IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 3 Issue 4, April 2016. www.ijiset.com ISSN 2348 – 7968 Review of Electrical Filters Andrew Matzik and Sohail Anwar Division of Business, Engineering, and Information Systems Technology, Pennsylvania State University Altoona College, Altoona, PA 16601, USA Abstract As it can be seen from the above example, active In electrical circuit theory, a filter is an electrical network filters do not utilize inductors. Inductors are that changes the amplitude and/or phase characteristics of a expensive and hard to fit into more discrete circuits. signal with respect to frequency. Thus a filter is designed to Instead, active filters utilize operational amplifier modify, reshape, or reject all unwanted frequencies of an circuits which are cheaper to manufacture and are electrical signal and accept or pass only those frequencies that are needed by the circuit designer. A common need for able to easily fit into discrete circuits. Another filters is in high performance stereo systems where certain advantage of active filters utilizing operational ranges of audio frequencies need to be amplified or amplifiers is that the circuits are able to produce suppressed for best sound quality and power efficiency. desired cutoff frequencies with more precision than Another well-known application of filters is in the passive filters [1]. The aforementioned advantage is conditioning of voltage waveforms in electrical power due to the ability to make higher order circuits using circuits. This manuscript provides a comprehensive review operational amplifiers. Along with having more of the operation, characteristics, categories, and precision in frequency selection, active filters allow applications of filters. for a very large range of ways to select the desired Keywords: analog, digital, power electronics, digital frequencies to be passed or blocked. signal processing, passive filter, active filter. Filters are used in numerous applications. Among these applications are harmonic current 1. Introduction compensation, reactive current compensation, voltage flicker compensation, voltage sag compensation, and A passive filter utilizes RL and RC circuits negative phase sequence current compensation [3]. as its main components while active filter utilizes The aforementioned applications are primarily for operational amplifiers as its main component. An power correction but filters have other applications as example of a basic type of passive filter is shown in well. Other applications include digital signal Fig. 1: processing and digital picture processing [10,11]. Digital signal and digital picture processing include digital and analog filtering. All these applications are found in industry such as: the power distribution industry, marine operations and the medical field to name a few [3,4,5,6]. Now that a brief overview of active and Fig. 1 RC low-pass filter circuit passive filters has been provided, a more detailed There are some differences between passive look into the aforementioned filters will be presented. and active filters. A simple example of an active The further explanation of active and passive filters filter is shown in Fig. 2: will include more detail on active and passive filters. Following a description of operation of filters, their applications will be discussed. 2. Filters This section presents a more in depth Fig. 2 Simple active filter circuit description of both active and passive filters. Content provided here includes a coverage of the operation of active and passive filters. 543 IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 3 Issue 4, April 2016. www.ijiset.com ISSN 2348 – 7968 = tan (5) 퐿 2.1 Passive Filters Where R is the resistance−1 푋 of the resistor and = 휃 − 푅 and = 2 . L is the inductance of the Passive filters utilize both resistive- 퐶 1 푋 capacitive (RC) and resistive-inductive (RL) circuits. inductor and is the frequency of the circuit. 2휋푓퐿 푋퐿 휋푓퐿 By utilizing the RC and RL circuits in different ways, The high-pass filter allows signals of a one is able to construct four basic kinds of passive higher frequency푓 to pass from the input to the output. filters. The four different types of passive filters are Like low-pass filters, the high-pass filter can also be low-pass, high-pass, band-pass, and band-stop [2]. made by utilizing RC and RL circuits. A low-pass filter allows signals of a lower frequency to pass from the input to the output. The frequency of the filter can be determined by using the following formulas: = for RC (1) 1 푓푐 2휋푅퐶 = for RL (2) 1 where R is the resistance푐 퐿in the circuit, C is the 푓 2휋 �푅 capacitance in the circuit, and L is the inductance in the circuit [2]. The low-pass filter can be made by using RC and RL circuits. Examples of these circuits are shown here: Fig. 4 RL high-pass and RC high-pass filters Fig. 3 RC low-pass and RL low-pass filter circuits In the RC circuit the output voltage is obtained across In the RC circuit, the output voltage is obtained from the resistor, while in the RL circuit, the voltage is across the capacitor. While in the RL circuit, the taken across the inductor. Like the low-pass filter, output voltage is taken across the resistor. When the when the output voltage is 70.7% of the maximum output voltage is 70.7% of the maximum voltage or voltage or higher, the range of frequencies that permit higher, then the range of frequencies that make it the output voltage to achieve that level will be happen will be allowed to pass [2]. The output allowed to pass [2]. To calculate the output voltage voltage can be calculated using the following of a high pass passive filter, one can utilize Eq. (3). equation: In this case, all of the frequencies above the critical frequency will allow the output voltage to be greater = .707 (3) than or equal to 70.7% of the maximum voltage. In 표푢푡 푖푛 In this case, the range푉 of frequencies푉 below the order to compute the critical frequency, Eq. (1) can critical frequency, which is the frequency that will be used if the circuit is RC and Eq. (2) may be used if allow the output voltage to be 70.7% of the the circuit is RL. To calculate the phase shift, Eq. (6) maximum voltage, will be allowed to pass, hence the is used for RC circuits and Eq. (7) is used for RL name low-pass filter. In order to find the phase angle circuits: of the circuit, use Eq. (4) for the RC and Eq. (5) for the RL low-pass filters. = tan (6) 푋퐶 = tan (4) −1 θ 푅 −1 푅 = tan (7) 푋푐 θ − −1 푅 휃 푋퐿 544 IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 3 Issue 4, April 2016. www.ijiset.com ISSN 2348 – 7968 where is the center frequency (resonant frequency) Another type of filter is known as the band- and Q =0 . is the reactance of the inductor, pass filter. The band-pass filter utilizes a 푓 푋퐿 which can be calculated as = 2 where is the combination of high-pass and low-pass filters in 푅 퐿 frequency of the푋 circuit and L is the inductance of the order to get the desired output [2]. A band-pass filter 퐿 inductor within the circuit [2]푋 . The휋푓퐿 filter only푓 allows does not just filter out high or low frequencies, it the band of frequencies to pass that make the output allows a band of frequencies to pass. The band of voltage 70.7% of the input voltage or higher. frequencies that are allowed to pass are the ones that Therefore, the circuit allows for a band of frequencies are equal to and between the critical frequencies of to pass, making the circuit a band-pass filter. the low and high-pass filters which constitute the The final type of passive filter is termed bandpass filter. Therefore, Eq. (1) can be used to band-stop filter. This kind of filter is the exact calculate the output voltage. To calculate the band opposite of the band-pass filter. Instead of having a width of the band-pass filter, which is the size of the band of frequencies to pass, the filter has a band of band of frequencies that the filter allows to pass, the frequencies to stop. The band-stop filter utilizes both following equation can be used: parallel and series circuits [2]. An example of these = (8) filters can be seen below. where is the upper cutoff frequency and is the 푐2 푐1 lower cutoff frequency퐵푊 [2]. 푓 − 푓 푐2 푐1 Band-pass푓 filters utilize both parallel and series푓 circuits. Some examples of these circuits are shown here: Fig. 6 Series resonant and parallel resonant band-stop filter circuits A final characteristic to calculate for all Fig. 5 Series resonant and parallel resonant band-pass filters is the gain of the filter. The following equation filter circuits can be used for all passive filters and the equation is written as: When utilizing the parallel resonant band-pass filter, the inductor has the most impedance when the circuit Gain in decibels = 20 log( ) (10) is at its center frequency. When the inductance is at 푉표푢푡 the maximum point, the output voltage will be at a 푉푖푛 maximum. Therefore, when the frequency is below 2.2 Active Filters or above the center frequency, the impedance decreases which allows for more voltage to be across An active filter is a filter that has four main the resistor in turn, causing the output voltage to types. The four types are the low-pass, high-pass, decrease [2]. The range of frequencies being allowed band-pass, and band-stop filters.