Basic Filter Types, Physics tutorial

Filters classification:

Filters can be categorized in numerous ways either by technology, topology or design methodology. Classification of filters by technology separates them in passive filters, active filters and digital filters.

Passive Filters:

Passive filters are linear networks that are created out of combinations of Inductors, Capacitors and Resistors. They don't have any active component like transistors or valves; neither do they need external power supply.

Passive filters are further categorized by electrical topology in single element filters, L-filters, T-filters and π -filters. Number of circuit elements in each of the sub classifications of passive filters is simply determined by number of inductors and capacitors that make up filter except when the Inductor-Capacitor pair forms the resonant tank circuit in which case pair is treated as the single circuit element. Multiple element Passive Filters generally have the ladder topology that can be viewed as replication of L-filter, T-filter and π -filter sections.

Active Filters:

Family of filters expressed as Active Filters are the combination of passive and active components. Active filters need the power source and frequently use high gain Operational amplifiers in designs to attain very high Q factors. It becomes possible with Active filters to get particularly modified response curves that are only restricted by bandwidth of amplifiers utilized in design.

Digital Filters:

Digital methods are utilized to process both digital and analogue signals that have been converted to appropriate digital form which computers programs can operate upon.

Powerful algorithms implemented in hardware for fast processing calculate output for particular filter response curves in frequency domain. The practical application of this in audio is tone control through digital equalizer.

Passive filters:

Passive Analogue Linear Filters that are built with only resistors, capacitors and inductors, and are known as RC and RL filters single-pole filters.

1817_RC-RL low pass filter.jpg

Realize that Multipole LC filters also exit with well documented and well understood features.

Passive Filter is frequency-selective as it filters out unwanted frequencies and circuit passes to output only those input signals which fall within the desired frequency range. This is known as Pass band.

Region outside Pass band is referred to as Stop Band and amplitude of signals within Stop band are really attenuated. In analyzing Passive Filter, signal source must have very low internal impedance while load must present very high impedance. This allows us to concentrate Voltage transfer function while ignoring Current Transfer Function as current is kept to a minimum.

2196_Ideal Low Pass Filter Transfer Function.jpg

In practical filters, pass and stop bands are not evidently stated but differs continuously from its maximum toward zero and cut-off frequency is stated as frequency at which amplitude is decreased to 0.7 of its maximum value. This corresponds to signal power being reduced by half.

This is given below.

2462_LC Low Pass Filter.jpg

In Low Pass Filter:

Voltage Transfer Function; ratio of output to input voltage is

V0/Vi = R/(R + jωL) = 1/(1+ j(ωL/R))

Cutoff frequency at which Transfer Function degenerates to 0.7 is

ωc = R/L

By substituting above Transfer Function is rewritten as:

H(jω) = 1/(1 + jω/ωc)

Input Impedance is:

Zi = Vi/Ii = jωL + R

While the output impedance is stated as

Z0 = jωL||R

Active filter:

Filters of all type find application over the broad spectrum of frequencies ranging from sub-audio applications through microwave frequencies. At frequencies higher than 1 Megahertz, filters comprise approximately completely of passive components like Inductors, Capacitors and resistors. In certain situations are hybridizations where parasitic effects of real world component imperfections are capitalized on like parasitic inductance of leads of a capacitor; to attain these filters.

1069_active filter.jpg

At sub-one-megahertz frequency range though, physical values of some passive filter components become prohibitively high and components themselves turn out to be bulky and expensive rendering production of filters difficult and uneconomical. All these situations that plague Passive Filter implementation at lower frequencies encourage use of Active Filters.

Active Filters are circuits which use operational amplifier as the active device in combination with resistors and capacitors to give LRC-like filter performance; and can usually be referred to as Network Synthesis Filters.

2311_active and passive filter.jpg

The family of network Synthesis Filters includes Butterworth filter, Tschebyscheff filter, Elliptic filter that is also known as Cauer filter, Gaussian filter, Bessel filter, Linkwitz-Riley filter and Optimum L filter derived from Legendre filter. Three main optimizations of Active filters are Butterworth, Tschebyscheff and Bessel filters. All active filters find application in high-pass, low-pass, band-rejection, band-pass, and all-pass filters.

Other filter methods - hum injector filter:

More than one offending frequency is present that needs numerous notch filters to be cascaded and if desirable frequency lies near one of the offensive frequencies, useful frequency will be eradicated and offensive one. This impossible condition arises when it is desirable to filter out 50 Hertz. Hum without affecting signal at exactly same frequency.

Obvious solution would be to use conventional notch filter in which input signal suffers the phase shift of 1800at some specified frequency, relative to input and when input and output signals are combined; null in response is created at that frequency.

Phase-shifted signal is utilized to oppose original input, and if two signal levels are accurately equal the result is complete cancellation. In cancelling 50 Hertz hum, opposing frequency need not be deduced from original signal, but instead is derived from sample of actual power line, and it can be utilized to exactly balance any hum in output without influencing desired range of helpful signal frequencies. This however should be done in real time, so that hum source and cancellation signals will be synchronized.

The higher the frequency, the more diminished in amplitude the harmonic amplitude and in this particular circuit, it was not necessary to have more than four stages. You should recognise this method of filtering out an undesirable frequency through cancellation as a very effective method which precisely cancels out the offending signal frequency while leaving desirable signal at that same frequency untouched.

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