Swept Measurements of Difference Frequency Intermodulation and Harmonic Distortion of Hearing Aids

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Swept Measurements of Difference Frequency Intermodulation and Harmonic Distortion of Hearing Aids by Philip S. White, Bruel & Kjaer

ntroduction In general, amplitude non-lineari

ties of a hearing aid may be measured using three different distortion measurements: harmonic, difference-frequency, and intermodulation distortion. Up to the present t ime, harmonic distortion measurements have been the easiest to make, and hence the most commonly used. However, with the advent of the new instrumentation discussed in this Application Note, the intermodulation and difference-frequency distortion measurements have become significantly easier and thus merit consideration.

Intermodulation distortion is the interaction of two or more frequencies in a complex signal that results in the generation of new frequency components not present in the original signal. These components are "mix ing" products, and hence their frequencies are equal to the sum and difference of the frequencies of the original signals and the integral multiples thereof. A special case of intermodulation distortion is differ-

distortion which ence-frequency only considers which are the

those components difference between

the original components, thus ignoring the sum components.

Intermodulation and difference-frequency distortion measurements are of considerable importance be

cause they represent a more realistic simulation of speech or music than a single tone which is used for harmonic distortion measurements. They are also useful in describing interaction phenomena between several frequencies, which is inherently impossible with a single tone. In addition, since intermodulation components are not musically re

lated, they are more audible, and in many cases, more annoying.

Another significant advantage of intermodulation distortion measurements, is that they permit the measurement of non-linearities up to the cut-off frequency of the system, because many of the distortion components generated are folded back

_n_ Analysis Frequency (2010) Output Frequency (1902) U A

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Frequency

750346/1

F ig .1 . Test signals and analysis frequencies for distortion measurement

1

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Copenhagen 5 0 [ ;

dB

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Measuring Obj.:

Rec. No^j. Date Sign.:

QP 1124

dB

20

30 15

2010

106

0>-0 10 20 Hz 50 100

Mult ip ly Frequency Scale by

500 1000 2000

Zero Level:

5000 10000 2000

1 6 1 2 / 2 1 1 2

0 40000D A B C

A B C 75108O

Fig.2. Impedance curve of a 2 cc coupler

into the band-pass section of the system. However, with harmonic measurements at higher frequencies, the distortion components wi l l fall above the cut-off frequency, and thus wil l be rolled off. Finally, inter-modulation measurements are a more sensitive test of non-linearities since the theoretical amplitude of the intermodulation components is higher than the harmonic components.

Let's take a look at the advantage of each of the three measuring methods.

Harmonic Distortion Looking at Fig.1a, harmonic dis

tortion is measured by exciting the hearing aid with a single sinusoidal tone, f2- The sound pressure level of f2 is to remain constant at the microphone of the hearing aid.

One of the merits of measuring harmonic distortion is that it requires a fairly simple instrumentation system. When using a spectrometer for this purpose, the harmonics are simply measured by offsetting the center frequency of the contiguous filters with respect to the sine generator by a constant factor corresponding to the number of the desired harmonic.

One of the disadvantages of measuring harmonic distortion is related to the hardware; the type of coupler used in conjunction wi th the earphone of the hearing aid normally has one or more resonances at high frequencies (Fig.2). With a resonance peak at 12 kHz it means that the amount of second order harmonic distortion at f = 6000 Hz wi l l be more than 20dB too high. Same for third harmonic at f = 4000 Hz.

Another disadvantage of harmonic distortion measurements is due to the frequency response of the hearing aid.

Looki ng at Fig. 3, showi ng frequency response and harmonic distortion of a behind-the-ear hearing aid, we see that the sharp roll-off of the frequency response above 5 kHz causes the harmonics to roll-off at correspondingly lower frequencies. This, however, does not imply that

the hearing aid does not exhibit amplitude non-linearity at higher frequencies within the pass-band of the hearing aid. This quantity can be measured as:

Difference Frequency (DF) Distortion

DF distortion {Fig. 1) is measured by exciting the hearing aid wi th a twin-tone test signal with frequencies f i and f2- The sound pressure levels of f i and f2 are equal. The two tones are swept through the frequency range of interest while keeping a small fixed interval in hertz between the two tones.

DF distortion considers only the components which are the difference between the original frequency components ( f i & f2> and their harmonics (Fig.4).

For hearing aids, normally second order (f2 — f i ) and third order (2 f i — f2) would be measured (Fig.5).

f2 — f1 w a s chosen to be 160 Hz, which means that when sweeping to measure the second order DF distortion, the filter of the analyzer is steadily tuned to 160 Hz. Some standards call for f2 — f i equal to 80 Hz. This may in some cases be inconvenient as some hearing aids have a very low output capability at 80 Hz. It is therefore suggested that f2 — f i be chosen such that the hearing aid has a reasonable output at f2 — f T . When sweeping to measure the third order minus DF distortion at (2 f i — f 2 ) Hz the analysis frequency of the filter is (f2 — f 1) Hz lower than the lower tone (f

Since the analysis frequency is very close to the test signal(s) when measuring third order DF distortion, a mandatory requirement is that the filter of the analyzer be very steep and have a narrow bandwidth. In other words, the filter must let through only the signal at the analysis frequency and cut-out the test signal(s). The filter should also have low distortion and a wide dynamic range.

Thus, for example, if f2 — f i = 80 Hz and we want to measure third order distortion (2 f i — f 2 ) down to 0 , 1 % (— 60 dB) we see from Fig.6 that the filter should have a bandwidth B ^ 8 0 / 3 , 5 - 23 Hz — a 10 Hz bandwidth would be appropriate.

Interpretation of DF Distortion Curves

Again, looking at Fig.5 we see that the third order distortion is quite significant and bears some semblance to the frequency sponse curve. Specifically we that the peaks in the frequency response curve also occur in the third order distortion curve offset by 320 Hz. This is due to the fact that f2 — f1 = 160 Hz and the analysts frequency fa = 2 f1 — f2 . Solving for fa we see that fa = f2 — 320, hence the frequency offset of the two curves. The peaks in the distortion curve may be attributed to the fact that at the peaks (high gain) in the frequency response, the "loop gain" wil l be lower because of saturation phenomena or too heavy drain on the power supply (battery). Symmetrical clipping of the signal wil l result in "odd order" distortion. The second order distortion ("even order") may e.g. be attributed to a rectification phenomenon. This could be the case if the hearing aid employs a compressor circuit or if an amplifier stage causes assymetri-cal clipping of the signal.

re-re-

Intermodulation (IM) Distortion IM distortion {Fig. 1) is measured

by exciting the test specimen with a twin-tone test signal ^ and f2 . Keeping the amplitude of both signals constant, the amplitude of f i is 12dB higher than the amplitude of f2 . ^ is kept at a fixed low frequency, while f2 is swept through the frequency range of interest. In a non-linear system the IM distortion

3rd 3rd +

2nd f f.

4th CM

CM

CM CM

CM

l I

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0 100 200 300 400 500 600 700 800 900 1k 1,1 k Hz

750845

Fig.4. DF distor t ion of 8 0 0 and 9 0 0 Hz signals

Bruel & Kjaer Bruel & Kjaer Bruel & Kjaer o n n n a a a a a a a D a n n n a n n n a n a a a a a o a o a n n a n n a n a n D D n n n Q Q D n t

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40

Measuring Obj.:

£req> response and diff. freq. distort of a behind-the-

45

aid

Rec. No.: Date Sign.:

QP 1124

ear hearing

AcQjjstjca gain 40 dB_ ^

10 20 Hz 60 100

Mult ip ly Frequency Scale by Zero Level: 1 6 1 2 / 2 1 1 2 A B C

7-QJ0

751078

Fig.5. Frequency response and DF distor t ion of a hearing aid

0

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CD 20

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Bandwidths from centre frequency 171104

Fig. 6. Typical filter characteristics of a Type 2 0 1 0 Heterodyne Analyzer

3

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B r u e t & K J 3 8 r Potentiometer Range:———dB Rectifier: Lower Lim. Freq.: - H z Wr. S p e e d : - — - m m / s e c . Paper Speed: .mm/sec Copenhagen 50r2

Measuring Obj.:|_

Freq. re-nd

3 OH 5 sponse and inter mod. distort, of a behind-the-ear hearing .

^ -2010

Acoustical gain 40 dB

Rec. N q ^ Date Sign.:

|10i75

QP1124

10 20 Hz 50 100 Multiply Frequency Scale by Zero Level:

20000 40000D A B C

1612 /2112 A B C 751077

Fig.7. Frequency response and IM distortion of a hearing aid

shows up as a number of side bands located on both sides of f2 — the distance between the side bands being equal to f 1.

Similarly to DF measurements, the filter of the analyzer should be very steep and have a narrow bandwidth, especially if f j is chosen such that the IM sidebands are very close to the upper test tone f 2.

An example of an IM distortion measurement is shown in Fig.7.

System Description With the advent of the

1 9 0 2 / 2 0 1 0 combination, a distortion measurement control unit and heterodyne analyzer, the user now has a unique tool for making swept harmonic, difference frequency (DF) and intermodulation (IM) distortion measurements accurately and conveniently on electroacoustic devices. The 1 9 0 2 / 2 0 1 0 combination automatically generates the necessary test signal(s) as well as tunes its filter to the desired distortion component, one through fifth order.

The 1 9 0 2 / 2 0 1 0 combination readily lends itself to harmonic distortion measurements of hearing aids, but things get slightly more complicated when it is desired to make difference frequency and intermodulation distortion measurements.

The problem is this: when making frequency response and distortion measurements the sound pressure level at the hearing aid should be kept constant throughout the frequency range of interest. IEC Recommendation No. 118 specifies that the sound source be kept at a

constant level (± 2%) between 200 Hz and 5 kHz. For this purpose a compressor loop is Often employed. In the case of harmonic distortion measurements this is straight forward and simple, but in the case of a twin-tone test signal such as used in IM and DF testing, special consideration has to be given to the compressor loop(s).

In the case of DF measurements, the two test signals f i and f2 are normally close to each other in frequency (typically f2 — f i = 80 Hz). When this twin-tone signal is fed into the sound source, e. g. the speaker of Hearing Aid Test Box, Type 4212 , there wil l be some difference in amplitude between the two tones because the frequency response of the speaker is not completely flat.

Fig.8 shows the relative deviation between the two test tones when using one common compressor. It is seen that if f2 — f i = 80 Hz, the difference in level is approximately 1 dB (300 — 10000Hz) (Fig.8a). An instrument set-up utilizing one common compressor is described la

ter. If the two test frequencies f2 and f i are further apart, larger amplitude deviations wil l occur (Fig.8b-c). The roll-off at lower frequencies of i-\ can be attributed to the roll-off of the speaker.

If better amplitude accuracy is desired and the test signals f2 and ^ lie far apart, we have to use two separate, filtered compressor loops. This could be accomplished by using two separate tracking/slave f i l ters. However, by using the B & K Type 2020 Heterodyne Slave Filter, only one filter is necessary. The concept is this:

The 2020 Slave Filter has two outputs: one is the regular bandpass output with the center frequency equal to the BFO frequency and the other a rejection output passing all frequencies except the BFO frequency. f2 is the BFO frequency and we can thus separate the two signals by taking f2 out of the bandpass output and f i out of the rejection output and feeding them into two separate compressors.

System for Measurement of Harmonic, Difference Frequency, In-termodulation Distortion with dual Compressor Loop

The system described here is particularly suited for twin-tone measurements where good amplitude stability of both test signals is required and where the frequency difference between f 1 and f 2 is large. The system is shown in Fig.9.

The two test signals ^ and f2 , although both normally available at the output of 1902, are in this case derived separately from the outputs of 1902 ( f i ) and 2010 (f2).

The compressor microphone hooked up to a measuring amplifier (2608) receives the twin-tone test signal and feeds it into a heterodyne slave filter (2020). The slave filter is tuned to the BFO frequency (f2) of the 2010 Heterodyne Analyzer and at the socket "Output" on 2020 we have f2 available while "Rejection Output" gives us f ^ The twin-tone signal is thus split up for two separate compressor loops. f 2 is via a Measuring Amplifier (2608) fed into the "Compressor Input" of the Heterodyne Analyzer (2010). The 2608 serves as a signal condi-

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2010

105

Rec. No^ P-Sli

2010

Rec. Nqj_ Date

106

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All SPL's are 67 dB nominally

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f2 - f1 = 80 Hz

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f2 — fT = 320 Hz

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Freq. scale ref. is f2 (f 1 is offset by f2 — f 1 ) mm

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QP 1124

10 20 Hz SO 100

Multiply Frequency Scale by

500 1000 2000

Zero Level:

5000 10000 20000 40000D A B C linr

1612/2112 A B C 751081

Fig.8. Amplitude deviation between f-| and f2 when using common compressor in conjunction with Hearing Aid Test Box, Type 4 2 1 2

tioner and readout for the level of fa-

f-|, originating from the generator section of 1902, utilizes the compressor circuitry of a 1405 Random Noise Generator, f 1 is from the "Rejection Output" of 2020 fed into a Measuring Amplifier 2608 serving as a signal conditioner and read

out of the level of f ̂ . From 2608 the signal is fed into the "Ext. Gen. Input" of 1405 which is operated in the compressor mode.*

* For 1405 Noise Generators w i th serial nos. pre 571 512 , a minor modification reducing compressor distortion is recommended; consult factory.

f.

Distortion Measurement Control Unit 1902

Noise Generator 1405

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• • • *

Compressor Microphone f1 and f

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Measuring Amplifier 2608

Measuring Microphone

f-l and f2

Heterodyne Analyzer 2010

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5 k£2

Power 2 5 * V 2 W Amplifier

2706

External Filter

Heterodyne Slave Filter 2020

Hearing Aid Test Box 4212

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Level Recorder 2307

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(2609) (2425)

751054

Fig.9. Set-up for diff. freq., harm, and IM distortion measurements with dual compressor loop

5

We have now formed two separate compressor loops. The two signals from the generator outputs of 1405 and 2010, ^ and f2 , are "summed" in two 5 kO resistors at the input of the Power Amplifier (2706), which drives the speaker of the Hearing Aid Test Box 421 2.*

The hearing aid parameters to be established are measured by means of the Microphone/Artificial Ear of 4212, the measuring amplifier and heterodyne filter of 2010 in conjunction with Distortion Measurement Control Unit 1902. A 2305 or 2307 Graphic Level Recorder serves as a read-out of test results. The artificial ear filter switch on the 4212 Hearing Aid Test Box should be in the "Off" position. This is important when measuring second order DF distortion, because the high pass filter cuts-off below 150 Hz. A summary of typical knob settings for a difference frequency test (f2 — f i = 80 Hz) is given in Fig. 10.

System for Measurement of Harmonic, Difference Frequency, In-termodulation Distortion with single Compressor Loop

If it is desired to make DF distortion measurements with a small interval between f2 and f ^, say around 100 Hz or less, and small deviations between the sound pressure levels of ij and f2 can be accepted, the system shown in Fig. 1 1 will suffice. The twin-tone signal from the Type 1902 Distortion Measurement Control Unit is fed into the compressor of the Type 1405 Noise Generator. It is recommended to keep the generator signal at 1 V or below. From the regulator microphone of the Hearing Aid Test Box, the feedback signal is fed into the compressor via a 2608 Measuring Amplifier serving as a signal conditioner and read-out of the sound pressure level of f2 .

With the system in the same configuration, it may also be used for harmonic distortion testing. By adding a high-pass or notch filter to

2608 0) Filters: Ext. Meter Function; Fast Ail other knobs: As required

2020 Input fi lter: In Output: 0° BFO Mode: Sine Bandwidth: 31.6 Gain: 0 dB Bandwidth Compensation: Off

2603(11) Filters: Linear, 2 - 200000 Meter Function: Fast All other knobs: As required

2010

1902 (Mode Selector): Difference — frequency Distortion Order: As required Difference — frequency: 80 Hz or as required Generator Stop: f^On) Output Voltage: Fully clockwise Attenuator: 1V

1405 Compr. Voltage: As required Compr. Speed: 30 (Mode Selector): Compr, only Output: n/a

2706 Current Limit: 1.8 A RMS Attenuator: 10 Gain Control: Fully clockwise

Read Out Selector:DC Lin Effective Averaging Time T: 0.1 sec. Selectivity Control: 10 Hz B&T program: Manual BFO Attenuator: IV BFO Output Voltage: 7 Frequency Scale: x 1 Log Compressor Speed: 100 All other knobs: As required

2307 Potentiometer Range: 50 Rectifier Response: DC Lower Limiting Frequency: 200 Writing Speed: 250 mm/sec Paper Speed: 1 mm/sec AM other knobs: As required

4212 Art. Ear Filter: Off Attenuator for speaker: H

Fig.10. Typical knob settings for a difference frequency distortion measurement

760124

the 2608 Measuring Amplifier and rerouting the cables as shown with the dotted lines, the system is ready for IM testing. As the tone f̂ has a fixed frequency and amplitude which is 12dB higher than f2 , it is necessary to filter out f -\ to be able to compress f 2- A high-pass or notch filter such as found in Frequency Analyzers 2 1 2 0 / 2 1 2 1 wil l suffice, but any other good 4-pole high-pass or notch filter, passive or active, which rejects f 1 by minimum 22dB, will do.

System for Measurement of Harmonic and Intermodulation Distortion

By eliminating the compressor (Type 1405) from the scheme described in Fig. 11 the system wil l perform harmonic and intermodulation distortion measurements. This system is shown in Fig. 12. The high-pass or notch filter used for IM testing is similar to the one shown in Fig.11. Note that the Power Amplifier Type 2706 has been omitted:

The generator outputs of 1902 and 2010 have some power capability — enough to drive 4212's speaker at low-to-moderate sound pressure levels (50 — 70dB SPL). Using the speaker (no current limiting resistor to be used) as a "floating" load, it is simply connected directly between the two center posts (hot leads) of the generator outputs. The two "grounds" of the generator outputs should be connected together. The two generators have a current drive capability of 70 mA, so voltage levels above approx. 0 ,4V into the speaker ( 6 0 ) should be avoided to keep the distortion of the test signal low (the outputs are protected against excessive currents). If higher sound pressure levels, up to approx. 90 dB are required, the power amplifier scheme outlined in Fig.9 and Fig. 11 should be used.

A word of caution here: since the speaker in 4 2 1 2 is rated at max. 4V-RMS and 2 7 0 6 is capable of delivering 15V-RMS in 3 0 , it is strongly recommended to insert a minimum 25 OV12 W resistor in series wi th the speaker leads to prevent speaker burn-out. When doing a sweep it is also recommended to turn down the "Gain Cont ro l " of 2 7 0 6 whi le the BFO is at low frequencies, say below 100 Hz, to avoid excessive excursions of the speaker diaphragm.

6

Measuring Microphone

Distortion Measurement Control Unit 1902

I Heterodyne ]_Analyzer2010

Level Recorder 2307

f l & f 2

Noise Generator 1405

Power Amplifier 2706

f,

-vwv-■-WW-

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Filter for IM testing

25 ohm vwv-12W

Compressor Microphone

High-pass, 4 pole, f0 = 2 f , or Notch, f = f , Hearing Aid

Test Box 4212 760126

Fig. 11 - Set-up for diff- freq-, harm, and intermod. distortion measurements wi th single compressor loop

Measuring Microphone f! & f2 Compressor Microphone

Distortion Measurement Control Unit 1902

■®»• * • * -

i '

"

Heterodyne Analyzer 2010

f 1

Measuring Amplifier 2608

s*

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4-pole High-pass or Notch Filter

Hearing Aid Test Box 4212

*) connect this lead to "common" for harmonic distortion measurements.

Level Recorder 2307 760127

Fig. 1 2 . Set-up for I M and harm measurements

Distortion Measurement Control Unit 1902

H.A. Electronics Earphone

Test Object

mechanical or electrical synchronization

Heterodyne Analyzer 2010

Level Recorder 2305 or 2307

760125

Fig. 1 3 . General set-up for measurement of individual parts of hearing aids

Distortion Measurements on Individual Parts of Hearing Aids

While the previously discussed set-ups were mainly for establishing the overall performance of the hearing aid under assumed, well defined working conditions, it is a simple affair also to use the 1 9 0 2 / 2 0 1 0 combination for measuring frequency response and distortion levels for individual parts of the hearing aid.

A general set-up is shown in Fig.13.

This type of measurement is valuable when it is desired, for design purposes, to relate distortion and frequency response to individual parts of the hearing aid. Amplifier and compressor circuits are typical examples of this. Also, utilizing an artificial ear, measurements on the ear-phone alone can be performed.

7

Performance of the Measurement System

To establish the overall performance of the system, we let the system analyze itself. The two main goals were:

1 Establishing accuracy of compressor regulated sound pressure level when using a) a single-tone test signal (harm, distortion) and b) a twin-tone signal (IM and DF distortion) with single or dua compressor loop(s).

2. Establishing the level of harmonic, difference frequency and intermodulation distortion of the system itself.

Compressor Loop(s) the outlined Using the system outnnea in

Fig.9, and looking at Fig. 14a to c, we see that in all cases the sound pressure level is kept constant to within a fraction of a dB throughout the frequency range of interest (200 Hz to 5 kHz). in graph 14b the combined sound level of f-| and f2 was recorded. Graph 14c shows the sound level of f2 only — f i remains at a fixed amplitude and frequency anyway.

The bandwidth of the 2020 Slave Filter was set at B = 31,6 Hz. This was found to yield the best compromise between compressor loop stability and compressor loop frequency selectivity.

When using the single compressor loop system for DF measurements as outlined in Fig.11, refer to Fig.8 and section System Description, where the merits of this method are discussed.

Residual Distortion of the Measurement System

While most of the distortion in the system no doubt can be attributed to the speaker in 4212 and the compressor (1405), it was found that the system's distortion was generally well below 0,3% at any distortion component in the frequency range of interest (200 Hz to 5 kHz). Generally, hearing aids exhibit distortion figures considerably higher than this. Figures 14a and 14c show second and third order

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Residual difference frequency distortion of system

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Fig. 14. Performance curves of hearing aid test system for harm., diff. freq. and I M distortion

harmonic and IM distortion curves. Fig. 14b shows only third order difference frequency distortion — the second order component was too low to be measured, because it approached the level of the ambient noise.

8

Conclusion The 1 9 0 2 / 2 0 1 0 combination,

Distortion Measurement Control Unit and Heterodyne Analyzer already covering a wide range of applications in the electro-acoustic field by providing convenient, accurate swept measurements of harmonic, difference frequency and intermodu-lation distortion components can also be used to measure these par

ameters on hearing aids. The use of frequency selective compressor loops ensure a uniform sound pressure level throughout the frequency range of interest when making twin-tone tests. When making DF measurements with* single compressor loop and f2 — f i equal to approximately 100 Hz or less, the relatively flat response of the speaker of the

4212 Hearing Aid Test Box ensures that only a small level difference between f i and f 2 wi l l occur.

The system itself has low residual distortion and is able to detect distortion components, second through fifth order, down to a fraction of one percent.

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Bruel & Kjaer Instruments, 185 Forest Street

Marlborough, Massachusetts 01752 (617)481-7000