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Corroborating technology with science. This is the basic concept behind science and technology. Instead of stopping at just manufacturing, we develop breakthrough theories that no one else has discovered. This is the true result of scientific and technological research. Needless to say, new theories are not created every day. Researchers need to review existing scientific theories and generalize basic theories found in our current textbooks in order to move on to higher-level concepts. Below, we will have a look at one example of a breakthrough theory that will force textbooks on electronic circuits to be rewritten.

If you open a textbook on electronic circuits for high school or university, you will come across the following equation:

This is a Q factor formula for a series circuit comprising a resistor and a coil shown in Fig. 1. Students generally memorize formulae and how to apply them verbatim. It is important to become familiar with equations such as the one above when you first start your studies, so this technique is somewhat useful. However, once you start to use these equations, you begin to wonder why they are written as they are. There is always some reasoning behind any physical phenomena. Finding out what that is, or “corroborating technology with science” is the true mission of technical universities.

Now, let’s look at Fig. 2. A condenser has been added to the circuit. We have learned that resonance occurs between a coil and a condenser in our last year of high school. The problem to solve here is to “calculate the Q factor in the circuit’s resonance state.” Although the problem itself is quite simple, it actually requires a lot of thought. Textbooks do not readily provide a formula that can be used to solve this problem. So, what are you supposed to do?

In order to solve this problem, you need to take a step back and really think about what a Q factor is. Throwing away our preconceived notions and ignoring general knowledge, we reached the concept of “natural logarithm impedance.” This is expressed as follows:

At first glance, this equation seems mysterious or enigmatic to solve, and is likely to be labeled as unorthodox. Generally speaking, Z is a complex number, and so ζ is also a complex number. By using this ζ, the Q factor in a resonance circuit of any structure can be determined by using the following equation:

Here, ωo represents resonance angular frequency of the circuit, and the two vertical lines represent the absolute value of the complex number. This theoretical expression was used in our IEEE journal and was selected for a Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology. The physical meaning of the logarithm impedance ζ is explained in “What in the world is Q?” (Ohira, 2016).

First, try and calculate the Q factor of the circuit shown in Fig. 1 using the above equation. You will need to derive the complex numbers part way through, and our second-year students learn how to do this. If your answer matches the following textbook equation, you have passed the first stage:

If you were able to calculate this, have a go at the problem in Fig. 2. The answer can be found in “Enigma on resonant quality.” (Ohira, 2017)

This theory applies not only to resonance circuits, but can also be expanded to various functional circuits such as those for filters or oscillators. The discovery of Log Z has given us engineers the ability to derive a Q factor equation under a resonance state from a given circuit diagram with just a pencil and paper.

The discovery of this resonance Q theory will contribute greatly to R&D into revolutionary systems that use the principle of resonance, such as those for telecommunications and wireless power transfer, and the implementation of those research results into society.