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Audio Filters - Basics of Audio Filters - 5/8

Written By: 

Diksha
In the previous tutorials, two of the most important building blocks of an audio system - Microphone  and Speaker were discussed. An audio system is designed to receive audio signals (via microphone), record audio in some storage, transmit audio (through wired or wireless communication channels) and reproduce audio signals (via speakers). So, the audio circuits perform signal processing for representing the sound in the form of electrical signals, manipulate the electrical (audio) signals like amplifying, filtering or mixing, reproduce sound from the audio signals, store audio into computer files or reproduce audio from an audio file. A general audio system can be represented by the following block diagram - 
 
Block Diagram of an Audio System
Block Diagram of an Audio System
 
Like microphones or audio source and speakers, audio filters are also basic building block of an audio system. The audio filters are actually amplifier or passive circuits having distinct frequency response. They can amplify or attenuate a range of frequencies from the audio input. This is different from a simple audio amplifier or input source which does not have a frequency dependant functioning. Any simple audio amplifier amplifies the complete input audio signal irrespective of its frequency or an audio source delivers the audio signal irrespective of the frequencies in the signal. 
 
By amplifying or attenuating specific range of frequencies in the audio signal, the tone of the audio input can be creatively enhanced. The audio crossover and equalizer are also types of audio filters. The Audio Crossover is an electronic filter used to split the input audio signal into different frequency ranges so that they could be sent to different drivers (Twitter, Mid Range and Woofers). The audio equalizer is a electronic filter used to amplify the audio signal according to a frequency dependant function. So, that the output from an equalizer has different amplified levels for different frequencies. The Crossover and Equalizer play a major role in the audio devices. In this tutorial, different types of filters and terms associated with them will be discussed. 
 
What is an Audio Filter
 
The audio filters are the electronic circuits which are designed to amplify or attenuate certain range of frequency components. This helps in eliminating the unwanted noise from the audio signal and improving the tone of the output audio. Filters play a major role in telecommunication and audio electronics.  
 
Types of Filters 
 
The filters are special type of amplifiers or passive circuits which have frequency dependant output. The filters can be classified in many ways like on the basis of construction, frequency response or both. 
On the basis of construction, the audio filters are classified as follow - 
1) Passive Filter
2) Active  Filter 
 
The terms Passive and Active are commonly used in context to electronic components. A component which needs a power supply for its operation is called active component like transistors and OPAM. While, those electronic components which do not require any power source for their operation are called passive components like resistor, capacitor and inductor. 
 
Passive Filter - A passive filter is designed using passive components like resistor and capacitor or resistor and inductance. The impedance of capacitors and inductances is frequency dependant which allows constructing filters using resistor-capacitor, resistor-inductance or resistor-capacitor-inductor combinations. These filters do not require any power source for their operation that why they are called Passive Filters. 
Active Filters - The active filters are designed using active components like transistors or operational amplifiers. The transistors or operational amplifiers require a DC power source for their biasing. By using active components, there remains no need of using inductance to construct the filter. This not only reduces the size and cost of the circuit but also improves the efficiency of the filter. Since, these filters require a DC biasing source for their active components, these are called Active Filters.  
 
The filters can also be classified on the basis of their frequency response. The range of frequencies which are amplified or allowed to pass by a filter is called its pass band. The pass band is the region in the frequency curve of filters where the voltage or power delivered by the circuit is maximum. On the basis of the frequency band allowed to pass by the filters, they are categorized as follow - 
 
1) High Pass Filter
2) Low Pass Filter
3) Band Pass Filter
4) Band Stop Filter 
5) Notch Filter
6) All Pass Filter
7) Equalization Filter
 
High Pass Filter – This filter passes all the frequencies which are above its cut off frequency and blocks all the frequencies below the cut off frequency. The cut-off frequency is the frequency where the voltage or amplitude of the signal falls to 0.707 or 3 dB of the pass band voltage. At this point, the power output of the circuit starts falling down. The typical frequency curve of a high pass filter is shown below - 
 
Frequency Response of a High Pass Audio Filter
Frequency Response of a High Pass Audio Filter
 
As can be seen from frequency response graph, at the cutoff frequency the low frequency signals are not completely attenuated. Frequencies below cut off frequencies are also passed by this high pass filter but with very less gain. So there is a roll off in the cut off frequency that’s way this is sometimes called as roll off frequency also. 
 
Low Pass Filter – This filter passes all the frequency which are below its cut off frequency and blocks the frequencies above it. The frequency  response of a low  pass filter is as follow - 
 
Frequency Response of a Low Pass Audio Filter
 
Frequency Response of a Low Pass Audio Filter
 
It can be seen from the frequency response graph, that at the cutoff frequency the high frequency signals are not completely attenuated. Frequencies above cut off frequencies are also passed by this low pass filter but with very less gain.
 
Band Pass Filter –This filter only passes a band of frequencies which are in its cut off frequency range. The band pass filter has two cut off frequencies, one is lower cut off and another one is upper cut off frequency. The center frequency and bandwidth of the filter decides the lower and upper cut off frequencies as shown in the frequency response graph below -  
 
Frequency Response of a Band Stop Audio Filter
Frequency Response of a Band Stop Audio Filter
 
Band Stop Filter - A Band stop filter passes all the frequencies except a specific range of frequencies. It passes all the frequencies below its lower cut off and all the frequencies above its higher cut off but not frequencies ranging between lower and higher cut off. The higher cut off and lower cut off frequencies are deviation of a centre frequency for which the gain of the filter circuit is ideally zero (practically minimum). The frequency response graph of a Band Stop filter is shown below - 
 
Notch Filter - A Notch filter is a band stop filter with a very narrow stop band. Due to very narrow stop band, these filters have a very high Quality Factor. 
 
All Pass Filter - An all pass filter allows to pass all the frequencies but it modifies the phase relationship between them. So, at the output of the all pass filter, different frequency ranges have phase difference with each other. The frequency response graph of an all pass filter has phase shifted frequencies as shown in the graph below - 
 
Phase Shifted Frequency Response of All Pass Audio Filter v
 
Phase Shifted Frequency Response of All Pass Audio Filter
 
Equalizer Filter - An equalizer filter does not completely attenuates or pass a specific range of frequencies but it variably amplifies frequencies according to a frequency dependant function. 
 
On the basis of both frequency response and the construction, the filters can be classified as follow - 
 
1) Passive High Pass Filter
2) Active High Pass Filter
3) Passive Low Pass Filter
4) Active Low Pass Filter
5) Passive Band Pass Filter
6) Active Band Pass Filter
7) Passive Band Stop Filter
8) Active Band Stop Filter
 
Passive High Pass Filter - A High Pass Filter blocks the lower frequency components and allow higher frequency components. A passive high pass filter can be constructed using a RC network. This type of filter is generally used to direct high frequency components of an audio signal to a tweeter. A simple passive high pass filter is shown below -  
 
First Order Passive High Pass Audio Filter Circuit Diagram

First Order Passive High Pass Audio Filter Circuit

 
For the RC network shown above, the cut off frequency is related with the resistor and capacitor as follow - 
 
FH = 1/ (2πRC)
 
So, by setting the value of resistor and capacitor, a high pass filter with desired cut off frequency can be designed. In the above circuit, the cut off frequency will be 160 Hz approximately. So, the above high pass filter will pass all the frequencies above 160 Hz but will attenuate the frequencies below it. 
 
A passive filter does not have any bandwidth limitation and can be designed by selecting suitable value of resistor and capacitor. It does not require any power source for DC biasing. Such filter requires less number of components to design and has a high current output. However, these filters are not able to amplify the audio signal and if an inductor is used for their construction, they are costly and bulky. 
Active High Pass Filter - An active high pass filter can be designed using transistors or operational amplifiers. A simple active high pass filter (first order filter) is shown below - 
 
First Order Active High Pass Audio Filter Circuit Diagram
First Order Active High Pass Audio Filter Circuit
 
This filter uses an OPAM (Operational Amplifier) at the output of RC network which makes it an active filter. While the RC network is blocking the low frequency components, the OPAM amplifies the allowed frequency range. Since the RC network is connected at non-inverting input pin of the operational amplifier, its output is not inverted. However, if it would have been connected at inverting pin of the OPAM, the output audio signal would have been out of phase by 180 degrees from the input audio signal. 
 
This filter has no loading effect. The OPAM has high input impedance and low output impedance so they do not suffer from loading of source and load. The filter has non unity gain which is generally very high. So, the output audio signal is not only noise free, it is also well amplified. These filters are also small in size and generaly the ICs or transistors used in their design are not bulky. However, the design of an active filter involves more number of components which require DC source for their biasing. So, the filter circuit requires external power supply for its operation. Also, due to use of operational amplifier, the filter circuit has bandwidth limitations. 
 
Passive Low Pass Filter - A passive low pass filter can be constructed using a RC network or RL network (for first order filter). A second order low pass filter can be constructed using RLC network. Higher order low pass filters which more precisely filter the audio signal, can be designed by combining many first order filters in series. In a simple passive low pass filter, the input audio signal is passed through the resistor (instead of capacitor like in high pass filter) and the capacitor is connected between the resistor and the ground. 
First Order Passive Low Pass Audio Filter Circuit Diagram
 
First Order Passive Low Pass Audio Filter Circuit
 
The cut off frequency of such filter is given by the following equation - 
 
FL = 1/ (2πRC)
 
The filter allows all the frequencies below the cut off frequency to pass but attenuates the frequencies above the cut off frequency. These filters do not have any bandwith limitaion and do not require any power surce for their operation. These are generally used to drive low frequency components of an audio signal to the woofers. 
 
Active Low Pass Filter - The active low pass filter uses an operational amplifier or transistor amplifier at the output before the low pass RC, RL, RLC or multiple order passive filter. The operational amplifier amplifies the allowed low frequency components before they are delived to a power amplifier or the speaker. The gain provided by the OPAM is the main advantage of such filter. However, such filter has a bandwidth limitation and requires a DC source for biasing the OPAM or transistor circuit. 
 
Passive Band Pass Filter - A Band Pass Filter is designed by combining a low pass and high pass filter. It is generally constructed using a RLC network. A simple passive band pass filter is shown bellow - 
 
First Order Passive Band Pass Audio Filter Circuit Diagram
   
First Order Passive Band Pass Audio Filter Circuit
 
In the Band Pass Filter shown above, a High Pass filter is connected in series with a Low Pass Filter. The cut off frequency of the high pass filter is actually the lower cut off frequency of this band pass filter and the cut off frequency of the low pass filter is actually the higher cut off frequency of this band pass filter. So, only the frequencies lying between the cut of frequencies of the combined high pass and low pass filter are allowed to pass at the output. 
 
These filters are generally used to direct a specific range of frequencies to mid range drivers. Due to increased number of components in their construction, these filters are quite bulky in size. 
 
Active Band Pass Filter - The active band pass filter has an operational amplifier or transistor amplifier connected before the output after the passive band pass circuit. The operational amplifier amplifies the allowed band of frequencies. In such filter, the bandwidth of the OPAM must match with the desired bandwidth of the band pass filter.  
 
Passive Band Stop Filter - A band stop filter attentuates a range of frequencies and allow passing frequencies lower than its lower cut off and higher than its higher cut off. A (first order) passive band stop filter is generally constructed using a RLC network where input signal is passed through the resistor and the LC network is connected between resistor and the ground. A simple passive band pass filter is shown below - 
 
First Order Passive Band Stop Audio Filter Circuit Diagram
First Order Passive Band Stop Audio Filter Circuit
 
Such circuit is a parallel combination of high pass and low pass filter. The cut off frequency of the high pass filter is the higher cut off frequency of this band stop filter and the cut off frequency of the low pass filter is the lower cut off frequency of this band stop filter. So, only the frequencies excluding the frequencies between the cut off frequencies of the combined high pass and low pass filter are allowed to pass at the output. These filters are also called Band Reject Filters, Band Elimination Filters and T-Notch Filters. 
 
Active Band Stop Filters - An active band stop filter has an operational amplifier or transistor amplifier at the output which amplifies the allowed frequency signals before they are delivered to a power amplifier or audio driver. The OPAM using in such amplifier must have suitable bandwidth to match with the desired frequency curve of the band stop filter. 
 
There are few terms that are frequently used in context to the audio filters. Some of these terms are explained below - 
 
1) Bandwidth - This is the range of frequencies allowed to pass by the filter. The bandwidth can be defined as the difference in upper and lower cut off frequency. Sometimes it is also known as Pass Band Bandwidth. The bandwidth determines the frequency response of the filter within the set range of frequencies. The bandwith of a low pass filter from its frequency response curve is shown in the figure below - 
 
Bandwidth of an Audio Filter shown in its Frequency Curve
Bandwidth of an Audio Filter shown in its Frequency Curve  
 
2) Quality Factor (Q-Factor) - The quality factor describes the losses in the resonator circuit. It is the ratio of energy stored at resonator to the energy supplied to it per cycle to maintain the amplitude of the signal constant. The more Q means fewer losses and vice versa.
Q = (Energy stored / Energy lost per cycle)
In terms of bandwidth, the Q is determined by the following equation - 
Q = (fc/ BW) 
Where, 
fc = Resonant Frequency
BW = Bandwidth or Resonance Width 
The Q-factor can be determined using the frequency curve of the audio filter - 
 
Quality Factor of an Audio Filter observed from its Frequency Curve
 

Quality Factor of an Audio Filter observed from its Frequency Curve  

 
In the next tutorial, audio crossover will be designed. The crossover is a filter circuit which splits the audio signal to different frequency ranges.  

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