Wilhelm Cauer facts for kids
Quick facts for kids
Wilhelm Cauer
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| Born | 24 June 1900 |
| Died | 22 April 1945 (aged 44) Berlin-Marienfelde, Germany
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| Nationality | German |
| Alma mater | Technical University of Berlin |
| Scientific career | |
| Fields | Mathematics |
| Doctoral advisor | Georg Hamel |
| Doctoral students | Vitold Belevitch |
Wilhelm Cauer (born June 24, 1900 – died April 22, 1945) was a German mathematician and scientist. He is best known for his important work on electrical filters. Filters are electronic circuits that separate desired signals from unwanted ones.
Cauer's work started a whole new field called network synthesis. Before him, designing electronic filters was tricky. Engineers often had to guess which parts to use. Cauer changed this by using strong math to create exact ways to design filters. This made filter design much more precise.
Wilhelm Cauer first studied general relativity, a complex physics topic. But he soon switched to electrical engineering. He worked for a German company linked to the Bell Telephone Company. This connected him with top American engineers who worked on filters.
During a tough economic time in Germany in the 1920s, Cauer moved to the United States. There, he learned about early computer techniques. He later returned to Germany. Sadly, the rise of Nazism made his career difficult because he had a distant Jewish ancestor. Cauer was killed by soldiers during the Battle of Berlin at the end of World War II.
Many of Cauer's important writings were lost during the war. But his family managed to put much of his work back together from his notes. A second volume of his main book was published after his death. Today, network synthesis is still the main way to design electronic networks.
Life and Career of Wilhelm Cauer
Early Life and Family Background
Wilhelm Adolf Eduard Cauer was born in Berlin, Germany, on June 24, 1900. He came from a family of many academics and scholars. He went to the Kaiserin Augusta Gymnasium for his early schooling. This school was started by his great-grandfather, Ludwig Cauer.
The school was on Cauerstrasse, a street named after Ludwig. This street is in the Charlottenburg area of Berlin. The school building is still there today, but it is now a primary school. Later, Wilhelm attended the Mommsen Gymnasium in Berlin.
His father, also named Wilhelm Cauer, was a professor of railway engineering. He taught at the Technical University of Berlin. Wilhelm became interested in mathematics when he was just thirteen years old. He continued to show a strong talent for academics as he grew up.
Cauer briefly served in the German army at the very end of World War I. In 1925, he married Karoline Cauer, who was a relative. They eventually had six children together.
Starting His Career in Engineering
Cauer began his career in a field very different from filters. From 1922, he worked with Max von Laue on general relativity. His first published paper in 1923 was about this topic. For reasons that are not fully clear, he then changed his focus to electrical engineering. He earned his degree in applied physics in 1924 from the Technical University of Berlin.
After graduating, he worked for Mix & Genest. This company was a part of the Bell Telephone Company. He used probability theory to study how telephone calls were switched. He also worked on devices called timer relays. During this time, he published two papers related to telecommunications. These papers were about "Telephone switching systems" and "Losses of real inductors."
Connections with Bell Labs Engineers
Mix & Genest's connection with Bell made it easy for Cauer to work with engineers at Bell Labs in the US. This was a huge help when Cauer started studying filter design. Bell Labs was a leader in filter design at that time. Engineers like George Ashley Campbell and Otto Zobel made big contributions there.
Cauer corresponded a lot with Ronald M. Foster. Cauer saw Foster's work as very important. Foster's paper, A reactance theorem, was a major step in filter theory. It inspired Cauer to expand on this idea. This expansion led to what is now known as network synthesis.
In June 1926, Cauer presented his main thesis paper. It was titled The realisation of impedances of specified frequency dependence. He presented it at the Technical University of Berlin. This paper is seen as the beginning of modern network synthesis.
In 1927, Cauer became a research assistant at the University of Göttingen. He worked at Richard Courant's Institute of Mathematics. In 1928, he earned his habilitation, which allowed him to become a university lecturer.
Time in the United States
Cauer found it hard to support his family during the economic crisis of the 1920s. So, in 1930, he took his family to the USA. He had received a scholarship called a Rockefeller fellowship. This allowed him to study at MIT and Harvard University.
In the US, he worked with Vannevar Bush. Bush was building machines to solve math problems. These were early analog computers. Cauer was interested in using them to solve linear systems. This would help him with his filter designs. He finished his work on Filter circuits in 1931 while still in the US.
Cauer met and worked closely with many key researchers in filter design at Bell Labs. These included Hendrik Wade Bode, George Ashley Campbell, Sidney Darlington, Foster, and Otto Zobel.
For a short time, Cauer worked for the Wired Radio Company in Newark, New Jersey. Then he returned to Göttingen. He planned to build a fast analog computer there. However, he could not get the money he needed because of the economic depression.
Challenges in Germany
Cauer seemed to have difficulty getting along with his German colleagues. His letters to them were usually short and formal. They rarely discussed topics in depth. But his letters to his American and European friends were warm and detailed. They often included personal news about his family. This showed a different side of him.
After leaving the Technical Institute for Mix & Genest, Cauer tried to be active in the Verband Deutscher Elektrotechniker (VDE). This was the German Electrical Engineers Society. However, he left the VDE in 1942 after a serious disagreement with Karl Willy Wagner. Wagner had been his PhD supervisor and a supporter.
Life During the Nazi Era
In November 1933, Cauer signed a pledge of loyalty to Adolf Hitler and the Nazi government.
The growing power of Nazism became a big problem for Cauer's work from 1933 onwards. The anti-Jewish feelings at the time forced many professors to leave their jobs. This included the director of the Mathematics Institute, Richard Courant. Even though Cauer was not Jewish, it became known that he had a Jewish ancestor. This ancestor was Daniel Itzig, a banker to Frederick II of Prussia.
This discovery was not enough to remove Cauer from his job under the Nazi race laws. But it stopped his career from moving forward. He earned the title of professor but was never given a full professorship.
By 1935, Cauer had three children. He found it harder and harder to support them. This led him to return to working in industry. In 1936, he worked for the aircraft maker Fieseler in Kassel. Then he became the director of the laboratory at Mix & Genest in Berlin. Despite this, he continued to lecture at the Technical University in Berlin from 1939.
In 1941, the first volume of his main book, Theory of Linear AC Circuits, was published. The original manuscript for the second volume was destroyed during the war. Cauer was able to rewrite this work, but he could not publish it. This second version was also lost during the war. However, after his death, his family arranged for some of his papers to be published as the second volume. This was based on notes about what the second volume was supposed to contain.
Cauer took his children to stay with relatives in Witzenhausen to keep them safe. He knew Berlin was about to fall to the Russians. But Cauer, against advice, went back to Berlin. After the war, his body was found in a mass grave. He had been shot dead in Berlin-Marienfelde by Soviet soldiers. Soviet intelligence was looking for scientists for their own research, and Cauer was on their list. But it seems the soldiers who killed him did not know this.
Wilhelm Cauer's Network Synthesis Work
Cauer's biggest contribution is his work on network synthesis for passive networks. He is seen as the founder of this field. When his main work was published in English in 1958, it was very well received.
Before network synthesis, filters were designed using the image impedance method. This method's predictions were only accurate if parts of the filter matched perfectly. This was hard to do, especially at the ends of the filter. Designers often had to use special end sections based on their experience, not exact calculations.
Network synthesis changed all this. It directly predicted how the filter would work. It also included the connections at the ends in the design process. Cauer saw network synthesis as the opposite of network analysis. Network analysis asks what a given circuit does. Network synthesis asks what circuits can produce a desired result. Cauer solved this by comparing electrical parts to mechanical ones. He then used known physics principles to solve the problem.
Cauer said network synthesis has three main goals:
- First, to figure out if a desired electrical function can actually be built as a circuit.
- Second, to find the simplest forms of these functions and how different forms relate to each other.
- Third, since it's usually impossible to build a perfect filter, to find ways to get as close as possible to the desired performance.
Initially, his work focused on one-port networks. These are circuits with only one pair of connection points.
Making Circuits Realisable
- Building on earlier work, Cauer explained the link between a one-port network's impedance and its function.
- He found the exact conditions needed for a one-port impedance to be built as a real circuit. Later, he expanded this to networks with multiple connection points.
Transforming Circuit Forms
- Cauer discovered that all possible ways to build a circuit for a given impedance could be found from one solution. This was done using a type of mathematical transformation.
- He expanded a common filter design (ladder realization) to include resistors. The original only used reactive components. He also found a link between all networks made of two types of components.
- He identified the simplest forms of filter designs. These include the ladder networks found using a math method called continued fraction expansion.
Approximation Techniques
- Cauer used a math method called Chebyshev approximation to design filters. His use of this method led to filters now called elliptic filters, or sometimes Cauer filters. These filters change from letting signals pass to blocking them very quickly.
- The well-known Chebyshev filters are a simpler type of elliptic filter. They can be designed using the same math. The Butterworth filter (which has a very smooth response) can also be designed this way. However, it was discovered independently by Stephen Butterworth using a different method.
Cauer's early work was sometimes ignored. This was because his simplest circuit forms used ideal transformers. These were not always practical for engineers to build. But soon, people realized that Cauer's approximation method could be used with more practical ladder circuits. This meant ideal transformers were not needed. From then on, network synthesis started to replace older design methods.
Further Research and Discoveries
Most of Cauer's main work is in his first two books. It mostly deals with one-port networks. In his advanced thesis, Cauer started to expand this work. He showed that a single, simple form could not be found for all networks with three types of components (resistors, inductors, and capacitors). This was different from networks with only two types of components.
Cauer also expanded on the work of others regarding symmetric two-port networks. These are networks with two pairs of connection points. He found several simple circuits for these. He also studied antimetric two-ports. He also expanded Foster's reactance theorem to networks with two types of components and multiple connection points in 1931. He showed that all equivalent networks could be created from each other using linear transformations.
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Wilhelm Cauer
