Who invented the butterworth filter

Research into filters and how they could be realised and their performance predicted was undertaken in many areas. In one development Stephen Butterworth of the Admiralty Research Laboratory in the undertook the development of a filter that produced a flat response within the pass-band.

Butterworth published a paper on his work in the UK in October The paper was entitled: "On the Theory of Filter Amplifiers" and in it he developed the basic equations for a maximally flat filter for use within RF valve amplifiers.

The article was published in a magazine entitled Experimental Wireless and Wireless Engineer. This title was published in the UK by Iliffe and Sons in the s and early s, later changing its title to:" Wireless Engineer and Experimental Wireless. Apart from the compactness of the system, the filter amplifier has an advantage over orthodox systems in that the effect of the resistance is under complete control so that we may construct filters in which the sensitivity is uniform in the pass region.

At the time, much of this technology was relatively new, and in addition to this, it would be many years before computer technology was available to analyse circuits.

As a result, filter designs tended to exhibit large levels of in-band ripple and this was a problem when people needed flatter responses. Butterworth was the first person to be able to achieve a nearly flat in-band response. In his paper, Butterworth produced equations for two- and four-pole filters. However to minimise the actual loss of the filter, he showed how further sections could interspersed with thermionic valve, vacuum tube amplifiers.

As mentioned above, the key feature of the Butterworth filter is that it has a maximally flat response within the pass-band, i. For higher orders, they are sensitive to quantization errors. For this reason, they are often calculated as cascaded biquad sections and a cascaded first order filter, for odd orders.

Comparison with other linear filters Here is an image showing the gain of a discrete-time Butterworth filter next to other common filters types. All filters are fifth-order. All filters are of the same order, in this case five, which means that all filters roll off by 5 times 20 dB per decade, or dB per decade The Butterworth filter rolls off more slowly around the cutoff frequency than the others, but shows no ripples.

Wikimedia Foundation. Butterworth filter — Batervorto filtras statusas T sritis radioelektronika atitikmenys: angl. Butterworth filter vok. Filter mit Butterworth Verhalten, n rus. Elektrischer… … Deutsch Wikipedia. Filter mit Butterworth-Verhalten — Batervorto filtras statusas T sritis radioelektronika atitikmenys: angl.

Bekannte Anwendungen… … Deutsch Wikipedia. Er bezeichnet ein zeitdiskretes lineares… … Deutsch Wikipedia. Filter-Transformation — Die Filter Transformation dient im Rahmen des Filterentwurfes dazu, elektronische Filter zwischen verschiedenen Filtertypen wie Tiefpassfilter, Hochpassfilter oder Bandpassfilter umzusetzen. Inhaltsverzeichnis 1 Allgemeines 1.

Above the critical frequency the damping is high, and almost independent of the cable losses. The transition at the critical frequency can be very sharp.

The critical frequency itself is determined by the spacing of the coils and corresponds to a wave length equal to twice the distance between them. This effect was used to answer the question of how many coils are to be inserted in a given length of cable, but it was also immediately clear that this effect could be utilized, and Campbell pointed out that he used this effect to eliminate harmonics in signal generators.

In fact he used the cable as a lowpass filter, and he even mentioned the possibility of using the cable as a bandpass filter by replacing the coils by combinations of coils and capacitors. A reel of cable is very large and therefore somewhat unwieldy as a filter, but the next step was so logical that it was undertaken independently in the same year in Germany by Karl Willy Wagner [ 3 ], and in America by Campbell [ 4 ]. The line was simulated by a ladder construction of impedances, an instance of which is shown in Figure 1.

Figure 1: A lowpass electrical wave filter with a signal generator. Karl Willy Wagner George A. These types are shown in Figure 2. The example of Figure 1 consists of two sections of the T-type.

The sections in a wave filter were chosen identically, so that the filter represented a homogeneous line. Usually, for the impedances, reactances were chosen. This could result in highpass, lowpass, bandpass or bandstop filters, or even filters with any number of disjunct passbands. The filters were to be terminated at both sides with their characteristic impedance Z c , as shown in Figure 1. To design these filters, the filter impedances were to be constructed as combinations of inductances and capacitances.

Design methods were developed by several people, under whom Otto J. Zobel has a prominent place, because in he introduced a strategy that allowed the design of filters with an unlimited number of capacitances and inductances [ 5 ]. One of his inventions was the m -type derived filter, which simplified the design of complicated filters, because these could be derived from relatively simple filters.

Figure 3 shows an example Figure 3: An m -type filter that has been derived from the filter of Figure 1. An m -type derived filter has the same passbands and stopbands, and also the same characteristic impedance as the filter it has been derived from. The differences are in the attenuation characteristics.

The transfer function of the filter of Figure 1 , for instance, is zero only at infinite frequency, whereas the transfer of the derived filter is zero at a finite frequency, and is nonzero at infinite frequency. The design theory of this type of filter bore the heritage from the transmission-line theory and was expressed in terms of characteristic impedances that should be matched if stages were cascaded, and wave-propagation constants that were used to describe the attenuation characteristics of the filter.

As a first-order approximation, it was usually assumed that the filter was terminated by its characteristic impedance at all frequencies, which is not practically possible, because the characteristic impedance varies with frequency. In theory, this assumption always gave rise to flat passbands in which--apart from parasitic losses--no damping at all occurred.

Variation of the attenuation in the passbands was regarded as a parasitic effect due to frequency-dependent mismatch. The mismatch was worst near the band limits of the filter, which usually resulted in large transmission peaks at those sites.

It has been described in a comprehensive and clear manner by M. Reed [ 7 ]. This theory was advantageous for designing complicated filters with a large number of sections.

The exact attenuation characteristic of a filter that consisted of a large number of stages, and was terminated in a fixed resistance, was very difficult to determine, and still much more difficult to design.

Therefore one had little control over the transmission characteristics in general and the transfer irregularities near the band limits in particular. This problem was solved by S. Butterworth by splitting the filter in sections of order maximally equal to four, and separating these sections by amplifiers constructed with tubes , so that there was no interaction between the separated parts, and the transfer function of the filter could be well designed [ 8 ].

In this way he was able to construct filters with the famous and well defined maximally-flat transfer functions that were named after him. His work was published in The work of Butterworth is unique in several ways, because he was one of the first to deviate from the image-parameter theory and accurately designed for transfer functions.