[PYTHON] I read "Basics of Electric Circuits and Transmission Lines"

A relatively new book published in 2017. I started reading to learn transmission lines. It has a relatively high degree of abstraction in electrical engineering books, and you can learn the basics of principles with a simple model. In this book, differential equations are theoretically set up according to the problem to be solved, but the solution is basically numerical calculation using a computer, and technical mathematics does not appear. Instead, it assumes basic Python knowledge. It's a modern approach and I think it makes sense. The first half deals with lumped constant circuits, and the second half deals with transmission line theory. The feature is that the transmission line theory is derived from Maxwell's equations. Many other books seem to be derived from the phenomenological assumption of Heaviside's distributed constant circuit. As a physics graduate, it is easier to understand how to derive from the more principle Maxwell's equations. However, it is unclear whether the modeling in this book is correct, as will be described later.

The overall idea is very good, but this book is too rough and error-prone to be read by beginners like myself. At the moment this is not a good book. I hope it will improve in future revisions.

Lumped circuit

The beginning is an explanation of basic mathematics and resistors, capacitors, and inductors, which are the basic elements of lumped constant circuits. It is simply introduced as a mathematical constant.

Then, the concept of nodes for making circuits and the concept of electric potential and element voltage were introduced. These are also well defined without ambiguity. Then, from the introduction of Kirchhoff's current law and voltage law, I explained the number of differential equations necessary and sufficient to solve the problem. It is clearly stated with references that it is derived from graph theory, although there is no proof. I'm glad that there is support for such a basic theory.

After that, a slightly more advanced concept for dealing with mutual inductors and subordinate power supplies, that is, transistors and operational amplifiers, appeared. However, this is just an introduction as an abstract concept, and does not specifically deal with realistic parts. I think the unification of this stance is good.

In a lumped constant circuit consisting of linear elements, the problem to be solved is an ordinary differential equation. And it can be solved almost analytically when the signal to be handled is an AC steady state with a constant frequency or a transient response. Learn it with a simple example.

If you read it as it is, you can naturally understand that in the case of AC steady state, signals and elements can be simply expressed by phasor display expressed by complex numbers. And from the superposition principle, Thevenin's theorem, and Norton's theorem, we can see that every circuit can be easily solved by a mechanical method.

Next, in order to solve it more mechanically, the circuit itself is represented by a matrix, and in general, all circuit problems can be solved numerically. Not only the AC steady state that can be handled by the phasor display, but also the transient response can be dealt with by numerically solving the differential equation by the difference method. In other words, you can get enough knowledge to make a circuit simulator like SPICE that can solve any circuit.

This is the first half of the lumped constant circuit. The second half is transmission line theory.

Transmission line theory

The transmission line theory in this book begins with Maxwell's equations. From the explanation of Maxwell's equations and simple vector analysis, we introduced scalar potential and vector potential, and explained gauge invariance and Lorentz condition. Derive the wave equation and understand that electromagnetic waves travel through the transmission line at the speed of light. Then, the integral Coulomb's law and Ampere's law are derived from Maxell's equation, which is the basis of transmission line theory.

But this argument really remains questionable. This is because these are the laws for electrostatic and static magnetic fields.

Next, consider a simple electric wire model in which electric charges are distributed on the wire, and think that current is generated by their movement. The electric charge is considered to generate an electric field in the radial direction, and the current is considered to generate a magnetic field in the rotation direction around the electric wire. Since it can be considered that the charge transfer speed is sufficiently slow in this model, it seems that Coulomb's law and Ampere's law are applied.

However, this model is different from the actual one in the first place. In the actual electric wire, a charged object is not moving. However, this model can also create a situation where the same current is flowing as a result, so the conclusion may be the same. There is no explanation in this book about that.

Anyway, the transmission line equation from this model The conclusion can be obtained. It seems that the same conclusion can be obtained from the approximation of Heaviside's distributed constant circuit, and the same conclusion can be obtained with a physically correct model. I have no choice but to confirm this in other books in the future, and I do not know exactly at present. Believe in the conclusion and move on.

In this book, the transmission line equation is solved numerically. It is a method that simply applies the difference method to each of the time domain and the one-dimensional spatial domain and calculates sequentially, and it seems to be called the FDTD method. The boundary of the transmission line is solved at the same time by connecting the above-mentioned numerical calculation method of the lumped constant circuit as it is. This makes it easy to simulate a transmission line.

For example, watch the change in voltage when sending a DC voltage of 30V with a 400m electric wire in slow motion. Reflection occurs due to impedance mismatch at the end. Over time, the whole gradually stabilizes at 30V. Really funny. https://twitter.com/Tw_Mhage/status/1323552833879207936

Even with a simple RC circuit, if the line length is longer than the wavelength, ringing will occur due to multiple reflection of signals. This is a phenomenon that cannot occur in a lumped constant circuit that ignores the line length.

It is interesting that these things can be confirmed immediately by simulation.

Finally, there is an explanation about common mode noise. In other words, in addition to the transmission line intentionally made of electric wires, current flows to the surrounding environment, so even if impedance matching is performed on the designed transmission line, it cannot absorb everything and the current through the environment will flow. The problem is that noise remains due to multiple reflections. This can also be realized by a simple simulation.

Advantages and disadvantages of this book

The advantage of this book is the simplicity of the story, which extracts only the essence of physical phenomena. It's a bit abstract because it's simple, but it's easy to understand for anyone learning physics or mathematics. And it is also good that the results are obtained by numerical calculation without touching on technical mathematics. It is easy to grasp the physical image without being bothered by the calculation method. These are really great points.

However, the disadvantage that more than compensates for it is the number of mistakes in this book. Clerical errors, calculation errors, text and logic errors, and chart errors are everywhere. Also, the answers to the exercises are on the Web, but this is full of mistakes in the text. If you think about it to some extent, you can notice the mistake, but a beginner who learns for the first time in this book like yourself takes a lot of time to decipher. It's a shame.