Audio Filters: Understanding Filters – Part 5

In previous tutorials, we discussed two of the most important components of an audio system: microphones and speakers.

As an overview, an audio system is designed to:

• Receive audio signals, typically through a microphone
• Record audio to a storage device such as a computer file
• Transmit audio, via wired or wireless communication channels
• Play audio signals through speakers

Audio circuits perform signal processing, essentially transforming sound waves into electrical signals, which can later be changed through amplification, filtering or mixing. These signals can also be stored and played back.

Audio filters are a part of this system, functioning as amplifiers or passive circuits with distinct frequency responses. Just like microphones and speakers, these filters are an important part of the basic components of an audio system. They can amplify or attenuate a range of audio input frequencies.

However, these filters are different from a simple audio amplifier or input source, which does not have frequency-dependent operation. Boosts the entire input audio signal, regardless of its frequency. However, an audio filter is a frequency-dependent amplifier that works in the range from 0 Hz to beyond 20 kHz. By specifically amplifying or attenuating a range of frequencies in the audio signal, it is possible to improve the tone of the input audio.

An audio crossover and an equalizer are types of audio filters. The audio crossover is an electronic filter used to divide the incoming audio signal into different frequency ranges, which are then sent to different drivers (such as tweeter, mid-range and woofer speakers). The audio equalizer is an electronic filter used to amplify the audio signal, according to a frequency-dependent function. The output of an equalizer has different amplified levels for different frequencies.

Crossover and equalizer play an important role in audio devices. Next, we will discuss the types of filters available and their features.

Types of filters
Audio filters are electronic circuits designed to amplify or attenuate a certain range of frequency components. They serve as a unique type of passive amplifier or circuit with frequency-dependent outputs. Essentially, they help eliminate any unwanted noise from an audio signal, improving the tone of the output.

These filters play an important role in telecommunications and audio electronics and can be classified based on their design, frequency response, or both.

Project

Audio filters classified based on their design are either passive or active filers. An electronic device that requires a power supply for its operation is an active component, and one that does not is a passive component.

Active filters – require a power source and are designed using active components such as transistors or operational amplifiers (op-amps). Transistors or operational amplifiers require a DC power supply for their biasing. When using active components, there is no need to use inductance to build the filter, which reduces circuit size and cost and improves filter efficiency.

Passive filters – do not require a power source to operate, these filters are designed using passive components such as resistors, capacitors or inductances. The impedance of capacitors and inductances depends on frequency, so the filter can be designed using resistor-capacitor, resistor-inductance, or resistor-capacitor-inductor combinations.

Frequency Response

Audio filters can also be classified based on their frequency response, which refers to the range of frequencies that are amplified or allowed to pass through a filter (the passband). The passband is the region on the frequency curve of a filter where the voltage or power of the circuit is at its maximum.

Depending on the frequency band, there are several types of filters, including high-pass, low-pass, band-pass, band-stop, notch, all-pass, and equalization.

Let’s review each one…

High Pass Filter (HPF) – passes signals with a frequency higher than the cutoff frequency and blocks all signals lower than the cutoff frequency. Cutoff frequency occurs when the signal voltage or amplitude drops to within 0.707 or 3 dB of the passband voltage. At this point, the circuit power begins to drop.

As can be seen from this graph, low frequency signals are not completely attenuated at the cutoff frequency. But the frequencies that break through the high-pass filter have very little gain. Technically, there is a “roll-off frequency” in the cut.

Low-pass filter – passes signals with a frequency lower than the cutoff and blocks frequencies higher than it.

As can be seen from this graph, high frequency signals are not completely attenuated at the cutoff frequency. Frequencies that break through the low-pass filter have little gain.

Band-pass filter – only passes frequencies within a certain cutoff range and rejects those outside the range. It has two cutoff frequencies: the lower cutoff and the upper cutoff. The center frequency and bandwidth of this filter determine the lower and upper cutoff frequencies.

Band Stop Filter – passes all frequencies except a specific band. This means that it passes all signal frequencies below the lower cutoff and above the upper cutoff – but not the frequencies between the lower and upper cutoff. The highest and lowest cutoff frequencies are deviations from the center frequency for which the filter circuit gain is ideally zero (practically minimal).

Notch filter – a bandstop filter with an extremely narrow stop band. As a result, these filters offer a high quality factor.

All-pass filter – passes all frequencies equal in gain, but modifies the phase relationship between them. The output of the frequency bands also displays phase differences between them.

Equalizer filter – never completely attenuates or passes a specific range of frequencies, but rather amplifies frequencies based on a frequency-dependent function.

Design + frequency response

Filters can also be classified based on both their design and frequency response. These include passive or active high-pass filters, passive or active low-pass, passive or active band-pass, and passive or active band-stop filters.

Passive High Pass Filter – Blocks lower frequency signals while allowing higher frequency signals. This type of filter is typically used to direct the high-frequency elements of an audio signal to a tweeter and is usually designed using a resistor-capacitor (RC) network – an electrical circuit made up of resistors and capacitors.

Passive high pass has no bandwidth limitation and can be designed by selecting resistor and capacitor values. As a passive filter, it does not require a power supply for DC bias, so it has few components. It offers a high current output but is not capable of amplifying audio signals.

Although an inductor can be used as part of the filter design, they are expensive and bulky.

fh = 1/ (2πRC)

By defining the resistor and capacitor value and the preferred cutoff frequency, it is possible to design a high-pass filter. In the circuit above, the cutoff frequency is about 160 Hz. A high-pass filter will pass all frequencies higher than 160 Hz and attenuate lower frequencies.

Active high pass filter – can be designed using transistors or operational amplifiers. The filter in the circuit diagram uses operational amplifier at the output of the RC network, making it an active filter. An operational amplifier is an integrated circuit that can amplify weak electrical signals. It has two high impedance inputs. Thus, while the RC network blocks any low-frequency elements, the operational amplifier amplifies an allowed frequency range.

In this case, the RC network is connected to the non-inverting input pin of the op-amp, so its output is not inverted. When connected to the inverting pin of the op amp, the output audio signal is phased 180 degrees from the input audio signal.

The active high-pass filter has a high, non-unity gain, which means the output audio signal is noise-free and well amplified. It also has no charging effect. The op amp has a high input impedance and a low output impedance, so loading into the source is not a problem either. However, because of the operational amplifier, the filter circuit will have bandwidth limitations.

Typically, these filters are small and compact. However, an active filter design involves more components that require a DC source for their bias and will require an external power supply to operate.

Passive low-pass filter – the input signal passes through a resistor (instead of a capacitor, as with a high-pass filter). The capacitor is connected between the resistor and ground.

However, passive low-pass filters can have different designs using:

• An RC or resistor-inductor (RL) network for a first order filter
• A resistor-inductor-capacitor (RLC) network for a second-order filter
• Combining multiple first-order filters in a series for a more accurate, high-order audio signal

So, for example, a first-order filter has a capacitor or an inductor, which affects the frequency response of the filter. Whereas a second-order filter has two RC filter sections – like two capacitors or two inductors – that affect its frequency response.

The passive low-pass filter allows all frequencies below the cutoff frequency to pass through, but attenuates those above the cutoff. These filters are not bandwidth limited and do not require a power source to operate. They are typically used to direct low-frequency elements of an audio signal to a woofer.

Active low-pass filter – uses an operational amplifier or a transistor amplifier at its output and before using passive RC, RL, RLC or multiple-order low-pass filters. An operational amplifier amplifies low-frequency elements before delivering the sound to a power amplifier or speakers.

The gain provided through the op amp is the main advantage of this filter – as well as reducing any high frequency noise or distortions. But it has bandwidth limitations and requires a DC source to bias the amplifiers or the transistor circuit.

Passive Bandpass Filter – Designed by combining a low-pass and high-pass filter and usually designed using an RLC network.

In this circuit, a high-pass filter is connected in series with a low-pass filter.

Observation:

• The cutoff frequency of the high-pass filter is the lowest cutoff frequency of the bandpass filter
• The cutoff frequency of the low-pass filter is the highest cutoff frequency of the bandpass filter
• Thus, only frequencies between these two cutoff frequencies can pass the filter output

These filters are typically used to target a specific range of frequencies for mid-range drivers. Because there are multiple components in their construction, these filters are large and heavy.

Active bandpass filter – has an operational amplifier or transistor connected before its output and after the passive bandpass circuit. The operational amplifier amplifies the allowed band of frequencies and its bandwidth must match that of the band-pass filter.

Passive band-stop filter – attenuates a range of frequencies, allowing both those lower and higher than its two cutoff frequencies to pass. A passive first-order band-stop filter is usually designed using an RLC network, where the input signal first passes through a resistor. The LC network is connected between the resistor and ground.

This circuit combines that of high-pass and low-pass filters.

Observation:

• The cutoff frequency of the high-pass filter is the highest cutoff frequency of the band-stop filter
• The cutoff frequency of the low-pass filter is the lower cutoff frequency of the band-stop filter
• Thus, only frequencies that exclude those between the cutoff frequencies of the high-pass and low-pass filters can pass through the output.

These filters are also called band-rejection, band-elimination, and T-notch filters.

Active bandstop filters – have an operational amplifier or transistor at the output, which amplifies the allowed frequency signals before they are delivered to a power amplifier or audio driver. This operational amplifier must have a bandwidth that matches the desired frequency curve of the band-stop filter.

Terms

Here are some terms that are often used in relation to audio filters.

Bandwidth: the range of frequencies allowed to pass through the filter or the difference in the upper and lower cutoff frequencies. Sometimes called the passband bandwidth, the bandwidth determines the frequency response of the filter within the defined frequency range.

Quality factor (Q factor): losses in the resonator circuit. The relationship between the energy stored in the resonator and the energy supplied per cycle to maintain the constant amplitude of a signal. The higher the Q means fewer losses and vice versa.

Q = (Energy stored / Energy lost per cycle)

In terms of bandwidth, Q is determined using this equation:

Q = (fc/ PN)

Where…

fc = resonant frequency
BW = bandwidth or resonance width

The Q factor can be determined using the audio filter frequency curve…