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:''This article is about the history and development of passive linear analogue filters used in electronics. For linear filters in general see Linear filter. For electronic filters in general see Electronic filter.'' Analogue filters are 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 telephony lines. #Network synthesis filters. The mathematical bases of network synthesis were laid in the 1930s and 1940s. After the end of 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-terminal〔A 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Analogue filter」の詳細全文を読む スポンサード リンク
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