 60.0, seed=3), -14.0, 14.0)
print(round(electroacoustics.compliance_voltage(load), 2))    # 9.9 V: clipping at ±14 V
print(round(electroacoustics.equivalent_input_noise_voltage(0.1, 1.6, 0.00032) * 1e6, 1))  # 20.0 µV
print(round(electroacoustics.amplifier_signal_to_noise_ratio(5.0, 0.00032), 1))            # 83.9 dB

emf = np.arange(-60.0, 1.0, 5.0)                                   # source e.m.f., dB
output = np.where(emf < -40.0, emf + 30.0, -10.0 + 2.5 * (emf + 40.0) / 40.0)
agc = electroacoustics.agc_characteristic(emf, output)
print(round(agc.agc_range_db, 1), agc.recommended_range_db)        # 40.5 32.0 dB

f = np.array([100.0, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1000]
             + [1250, 1600, 2000, 2500, 3150, 4000, 5000])
phase = 90.0 - 4.0 * np.log2(f / 700.0) ** 2 / 3.0                 # degrees between the currents
quadrature = electroacoustics.quadrature_phase_error(f, phase)
print(round(quadrature.max_deviation_deg, 2), quadrature.max_deviation_frequency_hz)  # 10.73 5000.0
print(round(quadrature.level_increase_db, 2), round(quadrature.level_decrease_db, 2))  # 1.48 -1.79 dB

A deviation $\delta$ from 90° leaves an in-phase component $\sin \delta$ of one field against the other, which raises the level by $20\lg (1+\sin \delta )$ where the two add and lowers it by $20\lg (1-\sin \delta )$ where they subtract. 5.4.14.1 gives the example of 85°, an in-phase part of 0.087, and prints the change as “increased or decreased by 0.72 dB”; the rise is 0.72 dB, the fall 0.79 dB.

The amplifier’s AGC holds its output within 3 dB over 40.5 dB of input, 8.5 dB more than 5.4.13.4 recommends; the quadrature network is within 11° of quadrature over the speech band, a rise of 1.5 dB and a fall of 1.8 dB where the two loops’ fields meet.

fig, (ax_agc, ax_phase) = plt.subplots(1, 2, figsize=(13.5, 5.6))
agc.plot(ax_agc)
quadrature.plot(ax_phase)
plt.show()

A neck loop is a small loop, often about 230 mm across, worn round the neck and fed from a phone, a music player or a larger piece of equipment. Clause 9, added by Amendment 1, specifies it on the non-metallic jig of Annex E, with the field measured at the telecoil position by a small inductor about 3 mm by 10 mm, the size of a behind-the-ear telecoil: the input voltage that produces 400 mA/m at 1 kHz (9.1), the smallest magnitude of the input impedance over 100 Hz to 5 kHz rounded to the nearest ohm (9.2.1), and the frequency response, stated in text as the frequencies where it differs from the one at 1 kHz by 3 dB (9.3.3). A passive loop is linear, so the voltage for 400 mA/m follows from a level measured at any voltage.

The draft Amendment 2 (prEN 62489-1:2010/prA2:2017, a draft for comment and cited as one) replaces Annex D with two example specifications: type 1, “Suitable for audio sources powered by two primary 1,5 V cells and higher voltage supplies”, with a DC resistance of 32 Ω ±5 %, and type 2, “Neck loops with transformer or amplifier”, with an input DC resistance of at least 32 Ω, both reaching 400 mA/m on the jig with at most 1.06 V at the input.

f = np.array([100.0, 200, 500, 1000, 2000, 5000, 8000, 10000])
z_in = np.abs(32.2 + 2j * np.pi * f * 0.53e-3)     # 32.2 ohm and 0.53 mH, about 25 turns
level = -6.0 + 20 * np.log10(z_in[3] / z_in)       # -6 dB at 1 kHz with 0.5 V applied
neck = electroacoustics.neck_loop_characteristics(f, level, z_in, input_voltage_v=0.5)
print(round(neck.reference_input_voltage_v, 3), neck.minimum_impedance_ohm)  # 0.998 V 32.0 ohm
print([round(v) for v in neck.frequencies_3db_hz])                           # [9723] Hz
draft = electroacoustics.verify_neck_loop(32.4, neck.reference_input_voltage_v, neck_loop_type=1)
print(draft.passes, draft.resistance_passes, draft.voltage_passes)           # True True True

The draft’s Table D.1, the field a type 1 loop reaches from a 3 V and a 9 V battery, rests on a model of the source it does not give, and is not reproduced.

The loop’s inductance, not its field, sets the response of a voltage-driven neck loop: 0.53 mH against 32 Ω puts the corner near 9.7 kHz, well above the 5 kHz of the system requirements.

fig, (ax_response, ax_verdict) = plt.subplots(1, 2, figsize=(13.5, 5.6))
neck.plot(ax_response)
draft.plot(ax_verdict)
plt.show()

• Covered

  IEC 60118-4:2014 with its Amendment 1:2017: the 400 mA/m reference and its levels (3.1, 4.3), the flux density and the telecoil’s cosine law (E.6, E.2), the true-RMS meter flat or A-weighted (6.1.3), the band-limited pink noise with its crest factor (6.4) and the combi signal (6.6, Table 2), the background noise classes of 7.2, the verdict on a system over its useful magnetic field volume (8.2.7, 8.3.7, 8.4.3, 10.4.7), the measurement points and the verdict of a refuge, call point or counter as the amendment writes clause 9, at the points of Figures 2 and 3 or of a useful volume that covers their heights (9.4, 9.5), and the overload test of 10.3 with Table 4, judged on the compliance voltage at the Table 4 frequency (10.3.3). The loop’s field by Biot-Savart at any point, which reproduces the centre formula of E.1 and the curves of Figure E.2 b), and the current and loop size of IEC 62489-1 5.4.10 and 5.4.11, which reproduce the currents of Figure H.1. The loop as a load (IEC 62489-1 Annex B): the resistance with the IEC 60028 resistivity and the inductance by Grover’s Formula (58), which reproduce Table B.1 as shown. The amplifier’s maximum output current, compliance voltage, noise, frequency response, AGC range and quadrature phase error (5.4.7, 5.4.8, 5.4.9, 5.4.12, 5.4.13, 5.4.14), and the neck loop’s characteristics (clause 9) with the two types of the draft Amendment 2, cited as a draft.

• Not covered

  The effect of metal in the building (Annex F) has no model in the standard and none here: it is the frequency response the installer measures. The peak programme meter of 6.1.4, the speech signals of 6.3 (ISTS, ITU-T P.50) and the subjective commissioning of 10.1 are not computations. The loop listener and assistive listening device of IEC 62489-1 Annex F, and the monitoring devices, are specified by single values to be met; the draft’s Table D.1 rests on a source model it does not give. The inductances of Table B.1’s neck loop and large loop are not reproduced by any formula tried. The field patterns of Figures E.3 to E.5 and A.1 are of the kind rectangular_loop_field computes and are not checked point by point. The 10 s for which 5.4.7 asks the maximum current to be held is a condition on the measurement. The electromagnetic exposure of IEC 62489-2 is outside this library.