Electronic filter

Television signal splitter consisting of a hi-pass and a lo-pass filter.

Electronic filters are electronic circuits which perform signal processing functions, specifically intended to remove unwanted signal components and/or enhance wanted ones. Electronic filters or audio filters can be:

passive or active
analog or digital
discrete-time (sampled) or continuous-time
linear or non-linear
infinite impulse response (IIR type) or finite impulse response (FIR type)

The most common types of electronic filters are linear filters, regardless of other aspects of their design. See the article on linear filters for details on their design and analysis.

History

The oldest forms of electronic filters are passive analog linear filters, constructed using only resistors and capacitors or resistors and inductors. These are known as RC and RL single pole filters respectively. More complex multipole LC filters have also existed for many years and the operation of such filters is well understood with many books having been written about them.

Hybrid filters have also been made, typically involving combinations of analog amplifiers with mechanical resonators or delay lines. Other devices such as CCD delay lines have also been used as discrete-time filters. With the availability of digital signal processing, active digital filters have become common.

Classification by technology

Passive filters

Single pole types

The simplest electronic implementations of linear filters are based on combinations of resistors, inductors and capacitors. These filters exist in so-called RC, RL, LC and RLC varieties. All these types are collectively known as passive filters, because they do not depend upon an external power supply. Inductors block high-frequency signals and conduct low-frequency signals, while capacitors do the reverse. A filter in which the signal passes through an inductor, or in which a capacitor provides a path to earth, therefore presents less attenuation to low-frequency signals than high-frequency signals and is a low-pass filter. If the signal passes through a capacitor, or has a path to ground through an inductor, then the filter presents less attenuation to high-frequency signals than low-frequency signals and is a high-pass filter. Resistors on their own have no frequency-selective properties, but are added to inductors and capacitors to determine the time-constants of the circuit, and therefore the frequencies to which it responds.

At very high frequencies (above about 100 megahertz), sometimes the inductors consist of single loops or strips of sheet metal, and the capacitors consist of adjacent strips of metal. These are called stubs.

Multipole types

Second order filters are measured by their quality or "Q" factor. A filter is said to have a high Q if it selects or rejects a narrow range of frequencies compared with its centre frequency. Q is defined as center frequency fo/3dB bandwidth.

Active filters

Active filters are implemented using a combination of passive and active (amplifying) components. Operational amplifiers are frequently used in active filter designs. These can have high Q, and achieve resonance without the use of inductors. However, their upper frequency limit is limited by the bandwidth of the amplifiers used.

Digital filters

File:FIR.png

A finite impulse response filter

Digital signal processing allows the inexpensive construction of a wide variety of filters. The signal is sampled and an analog to digital converter turns the signal into a stream of numbers. A computer program running on a CPU or a specialized DSP, less often a hardware implementation of the algorithm, calculates an output number stream. This output is converted to a signal by passing it through a digital to analog converter. There are problems with noise introduced by the conversions, but these can be controlled and limited for many useful filters. Due to the sampling involved, the input signal must be of limited frequency content or aliasing will occur. See also: Digital filter.

Other filter technologies

Quartz filters and piezoelectrics

In the late 1930s, engineers realized that small mechanical systems made of rigid materials such as quartz would acoustically resonate at radio frequencies, i.e. from audible frequencies (sound) up to several hundred megahertz. Some early resonators were made of steel, but quartz quickly became favored. The biggest advantage of quartz is that it is piezoelectric. This means that quartz resonators can directly convert their own mechanical motion into electrical signals. Quartz also has a very low coefficient of thermal expansion which means that quartz resonators can produce stable frequencies over a wide temperature range. Quartz crystal filters have much higher quality factors than LCR filters. When higher stabilities are required, the crystals and their driving circuits may be mounted in a "crystal oven" to control the temperature. For very narrow band filters, sometimes several crystals are operated in series.

Engineers realized that a large number of crystals could be collapsed into a single component, by mounting comb-shaped evaporations of metal on a quartz crystal. In this scheme, a "tapped delay line" reinforces the desired frequencies as the sound waves flow across the surface of the quartz crystal. The tapped delay line has become a general scheme of making high-Q filters in many different ways.

SAW filters

SAW (surface acoustic wave) filters are electromechanical devices commonly used in radio frequency applications. Electrical signals are converted to a mechanical wave in a piezoelectric crystal; this wave is delayed as it propagates across the crystal, before being converted back to an electrical signal by further electrodes. The delayed outputs are recombined to produce a direct analog implementation of a finite impulse response filter. This hybrid filtering technique is also found in an analog sampled filter. SAW filters are limited to frequencies up to 3GHz.

BAW filters

BAW (Bulk Acoustic Wave) filters are electromechanical devices. At research state for the moment. BAW filters can implement ladder or Lattice filters. BAW filters seem to be smaller than SAW filters with frequencies up to 16 GHz.

Garnet filters

Another method of filtering, at microwave frequencies from 800MHz to about 5 GHz, is to use a synthetic single crystal yttrium iron garnet sphere made of a chemical combination of yttrium and iron (YIGF, or yttrium iron garnet filter). The garnet sits on a strip of metal driven by a transistor, and a small loop antenna touches the top of the sphere. An electromagnet changes the frequency that the garnet will pass. The advantage of this method is that the garnet can be tuned over a very wide frequency by varying the strength of the magnetic field.

Atomic filters

For even higher frequencies and greater precision, the vibrations of atoms must be used. Atomic clocks use caesium masers as ultra-high Q filters to stabilize their primary oscillators. Another method, used at high, fixed frequencies with very weak radio signals, is to use a ruby maser tapped delay line.

The transfer function

The transfer function H(s) of a filter is the ratio of the output signal Y(s) to that of the input signal X(s) as a function of the complex frequency s :

H(s)={\frac {Y(s)}{X(s)}}

The transfer function of all linear filters generally share certain characteristics:

Since the filters are constructed of discrete components, their transfer function will be the ratio of two polynomials in s (i.e. a rational function of S ). The order of the transfer function will be the highest power of s encountered in either the numerator or the denominator.
The polynomials of the transfer function will all have real coefficients. Therefore, the poles and zeroes of the transfer function will either be real or occur in complex conjugate pairs.
Since the filters are assumed to be stable, the real part of all poles (i.e. zeroes of the denominator) will be negative: They will lie in the left half-plane in complex frequency space.

Classification by transfer function

Filters may be specified by family and bandpass. A filter's family is specified by certain design criteria which give general rules for specifying the transfer function of the filter. Some common filter families and their particular design criteria are:

Butterworth filter - no gain ripple in pass band and stop band, slow cutoff
Chebyshev filter(Type I) - no gain ripple in stop band, moderate cutoff
Chebyshev filter(Type II) - no gain ripple in pass band, moderate cutoff
Bessel filter - no group delay ripple, no gain ripple in both bands, slow gain cutoff
Elliptic filter - gain ripple in pass and stop band, fast cutoff
Optimum "L" filter
Gaussian filter - no ripple in response to step function
Hourglass filter
Raised-cosine filter

Generally, each family of filters can be specified to a particular order. The higher the order, the more the filter will approach the "perfect" filter of complete transmission in the pass band, and complete attenuation in the stop band.

Each family can be used to specify a particular pass band in which frequencies are transmitted, while frequencies outside the pass band are more or less attenuated.

Low-pass filter - Low frequencies are passed, high frequencies are attenuated.
High-pass filter - High frequencies are passed, Low frequencies are attenuated.
Band-pass filter - Only frequencies in a frequency band are passed.
Band-stop filter - Only frequencies in a frequency band are attenuated.
All-pass filter - All frequencies are passed, but the phase of the output is modified.

Classification by topology

The above classifications will specify completely the transfer function of the filter (i.e. its electronic behavior), but it remains to choose the particular circuit topology to implement the filter. In other words, there are a number of different ways of achieving a particular transfer function when designing a circuit. These topologies may be further subdivided into passive filters and active filters. Some common circuit topologies are:

External links and references

Zverev, Anatol, I (1969). Handbook of Filter Synthesis. John Wiley & Sons. ISBN 0-47-198680-1.{{cite book}}: CS1 maint: multiple names: authors list (link) Catalog of passive filter types and component values. The Bible for practical electronic filter design.
Williams, Arthur B & Taylor, Fred J (1995). Electronic Filter Design Handbook. McGraw-Hill. ISBN 0-07-070441-4.{{cite book}}: CS1 maint: multiple names: authors list (link)
National Semiconductor AN-779 application note describing analog filter theory
Fundamentals of Electrical Engineering and Electronics - Detailed explanation of all types of filters
Harmonic Filters - Harmonic Filters: De-tuned/Tuned Systems
BAW filter