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Low-pass filters: Sound engineering for measurement accuracy

By Jack Smith

Source: Thazoo at en.wikipedia

Many years ago, when I worked in the recording industry - as a technician, NOT a performer - I came to appreciate the wealth of knowledge the world of professional audio has to offer. That was before the digital recording era. Everything was analog, which meant lots of calculating, and lots of measuring (in case you’re wondering, yes, we used Fluke meters).

Working in recording studio or live venue environments tends to force one to learn about the value of power quality. Many times you can hear its effects in the form of hum fields, noise, and transients. Harmonics wrought havoc with sound systems as well. I’ll save these sound-related power quality topics for a future article or column. In this month’s column I’ll discuss filters - specifically low-pass filters.

What about low-pass filters?

So what do low-pass filters have to do with Fluke or with measurement? Plenty! Fluke patented low-pass filter technology. Low-pass filters are not only built into the Fluke instruments included in the following non-exhaustive list, they’re featured:

The low-pass filter feature reduces the ac measurement bandwidth to 1 kHz and below. The switchable low-pass filter makes these instruments extremely useful for accurately measuring and monitoring the output voltage and frequency of a variable frequency drive (VFD). Filtering the output signal allows these instruments to reject the high-frequency components associated with VFD waveforms.

VFD waveforms are complex because they use pulse-width modulation (PWM) to make a rapidly-switched DC signal appear as an AC sine wave to the motor. The motor’s inductance smoothes out the rapidly-changing PWM signal. Most digital multimeters have excellent frequency responses, typically having measurement bandwidths exceeding 20 kHz. This bandwidth causes a problem when using a digital multimeter to measure VFD outputs because they read the pulsating DC of the PWM instead of the apparent AC signal that the motor sees. The low-pass filter eliminates this problem, allowing the digital multimeter to display accurate readings.

What’s good for the VFD is also good for the inverter. Renewable energy applications such as solar photovoltaic and wind-turbine power are growing rapidly. Both solar and wind applications use inverters, which means more inverters in the field to install and maintain.

Where else are low-pass filters used? Not only can low-pass filters be used in testing and measurement, they can also be used in the normal operation of other types of equipment. Of course, audio comes to mind. Crossovers found in stereo speakers use low-pass filters to direct lower frequencies to the woofer. Other filters used in speaker crossovers are the bandpass for midrange and high-pass for the tweeter. Those familiar with electric guitars and amplifiers will recognize the tone controls. These controls limit the amount of treble the guitar and amplifier reproduce. Equalizers use filters to boost or cut specific audio frequencies.

Telephone lines with DSL internet service must have DSL splitters installed. These splitters use low-pass and high-pass filters to separate the DSL and voice service signals, which share the same pair of wires. Radio transmitters prevent harmonic emissions, which might cause radio-frequency interference, using low-pass filters.

Low-pass filter basics

A low-pass (or any type) filter can be very basic, or quite complex. A simple “one-pole” or “first order” filter can be as simple as a single resistor and capacitor combination. More complex filters have multiple stages and are frequently in the circuit structure of operational amplifiers and/or transistors. Then there are digital filters, which we definitely won’t get into in this column.

A capacitor is a reactive component because its electrical characteristics vary according to frequency. A one-pole or first-order filter has only one reactive component in the circuit, hence the name.

The resistor-capacitor (RC) combination that makes up a one-pole low-pass filter is constructed so that the resistor is in series with the load, and the capacitor is in parallel with the load. The capacitor reacts to and blocks low-frequency signals, causing them to go through the load. Reactance drops at higher frequencies, which causes the capacitor to appear as a short circuit to ground just for those higher frequencies. While trying very hard to avoid a great deal of math, simply put, multiplying the resistance and capacitance values yields the time constant of the filter.

From here, filters become complicated very quickly. At some point determined by the filter’s time constant, the frequency response starts to roll off. Those who deal with professional audio and instrument specifications talk in terms of decibels (dB). What’s the definition of dB? The answer is “it depends.” Simply defined, dB is a ratio. From there, it gets very complicated very quickly. Why can’t they make this easy?

Although dB is a ratio, how it’s figured for acoustic power (sound pressure level), for power, and for voltage and current are not quite the same. For this column, I’ll use the voltage/current definition because it’s most applicable. Decibel, or dB, is a unit used to compare two voltages or currents, equal to 20 times the common logarithm of the ratio of the voltages or currents measured across equal resistances.

For any filter, whether used in instruments, engineering, or audio, at the cutoff frequency, the filter attenuates the input by half, or 3 dB. This is also called the “3-dB down point.” The order of the filter - in other words, the number of poles - determines the amount and rate of attenuation for frequencies above the cutoff.

The frequency doesn’t chop off at the cutoff frequency. The amount of attenuation above the cutoff frequency slopes at a specific rate as the frequency increases. A first-order filter reduces the signal amplitude 6 dB per octave, which equates to 20 dB per decade. Adding a second pole to the filter doubles the steepness of the slope. A second-order low-pass filter reduces signal amplitude by 12 dB per octave, or 40 dB per decade. A three-pole filter follows the same pattern.

So, the next time you listen to your favorite tunes, or reach for your trusted Fluke meter, you can understand the complexity of engineering required to make our lives more simple and enjoyable.

Don’t make me break out my slide rule. Yes, I still have mine.

To comment on this or any of my “Solid Ground” columns or to suggest column topics, send me an e-mail at jacksmith.writes@gmail.com.

Until next time, keep standing on “Solid Ground.”