Otto Julius Zobel (October 20, 1887 – January 1970) was an electrical engineer who worked for the
American Telephone & Telegraph Company (AT&T) in the early part of the 20th century. Zobel's work on filter design was revolutionary and led, in conjunction with the work of
John R. Carson, to significant commercial advances for AT&T in the field of
frequency-division multiplex (FDM) telephone transmissions.
[Bray, p. 62.]
Although much of Zobel's work has been superseded by more modern filter designs, it remains the basis of filter theory and his papers are still referenced today. Zobel invented the
m-derived filter
m-derived filters or m-type filters are a type of electronic filter designed using the image method. They were invented by Otto Zobel in the early 1920s. This filter type was originally intended for use with telephone multiplexing and was a ...
[White, G]
"The Past"
''BT Technology Journal'', Vol 18, No 1, pp. 107–132, January 2000 .
and the
constant-resistance filter,
[Zobel, O J, ''Distortion Compensator'', , filed 26 June 1924, issued 12 Feb 1929.] which remains in use.
Zobel and Carson helped to establish the nature of noise in electric circuits, concluding that—contrary to mainstream belief—it is not even theoretically possible to filter out noise entirely and that noise will always be a limiting factor in what is possible to transmit.
Thus, they anticipated the later work of
Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory".
As a 21-year-old master's degree student at the Massachusetts Inst ...
, who showed how the theoretical information rate of a channel is related to the noise of the channel.
Life
Otto Julius Zobel was born on October 20, 1887, in
Ripon, Wisconsin.
[Dr. Otto Zobel]
, ''Oshkosh Daily Northwestern'', January 12, 1970, p. 21 (via Newspapers.com
Ancestry.com LLC is an American genealogy company based in Lehi, Utah. The largest for-profit genealogy company in the world, it operates a network of genealogical, historical records, and related genetic genealogy websites.
In November 2018, ...
, retrieved 23 November 2016. He was the son of Oscar Ewald "Herman" Zobel, who had emigrated to the United States from his native Germany in 1860, and his wife Ernestine, ''née'' Kahl.
["Dr Otto J. Zobel", '' Fond du Lac (Wisconsin) Commonwealth Reporter'', 12 January 1970, p. 26.]["Zobel Baby Quilt: Quilt Index Record: 15-11-1340"](_blank)
'' Quilt Index'' ( Michigan State University). Retrieved 31 January 2022. Zobel had seven siblings.
After attending
Ripon High School,
he first studied at
Ripon College, where he received his BA in 1909
with a thesis on ''Theoretical and experimental treatment of electrical condensers''. He later received a Distinguished Alumnus Award from Ripon. He then went to the University of Wisconsin and graduated with an MA in physics in 1910. Zobel stayed at the University of Wisconsin as a physics instructor from 1910 to 1915, and graduated with his PhD in 1914;
his dissertation concerned "Thermal Conduction and Radiation".
[American Association for the Advancement of Science,]
Doctorates Conferred by American Universities
, August 1914, ''Science'', vol. 40, no. 1025. , pp. 256–264. This followed his 1913 co-authoring of a book on the subject of
geophysical
Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' some ...
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of th ...
.
[Leonard ''et al.'', ''passim''] From 1915 to 1916 he taught physics at the University of Minnesota.
Having moved to
Maplewood, New Jersey, he joined AT&T in 1916, where he worked on transmission techniques. In 1926, still with the company, he moved to New York and in 1934, he transferred to Bell Telephone Laboratories (
Bell Labs
Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984),
then AT&T Bell Laboratories (1984–1996)
and Bell Labs Innovations (1996–2007),
is an American industrial Research and development, research and scientific developm ...
), the research organisation created jointly by AT&T and
Western Electric a few years earlier. He retired from Bell Telephone in 1952.
The last of Zobel's prolific list of patents
[Zobel, O J, ''Impedance Transformer'', , filed 30 Sept 1952, issued 16 Oct 1956.][Zobel, O J, ''Microwave Filter'', , filed 20 April 1950, issued 23 Dec 1952.] occurred for Bell Labs in the 1950s, by which time he was residing in
Morristown, New Jersey. He was a fellow of the
American Physical Society and of the
Acoustical Society of America
The Acoustical Society of America (ASA) is an international scientific society founded in 1929 dedicated to generating, disseminating and promoting the knowledge of acoustics and its practical applications. The Society is primarily a voluntary org ...
.
He died in Morristown of a heart attack in January 1970.
He had married Irene Staab on 28 May 1949; she was still living when he died but a son predeceased him.
Thermal conduction
![DSCN1739-thomson-tide-machine](https://upload.wikimedia.org/wikipedia/commons/d/d7/DSCN1739-thomson-tide-machine.jpg)
Zobel's early work on heat conduction
was not pursued in his later career. There are, however, some interesting connections.
Lord Kelvin
William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy at the University of Glasgow for 53 years, he did important ...
in his early work on the transmission line derived the properties of the electric line by analogy with heat conduction. This is based on
Fourier's law
Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its ''thermal conductivity'', and is denoted .
Heat spontaneously flows along a te ...
and the
Fourier conduction equation. Ingersoll and Zobel describe the work of Kelvin and Fourier in their book and Kelvin's approach to the representation of
transmission functions would consequently have been very familiar to Zobel. It is therefore no surprise that in Zobel's paper on the electric wave filter a very similar representation is found for the transmission function of filters.
Solutions to the Fourier equation can be provided by
Fourier series. Ingersoll and Zobel state that in many cases the calculation involved makes the solution "well-nigh impossible" by analytical means. With modern technology such a calculation is trivially easy, but Ingersoll and Zobel recommend the use of harmonic analysers, which are the mechanical counterpart of today's
spectrum analysers. These machines add together mechanical oscillations of various frequencies, phases and amplitudes by combining them through a set of pulleys or springs: one for each oscillator. The reverse process is also possible, driving the machine with the function and measuring the Fourier components as output.
Background to AT&T research
After the work of
John R. Carson in 1915 it became clear that
multiplexed
In telecommunications and computer networking, multiplexing (sometimes contracted to muxing) is a method by which multiple analog or digital signals are combined into one signal over a shared medium. The aim is to share a scarce resource - a ...
telephone transmissions could be greatly improved by the use of
single sideband
In radio communications, single-sideband modulation (SSB) or single-sideband suppressed-carrier modulation (SSB-SC) is a type of modulation used to transmit information, such as an audio signal, by radio waves. A refinement of amplitude m ...
suppressed carrier (SSB) transmission. Compared to basic
amplitude modulation (AM) SSB has the advantage of half the
bandwidth
Bandwidth commonly refers to:
* Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range
* Bandwidth (computing), the rate of data transfer, bit rate or thr ...
and a fraction of the power (one sideband can have no more than 1/6 of the total power and would typically be a lot less). AM analysed in the
frequency domain
In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a s ...
consists of a
carrier and two
sidebands. The
carrier wave
In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has ...
in AM represents the majority of the transmitted power but contains no information whatsoever. The two sidebands both contain identical information so only one is required, at least from an information transmission point of view. Up to this point filtering had been by simple
tuned circuit
An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can a ...
s. However, SSB required a flat response over the sideband of interest and maximum
rejection of the other sideband with a very sharp transition between the two. As the idea was to put another (completely different) signal in the slot vacated by the unwanted sideband it was important that all traces of it were removed to prevent
crosstalk. At the same time minimum distortion (i.e. flat response) is obviously desirable for the sideband being retained. This requirement led to a big research effort in the design of electric wave filters.
George A. Campbell and Zobel worked on this problem of extracting a single sideband from an amplitude-modulated composite wave for use in
multiplexing telephone channels and the related problem of extracting (de-multiplexing) the signal at the far end of the transmission.
Initially, the baseband
In telecommunications and signal processing, baseband is the range of frequencies occupied by a signal that has not been modulated to higher frequencies. Baseband signals typically originate from transducers, converting some other variable int ...
pass range used was 200 Hz to 2500 Hz but later the International Telecommunication Union
The International Telecommunication Union is a specialized agency of the United Nations responsible for many matters related to information and communication technologies. It was established on 17 May 1865 as the International Telegraph Unio ...
set a standard of 300 Hz to 3.4 kHz with 4 kHz spacing. Thus the filtering was required to go from fully pass to fully stop in the space of 900 Hz. This standard in telephony is still in use today and had remained widespread until it began to be supplanted by digital techniques from the 1980s onwards.
Campbell had previously utilised the condition discovered in the work of Oliver Heaviside
Oliver Heaviside FRS (; 18 May 1850 – 3 February 1925) was an English self-taught mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed ...
for lossless transmission to improve the frequency response of transmission lines using lumped component
The lumped-element model (also called lumped-parameter model, or lumped-component model) simplifies the description of the behaviour of spatially distributed physical systems, such as electrical circuits, into a topology consisting of discrete e ...
inductors ( loading coils). When Campbell started investigating electric wave filter design from 1910, this previous work naturally led him to filters using ladder network
Electronic filter topology defines electronic filter circuits without taking note of the values of the components used but only the manner in which those components are connected.
Filter design characterises filter circuits primarily by their ...
topology using capacitors and inductors. Low-pass
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filte ...
, high-pass
A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency d ...
and band-pass
A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range.
Description
In electronics and signal processing, a filter is usually a two-po ...
filters were designed. Sharper cut-offs and higher stopband rejection to any arbitrary design specification could be achieved merely by increasing the length of the ladder. The filter designs used by Campbell were described by Zobel as constant k filters
Constant k filters, also k-type filters, are a type of electronic filter designed using the image method. They are the original and simplest filters produced by this methodology and consist of a ladder network of identical sections of passive c ...
although this was not a term used by Campbell himself.
Innovations
After Zobel arrived at the Engineering Department of AT&T he used his mathematical skills to further improve the design of electric wave filters. Carson and Zobel developed the mathematical method of analyzing the behavior of filters now known as the image method whereby the impedance and transmission parameters of each section are calculated as if it is part of an infinite chain of identical sections.
Wave filters
Zobel invented the m-derived (or m-type) filter section in 1920, the distinguishing feature of this design being a pole
Pole may refer to:
Astronomy
*Celestial pole, the projection of the planet Earth's axis of rotation onto the celestial sphere; also applies to the axis of rotation of other planets
*Pole star, a visible star that is approximately aligned with the ...
of attenuation close to the filter cut-off frequency
In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced ( attenuated or reflected) rather than ...
. The result of this design is a filter response which falls very rapidly past the cut-off frequency. A fast transition between passband
A passband is the range of frequencies or wavelengths that can pass through a filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all the radio waves picked up by its antenn ...
and stopband was one of the primary requirements for cramming as many telephone channels as possible into one cable.
One disadvantage of the m-type section was that at frequencies past the pole of attenuation, the response of the filter started to increase again, reaching a peak somewhere in the stopband and then falling again. Zobel overcame this problem by designing hybrid filters using a mixture of constant k and m-type sections. This gave Zobel the advantages of both: the fast transition of the m-type and good stopband rejection of the constant k.
By 1921 Zobel had further perfected his composite filter designs. He was now using, in addition, m-type half sections at the ends of his composite filters to improve the impedance matching of the filter to the source and the load, a technique in which he held a patent.[Zobel, O J, ''Terminating network for filters'', , filed 30 April 1920, issued 13 Oct 1925.] The difficulty that he was trying to overcome was that the image impedance Image impedance is a concept used in electronic network design and analysis and most especially in filter design. The term ''image impedance'' applies to the impedance seen looking into a Port (circuit theory), port of a network. Usually a two-port ...
techniques being used to design filter sections only gave the mathematically predicted response if they were terminated in their respective image impedances. Technically, this was easy to do within the filter as it could always be arranged that adjacent filter sections had matching image impedances (one of the characteristics of m-type sections is that one side or the other of the m-type section will have an image impedance identical to the equivalent constant k section). However, the terminating impedances are a different story. These are normally required to be resistive but the image impedance will be complex. Even worse, it is not even mathematically possible to construct a filter image impedance out of discrete components. The result of impedance mismatch is reflections and a degraded filter performance. Zobel found that a value of for the end half sections, while not mathematically exact, gave a good match to resistive terminations in the passband.[
Around 1923, Zobel's filter designs were reaching the peak of their complexity. He now had a filter section to which he had doubly applied the m-derivation process resulting in filter sections which he called the mm'-type. This had all the advantages of the previous m-type, but more so. An even faster transition into the stopband and an even more constant characteristic impedance in the passband. At the same time one side would match into the old m-type, just as the m-type could match into the k-type. Because there were now two arbitrary parameters (m and m') that the filter designer could adjust, much better end matching half-sections could be designed. A composite filter using these sections would have been the very best that could have been achieved at that time. However, the mm'-type sections never became as widespread and well known as the m-type sections, possibly because their greater complexity has deterred designers. They would have been inconvenient to implement with microwave technology and the increased count of components, especially wound components, made them more expensive to implement with conventional LC technology. Certainly, it is hard to find a textbook from any period which covers their design.][Zobel, O J, ''Electrical Wave Filter'', , filed 25 Nov 1930, issued 22 March 1932.]
Transmission line simulation
Zobel directed much of his effort in the 1920s to constructing networks which could simulate transmission lines. These networks were derived from filter sections, which themselves had been derived from transmission line theory and the filters were used on transmission line signals. In turn, these artificial lines were used to develop and test better filter sections.
Zobel used a design technique based on his theoretical discovery that the impedance looking into the end of a filter chain was practically the same (within the limits of component tolerances) as the theoretical impedance of an infinite chain after only a small number of sections had been added to the chain. These "image" impedances have a mathematical characterization impossible to construct simply out of discrete components, and can only ever be approximated. Zobel found that using these impedances constructed out of small filter chains as components in a greater network allowed him to build realistic line simulators. These were not in any sense intended as practical filters in the field, but rather the intention was to construct good controllable line simulators without having the inconvenience of miles of cable to contend with.
Equalisers
Zobel invented several filters whose defining characteristic was a constant resistance as the input impedance. The resistance remained constant through the passband and the stopband. With these designs Zobel had completely solved the impedance matching problem. The main application of these sections has been not so much for filtering out unwanted frequencies (the k-type and m-type filters remained best for this) but rather to equalize the response in the passband to a flat response.
Perhaps one of Zobel's most fascinating inventions is the lattice filter section. This section is both constant resistance and flat response zero attenuation across the band, yet it is constructed out of inductors and capacitors. The only signal parameter it modifies is the phase of the signal at different frequencies.
Impedance matching
A common theme throughout Zobel's work is the issue of impedance matching. The obvious approach to filter design is to design directly for the attenuation characteristics desired. With modern computing power, a brute force approach is possible and easy—that is, simply incrementally adjusting each component while recalculating in an iterative process until the desired response is achieved. However, Zobel developed a more indirect line of attack. He realized very early on that mismatched impedances inevitably meant reflections, and reflections meant a loss of signal. Improving the impedance match, conversely, would automatically improve a filter's passband response.
This impedance matching approach not only led to better filters but the techniques developed could be used to construct circuits whose sole purpose was to match together two disparate impedances.[Zobel, O J, ''Electrical Wave Filter'', , filed 9 June 1923, issued 25 Jan 1927.] Zobel continued to invent impedance matching networks throughout his career. During World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposi ...
he moved on to waveguide filter
A waveguide filter is an electronic filter constructed with waveguide (electromagnetism), waveguide technology. Waveguides are hollow metal conduits inside which an electromagnetic wave may be transmitted. Filters are devices used to allow sign ...
s for use in the newly developed radar
Radar is a detection system that uses radio waves to determine the distance ('' ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, we ...
technology. Little was published during the war for obvious reasons but towards the end with Bell Labs in the 1950s, Zobel designs for sections to match physically different waveguide sizes appear. However, the circuit noted above which still bears Zobel's name today, the constant-resistance network, can be viewed as an impedance matching circuit and remains Zobel's finest achievement in this regard.
Loudspeaker equalisation
The name of Zobel is, perhaps, most well known with regard to impedance compensation networks for loudspeakers and his designs have applications in this field. However, none of Zobel's patents or articles appear to discuss this topic. It is unclear whether he actually designed anything specifically for loudspeakers. The closest we get to this is where he speaks of impedance matching into a transducer, but here he is discussing a circuit to equalize a submarine cable, or in another instance where clearly he has in mind the hybrid transformer which terminates a line going into a telephone instrument on a phantom circuit In telecommunication and electrical engineering, a phantom circuit is an electrical circuit derived from suitably arranged wires with one or more conductive paths being a circuit in itself and at the same time acting as one conductor of another circ ...
.
Noise
While Carson led the way theoretically, Zobel was involved in the design of filters for the purpose of noise reduction on transmission systems.
Background
At the beginning of the 1920s and through to the 1930s, the thinking on noise was dominated by the radio engineers' concern with external static
Static may refer to:
Places
*Static Nunatak, a nunatak in Antarctica
United States
* Static, Kentucky and Tennessee
*Static Peak, a mountain in Wyoming
**Static Peak Divide, a mountain pass near the peak
Science and technology Physics
*Static el ...
. In modern terminology, this would include random (thermal
A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...
and shot
Shot may refer to:
Arts, entertainment, and media
* ''Shot'' (album), by The Jesus Lizard
*''Shot, Illusion, New God'', an EP by Gruntruck
*'' Shot Rev 2.0'', a video album by The Sisters of Mercy
* "Shot" (song), by The Rasmus
* ''Shot'' (2017 f ...
) noise but those concepts were relatively unknown and little understood at the time despite an early paper by Schottky in 1918 on shot noise. To the radio engineers of the time, static meant externally generated interference. The line of attack against noise from the radio engineers included developing directional antennae and moving to higher frequencies where the problem was known not to be so severe.
For telephone engineers, what was then called "fluctuating noise", and would now be described as random noise, i.e. shot and thermal noise, was much more noticeable than with early radio systems. Carson broadened the radio engineers' concept of signal-to-static ratio to a more general signal-to-noise ratio and introduced a figure of merit for noise.
Impossibility of noise cancellation
The radio engineers' preoccupation with static and the techniques being used to reduce it led to the idea that noise could be totally eliminated by, in some way, compensating for it or canceling it out. The culmination of this viewpoint was expressed in a 1928 paper by Edwin Armstrong. This led to a famous retort by Carson in a subsequent paper, "Noise, like the poor, will always be with us". Armstrong was technically in the wrong in this exchange, but in 1933, ironically and paradoxically, went on to invent wideband FM, which enormously improved the noise performance of radio by ''increasing'' the bandwidth.
Carson and Zobel in 1923 had conclusively shown that filtering cannot remove noise to the same degree as, say, interference from another station could be removed. To do this they had analyzed random noise in the frequency domain and postulated that it contains all frequencies in its spectrum. This was the first use of Fourier analysis to describe random noise and hence described it in terms of a spread of frequencies. Also first published in this paper was the concept of what we would now call band-limited white noise. For Zobel this meant that characteristics of the receiving filter completely determine the figure of merit in the presence of white noise and that the filter design was key to achieving the optimum noise performance.[Carson, J R and Zobel, O J, "Transient Oscillation in Electric Wave Filters", ''Bell System Technical Journal'', vol. 2, July 1923, pp. 1–29.]
Although this work by Carson and Zobel was very early, it was not universally accepted that noise could be analyzed in the frequency domain in this way. For this reason, the aforementioned exchange between Carson and Armstrong was still possible years later. The precise mathematical relationship between noise power and bandwidth for random noise was finally determined by Harry Nyquist
Harry Nyquist (, ; February 7, 1889 – April 4, 1976) was a Swedish-American physicist and electronic engineer who made important contributions to communication theory.
Personal life
Nyquist was born in the village Nilsby of the parish Stora Ki ...
in 1928 thus giving a theoretical limit to what could be achieved by filtering.
This work on noise produced the concept, and led Zobel to pursue the design, of matched filters. In this context "matched" means that the filter is chosen to match the signal's characteristics in order to admit all of the available signal without admitting any noise that could have been excluded. The underlying insight is that admitting as much signal as is available without admitting any noise that could be excluded will maximize the signal-to-noise ratio, which in turn optimizes the noise performance of the equipment. This conclusion was the culmination of theoretical research into removing noise by the application of linear filters
Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in which case they can be analyzed exactly using ...
. This became important in the development of radar during World War II, in which Zobel played a part.
Use of work in genetic programming research
Zobel's work has recently found an application in research into genetic programming
In artificial intelligence, genetic programming (GP) is a technique of evolving programs, starting from a population of unfit (usually random) programs, fit for a particular task by applying operations analogous to natural genetic processes to t ...
. The purpose of this research is to attempt to demonstrate that the results obtained from genetic programming are comparable to human achievements. Two of the measures that are used to determine whether a genetic programming result is human-competitive are:
* The result is a patented invention.
* The result is equal to or better than a result that was considered an achievement in its field at the time of discovery.
One such problem set as a task for a genetic program was to design a crossover filter
Audio crossovers are a type of electronic filter circuitry that splits an audio signal into two or more frequency ranges, so that the signals can be sent to loudspeaker drivers that are designed to operate within different frequency ranges. Th ...
for woofer
A woofer or bass speaker is a technical term for a loudspeaker driver designed to produce low frequency sounds, typically from 50 Hz up to 1000 Hz. The name is from the onomatopoeic English word for a dog's bark, " woof" (in contrast to th ...
and tweeter
A tweeter or treble speaker is a special type of loudspeaker (usually dome, inverse dome or horn-type) that is designed to produce high audio frequencies, typically deliver high frequencies up to 100 kHz. The name is derived from the high ...
loudspeakers. The output design was identical in topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
to a design found in a patent of Zobel's for a filter to separate multiplexed low and high frequencies on a transmission line. This was judged to be human-comparable, not only because of the patent, but also because the high-pass and low-pass sections were " decomposed" as in Zobel's design, but not specifically required to be so in the programs parameters. Whether or not Zobel's filter design would be good for a hi-fi system is another question. The design does not actually cross over, but rather, there is a gap between the two passbands where the signal is not transmitted to either output. Essential for multiplexing, but not so desirable for sound reproduction.
A later genetic programming[Chakrabarti, A]
''Engineering Design Synthesis: Understanding, Approaches, and Tools''
p. 328, Springer, 2002. experiment produced a filter design which consisted of a chain of constant k sections terminated in an m-type half section. This was also determined to have been a design patented by Zobel.
References
Sources
* Bray, J, ''Innovation and the Communications Revolution'', Institution of Electrical Engineers
The Institution of Electrical Engineers (IEE) was a British professional organisation of electronics, electrical, manufacturing, and Information Technology professionals, especially electrical engineers. It began in 1871 as the Society of T ...
, 2002 .
*Leonard, R, Zobel, O J, Ingersoll, A C
''An Introduction to the Mathematical Theory of Heat Conduction with Engineering and Geological Applications''
1913, Ginn and Co, Boston, New York.
*Matthaei, G L; Young, L; Jones, E M T, ''Microwave Filters, Impedance-Matching Networks, and Coupling Structures'' McGraw-Hill 1964 (1980 edition is ).
*Schwartz, M,
Improving the Noise Performance of Communication Systems: 1920s to early 1930s
, ''Technologies, Technologists & Networks: A Symposium on the History of Communication Technologies'', October 17, 2007, Smithsonian National Postal Museum.
*Zobel, O J, ''Theory and Design of Uniform and Composite Electric Wave Filters'', Bell System Technical Journal, Vol. 2 (1923), pp. 1–46.
{{DEFAULTSORT:Zobel, Otto Julius
1887 births
1970 deaths
American electronics engineers
Engineers from Wisconsin
People from Ripon, Wisconsin
People from Morristown, New Jersey
Radio pioneers
Ripon College (Wisconsin) alumni
Scientists at Bell Labs
University of Minnesota faculty
University of Wisconsin–Madison College of Letters and Science alumni
Engineers from New Jersey
20th-century American inventors
Fellows of the American Physical Society