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Weighting Filter Set

ANSI A-Weighting Filter
ITU-R ARM Weighting Filter
20 kHz Bandwidth Limiting Filter

Brief Introduction

Weighting filters are used to determine the "loudness" of sounds, particularly noise. You can very much discuss and criticise sense and nonsense of different weighting filters. I fully agree with Rod's point of view in his article 'A' Weighting Filter For Audio Measurements which I also warmly recommend to read as an introduction to A-weighting filters. Whatever one may think about weighting filters - if it is to be used it has to be precise in order to make measurements reliable and comparable so that measurements of different meters are equal and comparable.

During my work on audio projects I experienced only three types of filters to be important:

I started a new project aiming them all on one board. Particularly tough was the ITU-R ARM- or ITU-R 468-weighting filter which I didn't want to implement using the original passive circuit with large inductors and odd valued capacitors.

Figure 1 - Frequency Responses of the Weighting Filters


ANSI A-Weighting Filter

The A-weighting filter is standardised in the ANSI document S1.4, together with B- and C-weighting filters. They are described there as pole-zero specifications which lead to this equation for the frequency response of the A-filter:

(Note: This equation is not, as usual, based on the angular frequency but directly on the frequency  in Hz.)

The ANSI document S1.4 also publishes a large table of gains at different frequencies. I don't copy it here but if you want to know gains at specific frequencies enter the frequency (in Hz) here:

Frequency: Hz,  Gain: dB  (Click outside to start calculation)

What they unfortunately do not publish in their document is a sample circuit that shows if and how the specified frequency response can be realised with standard electronic components. The following circuitis derived from a Sennheiser audio level meter UPM 550, only the dimensioning is slightly modified:

Figure 2 - Circuit and Dimensioning of the A-Weighting Filter

The A-weighting filter is meant to correspond to equal-loudness curve after Fletcher-Munson. Personally I do not appreciate this filter very much. It has an attenuation of 10 dB at 20 kHz only - this really does not match the sensitivity of the human ear. The ear's abrupt sensitivity loss between 10 kHz and 22 kHz (depending on the age) is not represented very well by any filter at all, but here it is worst. Note: Half of the energy of the audible band is contained between 10 kHz and 20 kHz in white noise!

For more information about A-weighting filters have a look at the corresponding wikipedia A-weighting article.



ITU-R ARM (similar to CCIR 468 or ITU-R 468) Weighting Filter

In the 1960s, the A-weighting filter turned out not to be sufficiently appropriate for noise measurments for the arising technologies. Driven by the BBC, measuring noise was refined and one result was this new filter characteristic. Due to its steep roll-off beyond 10 kHz and its high sensitivity around the nasty 5 kHz region it is quite useful and popular. For more information have a look at the corresponding wikipedia ITU-R 468 article.

There are a couple of standards and names around this weighting filter. Originally it was introduced by the German DIN as DIN 45 405 and later adopted by the CCIR as CCIR Recommendation 468 (CCIR 468). The CCIR was renamed to ITU-R, so the standard was renamed to ITU-R Recommendation 468 (ITU-R 468). As this standard describes a relatively costly true quasi-peak meter Dolby Laboratories proposed using an average-response meter instead. They further proposed shifting the 0 dB reference point from 1 kHz to 2 kHz, which practically means sliding the curve down 5.6 dB approx. This is known as the ITU-R ARM-weighting or ITU-R 2 kHz-weighting and is intended to be used for commercial equipment while the ITU-R 468 (or ITU-R 1 kHz) still is used for professional equipment.

In brief:

The ITU-R weighting filters are defined by this passive weighting network:

Figure 3 - Weighting Network according to ITU-R 468 and ITU-R ARM

Note: Until November, 30th, 2005 I erroneously have shown here a false dimensioning of the capacitors. I indicated them all to be 13.85nF. I appologise for that.

Because I don't like the odd capacitor values and the inductors I tried to find an equivalent active circuit. As I didn't find such a circuit anywhere else (and because I'm always looking for some challenge), I had to do it myself. Believe me, it took me rather weeks than days to find a way to not only get to acceptably close component values but really precise ones. This is not just trivial.

Here I publish component values for an ITU-R ARM weighting filter with a gain of 0 dB at 2 kHz. The passive circuit is a 5th order low-pass filter combined with a 1st order high-pass filter. As an active circuit it may look like this:

Figure 4 - Equivalent Active Circuit of the Weighting Filter according to ITU-R ARM

The resistor values shown here are the closest to the ideal ones out of the E-96 series. So they may deviate up to +/-1% from the ideal values.


20 kHz Bandwidth Limiting Filter

Measuring noise is quite useless without a bandwidth limiting filter. Keep in mind: White noise, for example, theoretically has an unlimited bandwidth and thus an infinite power. Practically, of course, it is always limited and its power therefore is limited, too. But this limitation is more or less random and usually unknown. Imagine you measure the noise of your amplifier directly at its output with your voltmeter: Your measurement will not only include the audible noise but the higher frequency portions likewise. But can you say how much that is? Additionally the measured voltage depends on the bandwidth of your voltmeter. Do you know it? Example: If the noise spectrum is limited to 20 kHz (either by the amplifier or by the voltmeter) you will read 50% of the voltage compared to a bandwidth of 80 kHz(!).

Specifiing noise always requires to specify the bandwidth used as well!

For audio equipment limiting the bandwidth from 20 Hz to 20 kHz is common. Under normal circumstances no namable noise below 20 Hz is present, so I provided just a simple RC-high-pass filter of 20 Hz in form of the input AC coupling capacitor.

The low-pass filter is a 5th order, 20 kHz butterworth filter with a gain of 1. Its component values are calculated using my Active Low-Pass Filter Design and Dimensioning utility. The resistor values once again are the closest to the ideal ones out of the E-96 series and may deviate up to +/-1% from the ideal values.

Figure 5 - Circuit and Dimensioning of the 20 kHz Low-Pass Filter


Putting It All Together - The Implementation

All three filters are on one board. With one rotary switch no signal, no filter, the A-weighting filter or the ITU-R ARM weighting filter can be selected. A second switch allows to loop in the 20 kHz low-pass filter and last but not least the third switch enables the 20 Hz high-pass filter (or AC-coupling capacitor resp.).

Figure 6 - Block Diagram

The complete circuit diagram does not surprise any more. I selected an input impedance of 1 MOhm so that optionally a 10:1 oscilloscope probe can be connected. All switches are pluggable. I selected OPA2134 because they are designed for low noise and very low distortion. They may not be the cheapest ones and not available everywhere, but on the other hand they are not too expensive or rare. For less requirements TL072 should do. Due to the 1 MOhm input resistor a FET-op-amp is to be recommended. I used resistors and capacitors with 1% tolerance - so the frequency responses are really precise.

Figure 7 - The Complete Weighting Filter Set

By the way, for a filter response according to ITU-R 468 (5.6 dB more gain than ITU-R ARM) you may modify the dimensioning like this:
R6 = 6k04, R7 = 4k42, R8 = 15k5, R9 = 3k, R10 = 1k8. All other values (including C6 and C7) remain the same.


Assembly

My favourite way is to use a special kind of square pad board (Vero) and to spend a lot of time designing the layout and its implementation because I very much enjoy the aesthetic aspects of electronics. Perhaps somebody else feels like me.

My Weighting Filter Set - Click to enlarge

Figure 8 - View of the Practical Implementation

More pictures about the assembly and its wiring you can find by clicking on the pictures above.

Figure 9 - Measured Frequency Responses
Doesn't look bad - does it?


Last update: October, 29th, 2006 Questions? Suggestions? Email Me! Uwe Beis