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.
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
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What they unfortunately do not publish in their document is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:
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.
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.
The ITU-R weighting filters are defined by this passive weighting
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
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
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.
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
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.
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
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.
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
R6 = 6k04, R7 = 4k42, R8 = 15k5,
R9 = 3k, R10 = 1k8. All other values (including
C6 and C7) remain the same.
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.