Milestone-Proposal:The Discovery of the Principle of Self-Complementarity in Antennas and the Mushiake Relationship, 1948

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Docket #:2016-12

This Proposal has been approved, and is now a Milestone

To the proposer’s knowledge, is this achievement subject to litigation? No

Is the achievement you are proposing more than 25 years old? Yes

Is the achievement you are proposing within IEEE’s designated fields as defined by IEEE Bylaw I-104.11, namely: Engineering, Computer Sciences and Information Technology, Physical Sciences, Biological and Medical Sciences, Mathematics, Technical Communications, Education, Management, and Law and Policy. Yes

Did the achievement provide a meaningful benefit for humanity? Yes

Was it of at least regional importance? Yes

Has an IEEE Organizational Unit agreed to pay for the milestone plaque(s)? Yes

Has an IEEE Organizational Unit agreed to arrange the dedication ceremony? Yes

Has the IEEE Section in which the milestone is located agreed to take responsibility for the plaque after it is dedicated? Yes

Has the owner of the site agreed to have it designated as an IEEE Milestone? Yes

Year or range of years in which the achievement occurred:

The discovery of the Principle of Self-Complementarity in antennas and the Mushiake Relationship was in 1948. Active extensions to the principle continued into the 1970s.

Title of the proposed milestone:

Discovery of the Principle of Self-Complementarity in Antennas and the Mushiake Relationship, 1948

Plaque citation summarizing the achievement and its significance:

In 1948, Prof. Yasuto Mushiake of Tohoku University discovered that antennas with self-complementary geometries are frequency independent, presenting a constant impedance, and often a constant radiation pattern over very wide frequency ranges. This principle is the basis for many very-wide-bandwidth antenna designs, with applications that include television reception, wireless broadband, radio astronomy, and cellular telephony.

In what IEEE section(s) does it reside?

The plaque will be located at Tohoku University. This is in the Sendai Section.

IEEE Organizational Unit(s) which have agreed to sponsor the Milestone:

IEEE Organizational Unit(s) paying for milestone plaque(s):

Unit: IEEE Antennas and Propagation Society
Senior Officer Name: Prof. Michael Jensen

IEEE Organizational Unit(s) arranging the dedication ceremony:

Unit: IEEE Sendai Section
Senior Officer Name: Prof. Masataka Nakazawa

IEEE section(s) monitoring the plaque(s):

IEEE Section: IEEE Sendai Section
IEEE Section Chair name: Prof. Masataka Nakazawa

Milestone proposer(s):

Proposer name: W. Ross Stone, representing IEEE AP-S History Committee
Proposer email: Proposer's email masked to public

Please note: your email address and contact information will be masked on the website for privacy reasons. Only IEEE History Center Staff will be able to view the email address.

Street address(es) and GPS coordinates of the intended milestone plaque site(s):

The location of the plaque will be Tohoku University Archives in the Katahira Campus. The address of the Katahira Campus is 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan and GPS coordinates of Tohoku University Archives are 38.253517, 140.873299

Describe briefly the intended site(s) of the milestone plaque(s). The intended site(s) must have a direct connection with the achievement (e.g. where developed, invented, tested, demonstrated, installed, or operated, etc.). A museum where a device or example of the technology is displayed, or the university where the inventor studied, are not, in themselves, sufficient connection for a milestone plaque.

Please give the address(es) of the plaque site(s) (GPS coordinates if you have them). Also please give the details of the mounting, i.e. on the outside of the building, in the ground floor entrance hall, on a plinth on the grounds, etc. If visitors to the plaque site will need to go through security, or make an appointment, please give the contact information visitors will need. Tohoku University was the location where the research that led to the discovery of the Principle of Self-Complementarity and the Mushiake Relationship was done. The plaque will be located inside the building of Tohoku University Archives. There are many historical materials of Tohoku University including the IEEE Milestone of the Yagi-Uda antenna (1995) in this building.

Are the original buildings extant?

To follow.

Details of the plaque mounting:

The mounting will be on the wall of the Tohoku University Archives.

How is the site protected/secured, and in what ways is it accessible to the public?

The plaque will be protected with other valuable historical materials by the office of Tohoku University Archives. Public visitors can visit Tohoku University Archives during daytime hours on weekdays. Visitors have to show an ID card issued by the office in the building.

Who is the present owner of the site(s)?

Tokohu University.

What is the historical significance of the work (its technological, scientific, or social importance)?

The frequency bandwidth of an antenna is critical to its useful operation. Prior to 1948, almost all antennas were designed based on resonant structures. As such, they operated over relatively narrow bandwidths, often over a range of less than 2:1 in frequency. The pattern, gain, and impedance of the antenna would vary over the operating frequency range. In fact, the operating bandwidth was typically defined in terms of the maximum allowable variation in one of these parameters over the frequency range.

In 1948, Prof. Yasuto Mushiake discovered the Principle of Self-Complementarity in antennas. A self-complementary antenna has a geometry such that its complement (where air is replaced by metal and metal replaced by air) can exactly overlay the original structure through translation and/or rotation. Figures 1-3 show truncated examples of such antennas (in the ideal case, the structures extend to infinity). The Principle of Self-Complementarity states that such self-complementary antennas have a constant impedance independent of frequency. Furthermore, Prof. Mushiake also derived what is referred to as the Mushiake Relationship, which is an expression for the impedance of such an antenna. In the case for such an antennas with two terminals, the Mushiake Relationship takes the form given in Equation (1) of Figure 4, where Z is the impedance of the antenna and Z0 is the impedance of the surrounding medium. If the surrounding medium is free space, then the Mushiake Relationship gives a value of 188.4 ohms as the impedance of the antenna. Media:Figure1.gifMedia:Figure2.gifMedia:Figure3.gifMedia:Figure4.gif

Part of the Principle of Self-Complementarity is that not only the impedance, but in cases where the current decreases rapidly as the distance from the driving point increases, the radiation pattern and gain of such antennas remains constant with frequency. If the structure is truncated so as to be finite (as must obviously be the case in all practical antennas), the upper and lower bounds of the operating frequency bandwidth of the antenna over which these parameters remain essentially constant are respectively determined by the dimensions of the feed region and the overall size of the antenna.

The Principle of Self-Complementarity was originally derived for two-terminal antennas. Prof. Mushiake soon showed that it also applied to multi-terminal antennas, such as that shown in Figure 5. The general Mushiake Relationship for an n-terminal self-complementary antenna excited by n-phase electric sources in a star configuration with mth-order rotation is given by Equation (2) in Figure 4. For the case shown in Figure 5, where n = 4 and the excitations are in phase, the antenna’s impedance is approximately given by the value in Equation (3) of Figure 4, again independently of frequency. Media:Figure5.gif

In subsequent years, the Principle of Self-Complementarity was extended from two-dimensional to three-dimensional antennas (e.g., see Figure 6), and the Mushiake Relationship was similarly extended to such cases. Media:Figure6.gif

The historical significance of this principle and the associated relationship was huge. From the standpoint of antenna design, for the first time there was a whole category of antenna designs that were inherently wideband in nature, and the physics underlying this property was well understood. Furthermore, the most important practical design parameter – the antenna impedance – could be accurately predicted based on simple geometrical knowledge of the antenna. This principle led directly to the invention of the class of antennas called log-periodic antennas, which had high gains and relatively constant radiation patterns and impedances over bandwidths of 10:1 and more. From a societal standpoint, the timing of the discovery of the Principle of Self-Complementarity and the resultant development of log-periodic antennas was tremendously important. This came at the dawn of the development of television broadcasting. The log-periodic antenna was one of the most widely used antennas for home TV reception from the 1950s through widespread use of the delivery of television by cable.

The Principle of Self-Complementarity is finding many new uses in modern antenna design. Ultra-wideband antennas have become tremendously important in several areas of modern telecommunications, particularly as a part of efforts to optimize spectrum usage by spreading signals over very wide ranges of frequencies with very low energy at any one frequency. The 5G wireless communication standards call for ultra-wideband MIMO (multiple-input, multiple-output) antennas, often with omnidirectional patterns. Such antennas are designed using the Principle of Self-Complementarity.

What obstacles (technical, political, geographic) needed to be overcome?

The biggest obstacle that had to be overcome was the concept that an antenna had to be a resonant structure. This concept inherently limited the bandwidth of antennas. Indeed, as described in the history of the development of the Principle of Self-Complementarity given in [1], the Principle of Self-Complementarity originally was discovered as an outgrowth of research into efforts to improve on the performance of the Yagi-Uda antenna, a resonant antenna.

The second major obstacle that had to be overcome was the failure to initially recognize the significance of the new discovery. When the expression for the impedance for an arbitrarily shaped mutually complementary antenna and its slot equivalent was first derived, it unexpectedly was identical in form to the limiting case of a complementary slot (or equivalent wire) antenna [1]. The papers on this new result were therefore rejected on the basis that there was nothing new in them. It was only after Mushiake showed that the expression applied to structures where the shape of the planar conducting sheet for a slot antenna was exactly identical to the shape of its complementary planar antenna. This new structure was a self-complementary antenna, and Mushiake’s result in fact showed that the impedance for such structures was always constant, independent of the source frequency. Furthermore, there is an infinite variety of such shapes. It was only after this was demonstrated that the results were finally accepted for publication and their significance was recognized.


1. Y. Mushiake, “A Report on Japanese Development of Antennas: From the Yagi-Uda Antenna to Self-Complementary Antennas,” IEEE Antennas and Propagation Magazine, 46, 4, August 2004, pp. 47-60.

What features set this work apart from similar achievements?

This work was the first discovery of the frequency-independent properties of self-complementary antennas. Rumsey and Deschamps used this work to develop the class of frequency-independent antennas known as log-periodic antennas. It was subsequently shown that it is the self-complementary aspect of the log-periodic antenna that is primarily responsible for its frequency-independent properties. Two major aspects of the significance of this work and that set it apart are the simplicity and universality of the Principle of Self-Complementarity and the Mushiake Relationship. It is easy to understand and simple to implement. Once a shape has been drawn in two or three dimensions, forming its complement to produce a self-complementary antenna is a simple, straightforward geometric construction. Given the self-complementary shape, the Mushiake Relationship immediately permits the impedance of the antenna to be calculated. Furthermore, because of the Principle of Self-Complementarity, the impedance, pattern, and gain of the antenna are independent of frequency, except for truncation effects.

The significance of this work can also be measured by the honors that have been given to Prof. Mushiake directly in recognition of the importance of the development of the Principle of Self-Complementarity and the Mushiake Relationship. In chronological order, Prof. Mushiake was elected an IEEE Fellow “For contributions to linear antennas and self-complementary antennas” (January 1976). This work was recognized with the Medal of Honor of the IEICE (Japan) in 1982. He received a Commendation for his distinguished achievements from the Minister of Science and Technology, Japan, in 1982. The work received the Medal of Honor with Purple Ribbon from the Emperor of Japan in 1985. (The Medal of Honor with Purple Ribbon is awarded by the Emperor of Japan for academic or artistic developments or accomplishments. As just one example, it is given to those who win medals in the Olympic games.) He received the Second Order of Merit with the Sacred Treasure from the Emperor of Japan in 1991. (The Order of Merit with the Sacred Treasure is awarded in eight classes, with the first being the highest. It is given by the Emperor of Japan for exceptionally distinguished civilian or military service.) His work was recognized with a Commendation from the Minister of Posts and Telecommunication, Japan in 1992, and he was made an Honorary Member of the IEICE, Japan.

Supporting texts and citations to establish the dates, location, and importance of the achievement: Minimum of five (5), but as many as needed to support the milestone, such as patents, contemporary newspaper articles, journal articles, or chapters in scholarly books. 'Scholarly' is defined as peer-reviewed, with references, and published. You must supply the texts or excerpts themselves, not just the references. At least one of the references must be from a scholarly book or journal article. All supporting materials must be in English, or accompanied by an English translation.

The following references have been uploaded as PDFs. The reference number is in square brackets at the front of the file name. If the original reference was in Japanese, the Japanese version has “J” appended to the end of the file name, and the English translation, provided by Prof. Sawaya of Tohoku University, has “E” appended to the end of the file name.

1. Y. Mushiake, “The Input Impedance of a Slit Antenna,” Joint Convention Record of Tohoku Sections of IEE and IECE of Japan, June 1948, pp. 25-26.

2. Y. Mushiake, “The Input Impedances of Slit Antennas,” J. IEE Japan, 69, 3, March 1949, pp. 87-88.

3. S. Uda and Y. Mushiake, “The Input Impedances of Slit Antennas,” Technical Report of Tohoku University, 14, 1, September 1949, pp. 46-59.

4. Y. Mushiake, “Multi-Terminal Constant Impedance Antenna,” 1959 National Convention Record of IECE of Japan, October 1959, p. 89.

5. V. H. Rumsey, “Frequency Independent Antennas,” 1957 IRE National Convention Record, Pt. 1, March 1957, pp. 114-118.

6. G. A. Deschamps, “Impedance Properties of Complementary Multiterminal Planar Structures,” IRE Transactions on Antennas and Propagation, AP-7, (special supplement), December 1959, pp. S371-S378.

7. Y. Mushiake and H. Saito, “Three-Dimensional Self-Complementary Antenna,” Joint Convention Record of Four Japanese Institutes Related to Electrical Engineering, Pt. 15, No. 1212, April 1963.

8. Y. Mushiake, “Constant-Impedance Antennas,” J. IECE Japan, 48, 4, April 1965, pp. 580-584.

9. Y. Mushiake, “A Report on Japanese Development of Antennas: From the Yagi-Uda Antenna to Self-Complementary Antennas,” IEEE Antennas and Propagation Magazine, 46, 4, August 2004, pp. 47-60.

Supporting materials (supported formats: GIF, JPEG, PNG, PDF, DOC): All supporting materials must be in English, or if not in English, accompanied by an English translation. You must supply the texts or excerpts themselves, not just the references. For documents that are copyright-encumbered, or which you do not have rights to post, email the documents themselves to Please see the Milestone Program Guidelines for more information.

Media:Figure1.gif Media:Figure2.gif Media:Figure3.gif Media:Figure4.gif Media:Figure5.gif Media:Figure6.gif Media:Ref1_Mushiake_1948E.PDF Media:Ref1_Mushiake_1948J.PDF Media:Ref2_Mushiake_IEEJ_1949E.PDF Media:Ref2_Mushiake_IEEJ_1949J.PDF Media:Ref3_Uda_Mushiake_1949.pdf Media:Ref4_Mushiake_1959E.PDF Media:Ref4_Mushiake_1959J.PDF Media:Ref5_01150565.pdf Media:Ref6_01144717.pdf Media:Ref7_Mushiake_Saito_1963E.PDF Media:Ref7_Mushiake_Saito_1963J.pdf Media:Ref8_Mushiake_1965E.PDF Media:Ref8_Mushiake_1965J.pdf Media:Ref9.pdf Media:Reference13.pdf

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