electroacoustics.induction_loop

Audio-frequency induction-loop systems for hearing aids: the performance of an installed system.

IEC 60118-4:2014 (read in BS EN 60118-4:2015), with its Amendment 1:2017 (read in the Spanish UNE-EN IEC 60118-4:2016/A1:2018, whose text replaces clauses 9 and 10), says what field an induction loop has to produce for a hearing aid switched to its telecoil, and how an installer shows that it does. The loop’s components, the amplifier, the loop as a load and the neck loop, are the subject of IEC 62489-1 and of phonometry.electroacoustics.induction_loop_components.

Everything is a level in decibels referred to a magnetic field strength of 400 mA/m (3.1), REFERENCE_FIELD_STRENGTH_A_PER_M: $L=20\lg (H/0,4A/m)$ (field_strength_level). A long-term average of -12 dB, 100 mA/m, at the telecoil gives the same acoustic output from the hearing aid as a sound pressure level of 70 dB at its microphone (4.3). The meter is either a true-RMS meter with the 125 ms “F” averaging of a sound level meter or a peak programme meter (6.1); in case of doubt the true-RMS one is definitive, and it is the one field_strength_meter implements, flat or A-weighted.

For a system covering a room, the useful magnetic field volume is where the requirements are met (8.4). They are:

• the field strength, 8.2.7 and 8.4.3: the maximum field, measured with a 1 kHz sine (or the equivalent combi signal) and the RMS meter, is 400 mA/m at one point at least of the useful magnetic field volume (8.2.1), and every selected point is within plus or minus 3 dB of it;
• the frequency response, 8.3.7: within plus or minus 3 dB of the response at 1 kHz from 100 Hz to 5 000 Hz, measured at least at 100 Hz, 1 kHz and 5 kHz;
• the magnetic noise with the system switched on and every input muted, 10.4.7 (10.2.7 before Amendment 1): if the reference signal-to-noise ratio of the site (7.2) is above 47 dB, no point above -47 dB; below 47 dB, no point more than 1 dB above its level with the system switched off. Neither sentence covers a ratio of exactly 47 dB; the 1 dB rule is applied there (see docs/ERRATA.md).

verify_induction_loop_system judges the three. The magnetic background noise of the site, 7.2, is a recommendation, not a requirement, and assess_background_noise classes it: a reference signal-to-noise ratio above 47 dB is the ideal, 32 dB the recommended minimum below which the shortfall “shall be reported and agreed with the system operator”, and 22 dB tolerable for short periods when the noise has no significant undesirable tonal quality or is mostly at low frequencies.

For a disabled refuge or call point and for a counter, Amendment 1 rewrites clause 9. The field is measured at fixed points (Figures 2 and 3), six at heights of 1,2 m and 1,7 m for a refuge and three at 1,2 m, 1,45 m and 1,7 m for a counter (small_volume_measurement_points), or, by contract, at representative points spread through a useful magnetic field volume which, at the minimum, meets the requirements at one position at least at each of the heights of 9.2 or 9.3 (9.4). At every point the level shall be within plus or minus 6 dB of 400 mA/m and meet 8.3.7, at one point at least it shall reach 0 dB, and nowhere where people are expected to stand shall it exceed +8 dB (9.5, verify_small_volume_system).

Two informative passages disagree with 9.5 and are not followed: Annex A.4 allows “up to, but not greater than, +12 dB” at 1,45 m for a counter, and calls a counter’s requirement “less stringent” than a refuge’s, where 9.5 applies the same limits to both (see docs/ERRATA.md).

Amendment 1 replaces the 1,6 kHz overload test with one tied to the programme (10.3, Table 4, OVERLOAD_TEST_FREQUENCIES): with a 1 kHz sine giving a field 7 dB below the required one, the frequency is raised at constant input until the loop voltage doubles or the frequency of Table 4 is reached, whichever is higher, and no clipping may appear at the frequency of Table 4 (10.3.3). One of the three ways the amendment offers to detect clipping is the comparison of the loop voltage with the amplifier’s compliance voltage of IEC 62489-1, and that one is computable from the loop’s impedance: verify_amplifier_overload.

The metal in a building lowers the field inside the loop, more at high frequencies (Annex F), which is why 8.3.3 recommends starting the frequency response survey at 5 kHz. Annex F gives no model of the loss: the correction is the frequency response the installer measures and equalizes, and the overload test above is what checks that the amplifier can afford it.

The pink noise of 6.4, band-limited by third-order Butterworth filters at 75 Hz and 6,5 kHz with a crest factor of 4 (loop_test_noise, also the signal of IEC 62489-1 5.4.8.2 b), and the combi signal of 6.6 and Table 2, 1 kHz tone bursts of at least 1 s interleaved with at least four times as much of that noise 6 dB lower (combi_signal). 6.4 NOTE 2 prints the theoretical responses of the band-limiting filters as -0,8 dB at 100 Hz and -0,7 dB at 5 kHz; they are -0,71 dB and -0,82 dB, the other way round (band_limit_response, docs/ERRATA.md).

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

AmplifierOverloadVerification(
    programme: OverloadTestFrequency,
    test_current_a: float,
    doubling_frequency_hz: float,
    end_frequency_hz: float,
    frequencies_hz: np.ndarray,
    voltage_v: np.ndarray,
    test_frequency_voltage_v: float,
    compliance_voltage_v: float,
)

The overload test of 10.3 as amended, judged on the compliance voltage.

10.3.3 as amended asks for no clipping “a la frecuencia de ensayo especificada en la tabla 4 y al nivel especificado en el apartado 10.3.2”, so the verdict is taken at the Table 4 frequency, which the sweep always reaches. Where the voltage doubles above that frequency, 10.3.2 carries the sweep on to the doubling; the voltage there is drawn and kept in max_voltage_v, and 10.3.3 does not judge it.

Attributes

property

The compliance voltage over the voltage at the Table 4 frequency, in dB.

property

The highest loop voltage of the whole sweep, in volts.

Higher than test_frequency_voltage_v when the sweep runs on past the Table 4 frequency to the doubling; 10.3.3 does not judge it.

property

Whether the voltage at the Table 4 frequency is within compliance (10.3.3).

AmplifierOverloadVerification.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Draw the loop voltage along the sweep against the compliance voltage.

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

Parameters

assess_background_noise(
    noise_levels_db: ArrayLike,
    *,
    noise_is_tonal: bool = False,
) -> BackgroundNoiseAssessment

How quiet is the site magnetically? (IEC 60118-4:2014 7.2).

The magnetic background noise is measured A-weighted with the loop switched off, everything else normally in use on and dimmable lighting half-dimmed, at enough points of the intended volume, normally at 1,2 m for seated and 1,7 m for standing listeners (7.1). Its difference from the reference level, the reference signal-to-noise ratio, is taken at the noisiest point, because that is where a listener hears the most of it.

7.2 sets no requirement, only recommendations: above 47 dB is the ideal for theatres and places where the aesthetic value of speech matters, 32 dB is the recommended minimum, and below it the ratio “shall be reported and agreed with the system operator”. As low as 22 dB may be tolerable for short periods when the noise “has no significant undesirable tonal quality or is mostly at low frequencies”; noise_is_tonal=True declares that it does not, and withholds that relaxation.

Parameters

Returns: A BackgroundNoiseAssessment.

BackgroundNoiseAssessment(noise_levels_db: np.ndarray, noise_is_tonal: bool)

The magnetic background noise of a site against 7.2 of IEC 60118-4:2014.

The ratio, the category and the reporting duty are read from the noise levels and the 47 dB, 32 dB and 22 dB that 7.2 prints, so they are not fields: an assessment cannot be built to place a site in a class its noise does not reach.

Attributes

property

The class 7.2 puts the site in.

"ideal" (above 47 dB), "acceptable" (32 dB to 47 dB), "tolerable_for_short_periods" (22 dB to 32 dB, only for noise without an undesirable tonal quality or mostly at low frequencies) or "below_tolerable".

BackgroundNoiseAssessment.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Draw the noise at each point against the 47, 32 and 22 dB lines.

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

Parameters

property

The reference level less the noisiest point, in dB.

The “reference signal-to-noise ratio” of 7.2: the levels are in dB re 400 mA/m, the reference level, so the ratio is the loudest level with its sign changed.

property

Whether the ratio is below 32 dB.

7.2: such a ratio “shall be reported and agreed with the system operator”.

band_limit_response(frequencies_hz: ArrayLike) -> np.ndarray

The theoretical response of the band limiting of the pink noise, in dB.

6.4 band-limits the pink noise with third-order Butterworth high-pass and low-pass filters, -3 dB at 75 Hz and 6,5 kHz, whose combined response is

At 100 Hz it is -0,71 dB and at 5 kHz -0,82 dB. 6.4 NOTE 2, and NOTE 3 to 5.4.8.2 of IEC 62489-1:2010, print -0,8 dB at 100 Hz and -0,7 dB at 5 kHz, the two exchanged (see docs/ERRATA.md). The plus or minus 1 dB flatness 6.4 requires from 100 Hz to 5 kHz holds either way.

Parameters

Returns: The response, in dB.

combi_signal(
    fs: int,
    *,
    sine_seconds: float = 1.0,
    noise_seconds: float = 4.0,
    cycles: int = 1,
    seed: int | None = None,
) -> np.ndarray

The combi signal of IEC 60118-4:2014 6.6 and Table 2.

Bursts of a 1 kHz sine at an RMS of 1, with 5 ms rise and fall times, interleaved with the pink noise of 6.4 at an RMS 6 dB lower: the sine’s peaks sit 3 dB below the maximum peak of noise of crest factor 4, as Table 2 notes ($\sqrt{2}$ against $4\times 10^{-6/20}$, -3,03 dB). Each burst lasts at least 1 s so that either meter settles, and the noise at least four times as long, so the amplifier runs cooler than on a steady sine while the level of the sine can still be read. Every transition is at a zero crossing: the bursts start and end on the sine’s zeros, under their ramps, and each stretch of noise is cut at its own zero crossings.

Parameters

Returns: The signal, starting with a sine burst.

field_strength(level_db: ArrayLike) -> np.ndarray

The magnetic field strength of a level in dB re 400 mA/m, in A/m.

The inverse of field_strength_level: -12 dB is the 100 mA/m of 4.3, and plus or minus 3 dB span 283 mA/m to 565 mA/m (10.2 as amended prints 566 mA/m, which is $400\sqrt{2}$).

Parameters

Returns: The RMS field strength, in A/m.

field_strength_level(field_strength_a_per_m: ArrayLike) -> np.ndarray

The magnetic field strength level, in dB re 400 mA/m (IEC 60118-4:2014 3.1).

Parameters

Returns: The level, in dB re 400 mA/m.

field_strength_meter(
    x: ArrayLike,
    fs: int,
    *,
    weighting: str = 'Z',
) -> FieldStrengthReading

Read a magnetic field strength record like the true-RMS meter of 6.1.3.

The meter of IEC 60118-4:2014 6.1.3 is a sound level meter with a magnetic pick-up coil in place of the microphone, equalized flat within plus or minus 1 dB from 50 Hz to 10 kHz, with a true-RMS detector and the 125 ms averaging of its “F” mode. The A-weighting of IEC 61672-1 is what clause 7 and 10.4 measure noise with. In case of doubt this meter, not the peak programme meter of 6.1.4, is definitive (6.1.1).

Parameters

Returns: A FieldStrengthReading.

FieldStrengthReading(
    fs: int,
    weighting: str,
    times_s: np.ndarray,
    levels_db: np.ndarray,
    maximum_db: float,
    equivalent_db: float,
)

What the true-RMS field strength meter of IEC 60118-4:2014 6.1.3 reads.

Attributes

FieldStrengthReading.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Draw the meter reading against time, with the 0 dB reference.

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

Parameters

InductionLoopVerification(
    clause: str,
    layout: str,
    requirements: tuple[LoopRequirement, ...],
    background_noise: BackgroundNoiseAssessment | None = None,
)

The IEC 60118-4:2014 verdict on an installed induction-loop system.

Attributes

property

The names of the requirements that are not met.

property

Whether every requirement measured is met; False when none was.

InductionLoopVerification.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Draw the worst margin of every requirement as a bar.

A requirement is met when its bar stands at or above zero.

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

Parameters

InductionLoopVerification.requirement(name: str) -> LoopRequirement

The verdict on one requirement.

Parameters

Returns: The LoopRequirement.

Raises

loop_test_noise(
    fs: int,
    seconds: float,
    *,
    rms: float = 1.0,
    seed: int | None = None,
) -> np.ndarray

The pink noise test signal of IEC 60118-4:2014 6.4.

Pink noise band-limited by third-order Butterworth high-pass and low-pass filters, -3 dB at 75 Hz and 6,5 kHz, with “a peak-to-peak voltage (as measured with an oscilloscope) to true r.m.s. voltage ratio of at least 18 dB (crest factor = 4)”. The same signal drives the compliance voltage measurement of IEC 62489-1:2010 5.4.8.2 b), which asks for 18 dB plus or minus 2 dB.

Gaussian noise has no crest factor of its own: in 60 s at 48 kHz it reaches about 5,5 times its RMS, a ratio of 21 dB, which meets 6.4 and fails 5.4.8.2 b). The noise is therefore clipped at 4 times its RMS and rescaled, which gives a peak-to-peak ratio of 18,1 dB and meets both, once the record is long enough to reach 4 times its RMS both ways: some tens of seconds make that certain, which is the length both measurements run for. The filters are the bilinear transforms of the Butterworth prototypes at fs, so the response at 5 kHz differs from the analog one of band_limit_response by a tenth of a decibel at 48 kHz; 6.4 allows plus or minus 1 dB for exactly that.

Parameters

Returns: The signal.

LoopRequirement(
    name: str,
    clause: str,
    values_db: tuple[float, ...],
    lower_db: tuple[float, ...],
    upper_db: tuple[float, ...],
)

One requirement of IEC 60118-4:2014, judged on every value it covers.

Each judged value has its own lower and upper limit (minus or plus infinity where the requirement sets none), because the system-noise limit of 10.4.7 can differ from point to point.

Attributes

property

How far inside its limits each value lies, in dB (negative outside).

Each margin is settled to nine decimal places, a nanodecibel, so that a value on a limit reached through floating-point arithmetic is on it: a response of -18,6 dB against -15,6 dB at 1 kHz has a margin of 0 dB, not -0,000 000 000 000 001 8 dB.

property

Whether every value lies within its limits, both inclusive.

Judged on the settled margins_db, so an edge reached from decimal readings passes.

LoopRequirement.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Draw each judged value against its limits.

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

Parameters

property

The smallest margin, in dB: negative when the requirement fails.

magnetic_flux_density(field_strength_a_per_m: ArrayLike) -> np.ndarray

The magnetic flux density in air of a field strength (IEC 60118-4:2014 E.6).

$B={\mu }_0{\mu }_{\mathrm{r}}H$ with ${\mu }_{\mathrm{r}}=1$ in air, so 1 A/m is $1,2566\mu \mathrm{T}$ and 400 mA/m about $0,503\mu \mathrm{T}$. E.6 prints 1,256; the last digit rounds to 7 (see docs/ERRATA.md).

Parameters

Returns: The flux density, in tesla.

Constant (mapping).

OVERLOAD_TEST_FREQUENCIES = {'transient_speech': OverloadTestFrequency(programme='speech for transient use, for example small-volume systems', power_bandwidth_limit_hz=1250.0, test_frequency_hz=2500.0), 'speech': OverloadTestFrequency(programme='speech (default)', power_bandwidth_limit_hz=1600.0, test_frequency_hz=3150.0), 'music': OverloadTestFrequency(programme='music', power_bandwidth_limit_hz=2000.0, test_frequency_hz=4000.0)}

OverloadTestFrequency(
    programme: str,
    power_bandwidth_limit_hz: float,
    test_frequency_hz: float,
)

One row of Table 4 of IEC 60118-4:2014/A1:2017.

Attributes

Constant (float).

REFERENCE_FIELD_STRENGTH_A_PER_M = 0.4

small_volume_measurement_points(layout: str) -> np.ndarray

The measurement points of a disabled refuge or a counter (clause 9 as amended).

"refuge_small" is Figure 2 a), for a magnetic field source of small dimensions: along the perpendicular and plus or minus 45 degrees from it, at 300 mm and 500 mm from the reference point. "refuge_large" is Figure 2 b), for a larger source such as a vertical loop: three points on a row 424 mm wide at 300 mm from the reference line and three on a row 700 mm wide 200 mm further. Both are taken at 1,2 m and 1,7 m (9.2). "counter" is Figure 3: on the semicircle of 300 mm radius around the reference point, at its bottom and 150 mm to either side, at 1,2 m, 1,45 m and 1,7 m (9.3).

Amendment 1 corrects the key of Figure 2 a): the outer radius is $l_2+l_3$ = 500 mm, where the 2014 key printed ”$l_3$ outer radius 200”, smaller than the inner one (see docs/ERRATA.md). The offset $l_1$ between the source and the reference is the installer’s choice and is not part of the points.

Parameters

Returns: The points, shape (heights, points, 3): $x$ across, $y$ away from the reference into the area where people stand, $z$ the height above the floor, all in metres.

telecoil_response(angle_deg: ArrayLike) -> np.ndarray

The relative response of a telecoil off its axis, in dB (IEC 60118-4:2014 E.2).

A telecoil follows a cosine law, $20\lg |\cos \theta |$: 3 dB down at 45 degrees off its magnetic axis and 9,3 dB down at 70 degrees (Figure E.6). A telecoil at right angles to the field picks up nothing, which is why the measurements of 8.1 are made with the coil vertical unless the users kneel or lie.

The cosine is taken as the sine of the angle from the nearest null, $|\cos \theta |=\sin |90^{\circ }-(\theta \mathrm{mod}180^{\circ })|$, so a right angle gives exactly zero: $\cos (\pi /2)$ in floating point is $6\times 10^{-17}$, which would read as about -324 dB instead.

Parameters

Returns: The response relative to the one on axis, in dB; minus infinity at 90 and 270 degrees.

verify_amplifier_overload(
    required_current_a: float,
    impedance: LoopImpedance,
    compliance_voltage_v: float,
    *,
    programme: str = 'speech',
    current_response: AmplifierFrequencyResponse | None = None,
) -> AmplifierOverloadVerification

Does the amplifier clip in the overload test of 10.3 as amended?

10.3.2 as amended: a 1 kHz sine is set 7 dB below the field required at a point, the voltage across the loop is measured, and the frequency is raised at the same input until that voltage doubles or the frequency of Table 4 is reached, whichever is the higher frequency. No clipping may appear at the frequency of Table 4 and the level of 10.3.2 (10.3.3), and that is where the verdict is taken; the rest of the sweep is drawn and its highest voltage kept, but not judged. Of the three ways to detect clipping the amendment lists, the second compares the loop voltage with the amplifier’s compliance voltage of IEC 62489-1, and that is the one computed here: the loop is a series resistance and inductance, and the current follows the amplifier’s frequency response into it, which is where a correction for metal loss shows (10.3.1).

The sweep looks for the first frequency where the voltage doubles, up to 20 kHz, the top of the audio band, or up to the highest frequency of the given current response; a loop that is mostly resistive and flat may not double at all, and then the test ends at the Table 4 frequency. A current response that peaks and falls again, as a correction for metal loss can, may double the voltage and then bring it back below twice its start; the sweep stops at that first doubling. It is found exactly: the response is read log-linearly between its measured frequencies, and between two of them the logarithm of the voltage, a straight line in the logarithm of frequency plus $\frac{1}{2}\ln (R^2+(2\pi fL{)}^2)$, is convex in it, so the voltage crosses twice its start at most once going up in each interval, and the first interval whose upper end has doubled holds the first doubling.

Parameters

Returns: An AmplifierOverloadVerification.

verify_induction_loop_system(
    field_strength_levels_db: ArrayLike,
    *,
    specified_level_db: float = 0.0,
    frequencies_hz: ArrayLike | None = None,
    response_db: ArrayLike | None = None,
    background_noise_levels_db: ArrayLike | None = None,
    system_noise_levels_db: ArrayLike | None = None,
    noise_is_tonal: bool = False,
) -> InductionLoopVerification

Does an installed loop meet IEC 60118-4:2014 over its useful volume?

The requirements of clause 8 and of 10.4 as amended, on the measurements an installer makes at the selected points of the useful magnetic field volume, normally at 1,2 m for seated and 1,7 m for standing listeners (8.4.2):

• "field_strength" (8.4.3): every level within plus or minus 3 dB of the level specified according to 8.2.7, which is 400 mA/m, 0 dB, with a 1 kHz sine or the combi signal and the true-RMS meter. Measured with another signal or meter, the specified level is the reading the manufacturer states for 400 mA/m (Table 3 gives -6 dB for pink noise on the RMS meter), passed as specified_level_db;
• "field_strength_reached" (8.2.7): the maximum value of the field is 400 mA/m “at one point, at least, within the useful magnetic field volume” (8.2.1), so the highest level reaches the specified one. A spread that sits within its window but wholly below the reference, set too low, fails here;
• "frequency_response" (8.3.7): at every point, within plus or minus 3 dB of the response at 1 kHz from 100 Hz to 5 000 Hz, measured at least at 100 Hz, 1 kHz and 5 kHz. The response is the field spectrum less the source spectrum (8.3.2 d), or the field at each sine frequency;
• "system_noise" (10.4.7, which was 10.2.7 before Amendment 1): the A-weighted level with the system on and every input muted. The site’s reference signal-to-noise ratio is taken at the noisiest point with the system off. Above 47 dB, no point may exceed -47 dB; otherwise no point may exceed its own level with the system off by more than 1 dB, so the two sets of levels are paired point by point. 10.4.7 prints “greater than 47 dB” and “less than 47 dB”, so a ratio of exactly 47 dB falls in neither sentence; the 1 dB rule is applied there, since 7.2 calls only a ratio above 47 dB ideal (see docs/ERRATA.md).

Every requirement is judged on what was given; one not measured is not judged, and a verdict with none fails. The background noise with the loop off is also assessed against the recommendations of 7.2 (assess_background_noise), which are not requirements.

Parameters

Returns: An InductionLoopVerification.

verify_small_volume_system(
    field_strength_levels_db: ArrayLike,
    *,
    layout: str,
    heights_m: ArrayLike | None = None,
    standing_area_levels_db: ArrayLike | None = None,
    frequencies_hz: ArrayLike | None = None,
    response_db: ArrayLike | None = None,
) -> InductionLoopVerification

Does a refuge, call-point or counter loop meet clause 9 as amended?

The requirements of 9.5 as Amendment 1 writes them, at the measurement points of Figure 2 (a refuge) or Figure 3 (a counter), or at the representative points of a useful magnetic field volume agreed by contract in their place (9.4):

• "field_strength_range": at every point within plus or minus 6 dB of 400 mA/m, measured according to 8.2;
• "field_strength_reached": at one point at least, 0 dB or more;
• "standing_area": nowhere in the area where people are expected to stand above +8 dB, judged on the measurement points and on any survey of that area given as standing_area_levels_db;
• "frequency_response": 8.3.7 at every point.

A useful volume replaces the points of 9.2 ("refuge_useful_volume") or of 9.3 ("counter_useful_volume"), and 9.4 asks it, as a minimum, to meet the requirements at one position at least at each height of the clause it replaces: 1,2 m and 1,7 m for a refuge, and 1,2 m, 1,45 m and 1,7 m for a counter. Every point is held to 9.5 all the same, so the minimum comes down to the points including each of those heights, and heights_m says which height each point was taken at.

The informative Annex A.4 allows up to +12 dB at 1,45 m for a counter; 9.5 does not, and 9.5 is what is applied (see docs/ERRATA.md).

Parameters

Returns: An InductionLoopVerification.

Raises