An analogue filter is a basic building block of signal processing much used in electronics. Amongst their many applications are the separation of an audio signal before application to bass, mid-range, and tweeter loudspeakers; the combining and later separation of multiple telephone conversations onto a single channel; the selection of a chosen radio station in a radio receiver and rejection of others.
Passive linear electronic analogue filters are those filters which can be described with linear differential equations (linear); they are composed of capacitors, inductors and, sometimes, resistors (passive) and are designed to operate on continuously varying analogue signals. There are many linear filters which are not analogue in implementation (digital filter), and there are many electronic filters which may not have a passive topology – both of which may have the same transfer function of the filters described in this article. Analogue filters are most often used in wave filtering applications, that is, where it is required to pass particular frequency components and to reject others from analogue (continuous-time) signals.
Analogue filters have played an important part in the development of electronics. Especially in the field of telecommunications, filters have been of crucial importance in a number of technological breakthroughs and have been the source of enormous profits for telecommunications companies. It should come as no surprise, therefore, that the early development of filters was intimately connected with transmission lines. Transmission line theory gave rise to filter theory, which initially took a very similar form, and the main application of filters was for use on telecommunication transmission lines. However, the arrival of network synthesis techniques greatly enhanced the degree of control of the designer.
Today, it is often preferred to carry out filtering in the digital domain where complex algorithms are much easier to implement, but analogue filters do still find applications, especially for low-order simple filtering tasks, and are often still the norm at higher frequencies where digital technology is still impractical, or at least, less cost effective. Wherever possible, and especially at low frequencies, analogue filters are now implemented in a filter topology which is active in order to avoid the wound components (i.e., inductors, transformers, etc.) required by passive topology.
It is possible to design linear analogue mechanical filters using mechanical components which filter mechanical vibrations or acoustic waves. While there are few applications for such devices in mechanics per se, they can be used in electronics with the addition of transducers to convert to and from the electrical domain. Indeed, some of the earliest ideas for filters were acoustic resonators because the electronics technology was poorly understood at the time. In principle, the design of such filters can be achieved entirely in terms of the electronic counterparts of mechanical quantities, with kinetic energy, potential energy and heat energy corresponding to the energy in inductors, capacitors and resistors, respectively.
Historical overview
There are three main stages in the history of passive analogue filter development:
Simple filters. The frequency dependence of electrical response was known for capacitors and inductors from very early on. The resonance phenomenon was also familiar from an early date and it was possible to produce simple, single-branch filters with these components. Although attempts were made in the 1880s to apply them to telegraphy, these designs proved inadequate for successful frequency-division multiplexing. Network analysis was not yet powerful enough to provide the theory for more complex filters and progress was further hampered by a general failure to understand the frequency domain nature of signals. Image filters. Image filter theory grew out of transmission line theory, and the design proceeded in a similar manner to transmission line analysis. For the first time, filters could be produced that had precisely controllable passbands and other parameters. These developments took place in the 1920s, and filters produced to these designs were still in widespread use in the 1980s, only declining as the use of analogue telecommunications has declined. Their immediate application was the economically important development of frequency division multiplexing for use on intercity and international lines. Network synthesis filters. The mathematical bases of network synthesis were laid in the 1930s and 1940s. After World War II, network synthesis became the primary tool of filter design. Network synthesis put filter design on a firm mathematical foundation, freeing it from the mathematically sloppy techniques of image design and severing the connection with physical lines. The essence of network synthesis is that it produces a design that will (at least if implemented with ideal components) accurately reproduce the response originally specified in black box terms.
Throughout this article, the letters R, L, and C are used with their usual meanings to represent resistance, inductance, and capacitance, respectively. In particular, they are used in combinations, such as LC, to mean, for instance, a network consisting only of inductors and capacitors. Z is used for electrical impedance, any 2-terminalA terminal of a network is a connection point where current can enter or leave the network from the world outside. This is often called a pole in the literature, especially the more mathematical, but is not to be confused with a pole of the transfer function which is a meaning also used in this article. A 2-terminal network amounts to a single impedance (although it may consist of many elements connected in a complicated set of meshes) and can also be described as a one-port network. For networks of more than two terminals, it is not necessarily possible to identify terminal pairs as ports. combination of RLC elements and in some sections D is used for the rarely seen quantity elastance, which is the inverse of capacitance.
Resonance Early filters utilised the phenomenon of resonance to filter signals. Although electrical resonance had been investigated by researchers from a very early stage, it was at first not widely understood by electrical engineers. Consequently, the much more familiar concept of acoustic resonance (which in turn, can be explained in terms of the even more familiar mechanical resonance) found its way into filter design ahead of electrical resonance. Resonance can be used to achieve a filtering effect because the resonant device will respond to frequencies at, or near, the resonant frequency but will not respond to frequencies far from resonance. Hence, frequencies far from resonance are filtered out from the output of the device.
Electrical resonance
Resonance was noticed early on in experiments with the Leyden jar, invented in 1746. The Leyden jar stores electricity due to its capacitance, and is, in fact, an early form of a capacitor. When a Leyden jar is discharged by allowing a spark to jump between the electrodes, the discharge is oscillatory. This was not suspected until 1826, when Felix Savary in France, and later (1842) Joseph Henry in the US noted that a steel needle placed close to the discharge does not always magnetise in the same direction. They both independently drew the conclusion that there was a transient oscillation dying with time.
Hermann von Helmholtz in 1847 published his important work on conservation of energyHermann von Helmholtz, Uber die Erhaltung der Kraft (On the Conservation of Force), G Reimer, Berlin, 1847 in part of which he used those principles to explain why the oscillation dies away, that it is the resistance of the circuit which dissipates the energy of the oscillation on each successive cycle. Helmholtz also noted that there was evidence of oscillation from the electrolysis experiments of William Hyde Wollaston. Wollaston was attempting to decompose water by electric shock, but found that both hydrogen and oxygen were present at both electrodes. In normal electrolysis, they would separate, one to each electrode.
Helmholtz explained why the oscillation decayed, but he had not explained why it occurred in the first place. This was left to Sir William Thomson (Lord Kelvin), who, in 1853, postulated that there was inductance present in the circuit as well as the capacitance of the jar and the resistance of the load. This established the physical basis for the phenomenon – the energy supplied by the jar was partly dissipated in the load but also partly stored in the magnetic field of the inductor.
So far, the investigation had been on the natural frequency of transient oscillation of a resonant circuit resulting from a sudden stimulus. More important from the point of view of filter theory is the behaviour of a resonant circuit when driven by an external AC signal: there is a sudden peak in the circuit's response when the driving signal frequency is at the resonant frequency of the circuit.The resonant frequency is very close to, but usually not exactly equal to, the natural frequency of oscillation of the circuit James Clerk Maxwell heard of the phenomenon from Sir William Grove in 1868 in connection with experiments on dynamos,William Grove, "An experiment in magneto–electric induction", Philosophical Magazine, vol 35, pp.184–185, March 1868 and was also aware of the earlier work of Henry Wilde in 1866. Maxwell explained resonanceOliver Lodge and some other English scientists tried to keep acoustic and electric terminology separate and promoted the term "syntony". However, it was resonance that was to win the day. mathematically, with a set of differential equations, in much the same terms that an RLC circuit is described today.
Heinrich Hertz (1887) experimentally demonstrated the resonance phenomenaHeinrich Hertz, "Electric waves", p.42, The Macmillan Company, 1893 by building two resonant circuits, one of which was driven by a generator and the other was tunable and only coupled to the first electromagnetically (i.e., no circuit connection). Hertz showed that the response of the second circuit was at a maximum when it was in tune with the first. The diagrams produced by Hertz in this paper were the first published plots of an electrical resonant response.
Acoustic resonance As mentioned earlier, it was acoustic resonance that inspired filtering applications, the first of these being a telegraph system known as the "harmonic telegraph". Versions are due to Elisha Gray, Alexander Graham Bell (1870s), Ernest Mercadier and others. Its purpose was to simultaneously transmit a number of telegraph messages over the same line and represents an early form of frequency division multiplexing (FDM). FDM requires the sending end to transmit at different frequencies for each individual communication channel. This demands individually tuned resonators, as well as filters to separate out the signals at the receiving end. The harmonic telegraph achieved this with electromagnetically driven tuned reeds at the transmitting end, which would vibrate similar reeds at the receiving end. Only the reed with the same resonant frequency as the transmitter would vibrate to any appreciable extent at the receiving end.
Incidentally, the harmonic telegraph directly suggested to Bell the idea of the telephone. The reeds can be viewed as transducers converting sound to and from an electrical signal. It is no great leap from this view of the harmonic telegraph to the idea that speech can be converted to and from an electrical signal.
Early multiplexing