Project

Building a Circuit to Measure the Effect of Noise on Audio Signals

December 10, 2023 by John Woodgate

This project will cover the design, construction, and testing of an analog filter meeting the ITU-R BS.468-4 specification, which aims to evaluate the disturbing effects of noise on audio broadcast signals.

In my previous project articles, I introduced three filters for measuring noise in the audio spectrum:

  1. Z-weighting
  2. A-weighting
  3. C-weighting

You may be asking, “Why do we need another one?” Those filters measure the noise, but the ‘468-4’ filter aims to provide a standardized measurement that correlates well with the subjective assessments of people listening to audio programs, including music and talk. How the noise impairs how we hear the audio signals is a very different thing than the noise level itself.

 

Author’s note: BBC Report EL-17 on the assessment of noise in audio-frequency circuits is an interesting resource that you might want to check out. It acknowledges that there is “a bewildering variety of methods” for measuring audio-frequency circuit noise.

 

Introducing the 468-4 Frequency Spectrum

Figure 1 shows the frequency response specified in the ITU document, Measurement of Audio-Frequency Noise Voltage Level in Sound Broadcasting.

 

Frequency response of the 468-4 weighted noise filter

Figure 1. Frequency response of the 468-4 weighted noise filter

 

The rising part of the curve has a gradient of 6 dB/octave, so it is a first-order high-pass section. The falling part has a gradient of -30 dB/octave, making it a fifth-order low-pass section.

 

The Original Passive Filter Solution

The ITU document also includes the passive filter circuit shown in Figure 2. This circuit can achieve the desired response. The document also notes that the inductors must have a Q of at least 200 at 10 kHz and that it may require some tweaking of the value of C3 to meet the specified tolerance limits of the curve. (We’ll discuss tolerances later.)

 

Passive network implementation of the 468-4 filter for 600 Ω circuits

Figure 2. Passive network implementation of the 468-4 filter for 600 Ω circuits (click to enlarge)

 

The filter circuit of Figure 2 was originally developed in the late 1960s and based on even earlier work in the early 1950s when broadcast audio interconnection technology was still mostly based on 600 Ω iterative matching. The passive network of Figure 2 has significant insertion loss, so an additional amplifier is required to achieve the 12.2 dB gain at 6.3 kHz specified for the 468-4 filter.

 

Modern Audio System Requirements

These days, 600 Ω matching is not used. Instead, audio signal sources are designed to have a source resistance of 100 Ω or less, and inputs are designed to have an impedance of 10 kΩ or greater.

There are two primary ways of making an active filter that meets these impedance targets and provides the 468-4 frequency response:

  1. Merge conventional low and high-pass active filters around 6.3 kHz.
  2. Derive an active circuit from the passive circuit using clever mathematical techniques.

The rest of this article will cover the first method. Unfortunately, the process is not easy, and at least part of the problem is with the original frequency response specification and the specified tolerances.

 

Analyzing the 468-4 Noise Filtering Spectrum

The frequency response specification was probably obtained by measuring an actual network that would be affected by inductor losses that vary non-linearly with frequency. This cannot be modeled by adding series and parallel resistors, or the equivalent, in active-filter technology.

Even a linear model is complex. One formula for its frequency response indicates that a sum of sixth- and fifth-order low-pass responses is involved, although the fifth-order response dominates above about 16 kHz, as can be seen by the gradient of 30 dB/decade. It is possible to meet the specifications without a sixth-order filter, but the tolerances are smaller where that filter would have the most effect.

The circuits for first-order high-pass and fifth-order low-pass filters are well-known; the only issues are determining the critical frequencies of the filter sections and whether the fifth-order filter can be maximally flat or not. The critical frequency f is the frequency at which the response is -3 dB.

This is by no means a simple matter: the required value of the critical frequency of the high-pass section depends on the shape of the low-pass filter response, and a simple trial design shows that neither section of this filter is maximally flat or similar to any of the other ‘standard’ responses (Chebyshev, Bessell, etc.).

There are too many variables for a simple ‘cut and try’ tweaking to produce good results in an acceptable time, so it is necessary to use an optimization app.

 

Author’s note: I am grateful to Tony Casey, a fellow member of the LTspice user group (LTspice@groups.io), for assistance with using the Solver add-in for Microsoft Excel to help solve these equations.

 

An Active Filter Design For 468-4 Noise Filtering

Figure 3 provides two schematics: (top) the original passive filter with a generic op amp amplifier added to compensate for the insertion loss, and (bottom) the optimized active filter.

 

Simulation schematic of the passive filter and the optimized active filter

Figure 3. (Top) Simulation schematic of the passive filter and (bottom) the optimized active filter (click to enlarge)

 

The resistance values are those calculated by the optimizer. To achieve the desired resistance, I have combined two E12 value resistors with 1% tolerance. To support fine-tuning, it is best to follow these three steps:

  1. Select one resistor that is closest to the target value.
  2. If the resistor value is below the target, add a small value resistor in series.
  3. If the resistor value is above the target, add a large value resistor in parallel.

For the active filter section, C2 and R2 at the output of the first amplifier form the first-order high-pass filter. R3 and C3 form the first-order low-pass section of the fifth-order Sallen and Key filter. The buffers U1 and U3 isolate the filter sections from the surrounding source and load impedances because the responses must be very accurate.

The circuit around U4 is one of the two second-order sections, and that around U5 is the other second-order section. The value of R11 is critical. It must be adjusted to 1.413 times the measured value of R10.

 

Simulation of the 468-4 Weighted Noise Filter Design

I simulated the designs of Figure 3 using LTspice. Figure 4 shows the separated frequency responses of the active filter sections. The overall 5th-order low-pass filter response is slightly peaked, but the third section, the 2nd-order part, alone is quite peaky, which is why the value of R11 is critical.

 

Frequency responses of the individual active filter sections

Figure 4. Frequency responses of the individual active filter sections

 

Figure 5 compares the Figure 3 active filter response with the specification tolerances. Note that there is zero tolerance at 6.3 kHz because this is the reference frequency for setting the gain of the filter.

 

Simulated filter response deviation and the specified tolerances

Figure 5. Simulated filter response deviation and the specified tolerances

 

Building and Testing the 468-4 Weighted Noise Filter

Figure 6 shows the schematic of the constructed filter.

 

Schematic of the constructed filter

Figure 6. Schematic of the constructed filter (click to enlarge)

 

The resistors R2, R3, R4, R5, R8, and R10 set the critical frequencies of the filter sections, along with the actual values of the 1 nF capacitors, which should, in any case, have as close a tolerance as you can afford.

If you can measure the capacitor values in picofarads, you can tweak each resistor value to take the actual value C of the capacitor connected to it into account using the formula:

$$R = R_{sch} \times \big( \frac{1000}{C} \big)$$

 

where Rsch is the resistor value in the schematic. This adjustment compensates the circuit to achieve the desired -3 dB frequency, which is given by:

$$f_{3dB} = \frac{1}{2 \pi RC}$$

 

The circuit around the U3B op amp needs some explanation. The variation of gain up to the output of the U3A op amp is unlikely to exceed ±1 dB, but to be safe, we will make a ±2 dB adjustment range with potentiometer RV1. However, this last stage is non-inverting, so it cannot have a gain of less than 1.

To overcome this, R12 and R13 form a 3 dB attenuator, while R14 and R15 with RV1 give a gain adjustment range of 1 dB to 5 dB. The gain is 3 dB with RV1 set at 4.4 kΩ, reasonably near the middle.

Figure 7 shows the response error curve of the constructed filter in comparison with the specified tolerances.

 

Constructed filter response deviation and the specified tolerances

Figure 7. Constructed filter response deviation and the specified tolerances

 

Connecting the Filter to My Wideband Voltmeter

In my previous noise filter projects, I set up the filters at 1 kHz. For this one, it needs to be adjusted to achieve a 12.2 dB gain at 6.3 kHz by adjusting RV1. Figure 8 shows the measured frequency response of the filter when connected to my Wideband Voltmeter.

 

FFrequency response of the wideband voltmeter with the 468-4 filter connected

Figure 8. Frequency response of the wideband voltmeter with the 468-4 filter connected (click to enlarge)

 

As we have seen in this series, selecting the best filter to measure noise can be subjective, just like our individual hearing responses. In this case, the 468-4 filter is designed to approximate the impact noise will have on an audio broadcast signal. Its shaped bandpass response does not tell us how much noise is in the signal but can be more useful in specific applications.

 

All images used courtesy of John Woodgate