This article describes the concept of an undoped (Z-weighted) audio filter that has a unidirectional frequency response of 20Hz to 20kHz, for the evaluation of the audio noise.
There are many methods of recording audio noise which are utilized by audio level meters. They are typically identified with the frequency-response curves that are used by filters. Although certain audio filters are made to replicate their frequency responses to human ears at different sound levels, The focus of this article is on the design details of Z-weighted (unweighted) audio filters with a frequency response being flat from 20Hz up to 20kHz. The filter is able to be used together with the wideband current and voltage meter that I have described in one of my earlier posts.
The Unweighted (Z-Weighting) Frequency Response
The flat, unweighted frequency response curve can be seen in Figure 1. The band limiting frequency of the filter response bounds is described as a “mask” within the ITU Recommendation ITU-R BS.468-4 for the measurement of audio-frequency noise Voltage Levels within Sound Broadcasting. International Standard IEC 61672 defines the same flat response across the audio frequency as “Z-weighted” or zero-weighted.
Figure 1. Frequency response bounds for an unweighted filter. Image is as a courtesy of ITU
We measure the response to our filter. The one we create must fit within that mask. This demands a uniform response across almost every frequency range. This method gives results, which are recorded as RMS values, which can be used to create designs to reduce noise levels.
Design of the Unweighted Audio Filter
The unweighted filter consists of two filters which are linked in series
- A high-pass filter with a 12dB/octave rating with a cutoff frequency of -3dB near to 20 Hz
- A lowpass filter with 18 dB/octave with a cutoff of -3dB. frequency that is close to 20 kHz.
There is a way to satisfy the requirements for masking using Butterworth filters (which do not feature any peak within the curve of frequency) modified to include a 0.5 DB peak. The frequency response is expressed by an in decibels of the Butterworth filter of the order n, which is provided by:
A=10log10(1+O2n)=10log10(1+O2)
O is dependent on the type of filter used:
- Low-pass filter: O=o/ocO=/
- High-pass filter: O=oc/or=/
where:
O is the frequency of the signal
O is the cut-off frequency for HTML0. is the cut-off frequency of -3 dB
This mask needs a high-pass second-order filter to give the rising response of 12 dB/octave between well below 1 Hz up to 22.4 Hz and a third-order low-pass filter for the decreasing response beginning at 22.4 kHz.
Figure 2 illustrates the schematic of the modified Butterworth solution.
Figure 2. Schematic for the quasi-Butterworth, unweighted audio filter (click to increase the size)
Adjusting the Filter Response
The filters employ equal component values from the Sallen as well as the Key configuration. The tweaking is easily done by increasing the value of gain setting resistors, R7 and R12, until the response increases by 0.5 DB when compared to the response of 1 kHz at both ends.
R2 is marked “Adjust on test.” What this means is that with the filter connected with the Wideband Voltmeter, it is possible to place 1 Vrms at a frequency of 1 KHz into the voltage meter (on one V, of course), obviously) and then adjust R2 till the result is 1 V.
Output Resistance Compensation
It’s possible to be curious about the amplifier U1B in the center of Figure 2. It’s because the U2A output resistor is connected to C3, and at frequencies above 20 kHz, the resistance isn’t negligible when compared to the reaction of C3, and the 18 dB/octave rolloff isn’t attained. This isn’t negligible since the output resistivity of an open loop (not mentioned on the information sheet) is reduced due to negative feedback. However, the gain of the open loop is low at higher frequencies, which is typical when using opamps.
For the TL072 general-purpose op amplifier, the gain of the open loop is around 30 kHz at 100 kHz. This means that feedback doesn’t impact the output resistance by much. The LM4562 audio Op amp is not much superior in this way. U1B offers less output resistance, which allows the response needs to be fulfilled.