High-performance A-Weighting filter design emulates human ear

One way to evaluate and compare the audio performance of a circuit or piece of equipment is to use A-Weighting filters to emulate human perception of acoustic energy. Human hearing is most sensitive between 1kHz and 6kHz. Noise and distortion outside of this band, while undesirable, are less perceptible than noise within this band. The A-Weighting filter is designed to roughly replicate this psychoacoustic property. The filter transfer function as defined by ANSI document S1.4 is:

This equation translates into:

  • A double-pole at 20.6Hz
  • A pole at 108Hz
  • A pole at 738Hz
  • A double-pole at 12.2kHz
  • Four zeros at 0Hz
  • 0-dB pass band gain at 1kHz

The A-Weighting filter, simply put, is a band-pass filter. Several designs that implement this filter are available on the internet, but most are flawed in that they either choose large valued resistors, adding excessive noise; or they use several amplifiers, adding both noise and distortion.

The design of Figure 1 shows a high-performance A-Weighting filter, using an AD8656 precision, low-noise, dual CMOS operational amplifier.

Figure 1: A high performance A-Weighting filter uses the AD8656 op amp.

Each amplifier contributes less than 3 nV/rt-Hz of voltage noise over a 20-kHz bandwidth. Both amplifiers are configured for inverting gain. This maintains a constant common-mode voltage at the input of the op amps, thus keeping distortion to a minimum.

Polypropylene capacitors
Audio signal levels swing around 0 V, so no DC bias voltage is available to linearize polarized capacitors. Electrolytic capacitors would introduce distortion in the signal path, and should thus be avoided. Instead, high-quality polypropylene film capacitors with 5% tolerance should be used for C1 through C4. They are rather large (25- to 30-mm length), and are rated to over 200 V, but this is a high-accuracy measurement circuit, so compactness is not an important design criteria.

As shown in Figure 2 , the error in the filter magnitude between measured magnitude and the theoretical magnitude from equation is within 0.3 dB across a 20-kHz bandwidth.

Figure 2: Measured response of A-Weighting filter shows small error from ideal.

The filter has 1.6μVRMS noise measured across a 30-kHz bandwidth, exhibiting roughly 10-nV/rt-Hz spectral noise density between 100Hz and 6kHz. The total harmonic distortion plus noise (THD+N) with a 1-VRMS input signal at 1kHz is 0.001%.

The input impedance of the filter is equal to R4, or 768Ω for the presented design. To increase input impedance, increase both R4 and R5 to maintain their ratio and proportionally decrease C4 and C5. The downside is that system noise will increase as R4 and R5 increase. To measure ±15V input signals, replace the AD8656 with an AD8672 precision low-noise (3.8-nV/rt-Hz) dual operational amplifier.

About the Author
Troy Murphy is an applications manager at Analog Devices, Inc

1 comment on “High-performance A-Weighting filter design emulates human ear

  1. delal2000
    August 26, 2019

    Hello, I can not view images. When I click over it, the browser says that they not found:
    “No se ha encontrado ninguna página web para la dirección” HTTP ERROR 404.

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