(a) Why do you need to learn the basics of circuit mathematics to study analog circuits?
How to learn circuit mathematics efficiently?
We know that the six basic circuit variables of interest in circuit analysis theory are voltage, current, charge, magnetic chain, work and energy, and the mathematical relationship between these six quantities is
It is easy to see that the relationship between them is described by calculus. Therefore, without calculus, there would be no theory of circuit analysis.
The parametric quantities in a circuit have a common feature: their amplitude not only varies with time, but at the same time the amplitude varies with frequency. We call the former time domain variation and the latter frequency domain variation.
When solving the differential equation, we find it troublesome to solve it directly, but by transforming it into the complex space, the differential equation becomes algebraic form. In this way, the analytical difficulty is greatly reduced. This operation is called Laplace transform. If we want to understand the ins and outs of Laplace transform, we need to learn Fourier series and Fourier transform.
We also have to learn the phase volume analysis of sinusoidal steady-state circuits, which is based on the mathematics of the Functions of Complex Variables, that is, higher mathematics in the complex plane, which is obviously also based on calculus. Also, the decomposition of signals in the time domain, impulsive and convolutional integration are studied, which is also based on calculus.
The mathematical basis of circuit analysis is very broad, such as calculus, Fourier series, Fourier transform, Laplace transform, and convolution.
For interdisciplinary hardware engineers, it is estimated that it is difficult to learn mathematics purely, and more efficient to apply it as a common operation in practical problems. As many people for efficient learning C language, the C language and microcontroller combined together to learn. Similarly, combining the mathematical foundation of circuits with the principles of circuit analysis is an efficient way to learn.
(b) What is the difficulty in learning analog circuits?
What are the methods of analysis of analog circuits?
For hardware circuits, there are two main types of circuits that we are dealing with.
The first is the finite output state type, for this type of circuit, given an input, it will produce an output, but this output is in a relatively rough state.
For example, in a comparator, the output is considered a “0” or “1” as the input voltage goes up or down, and the voltage representing the “0” or “1” varies with the input voltage. The voltage representing “0” or “1” varies with the type of digital circuit, but regardless of the type of digital circuit, the voltage representing “0” or “1” will not be a precise value, but will be a relatively wide range.
Another example is a circuit that uses a transistor as a switch. Given an input voltage, the transistor may turn on or off, and the current flowing through it is usually determined by the external load, not by the input voltage, if the design is correct. For such a circuit, the output is usually obtained with a simple analysis and without many surprises, such as a “0.5” output for a comparator or an amplified state for a transistor.
For this open-loop type of circuit, given the input, the output is one of a limited number of predictable states, and at relatively low frequencies, a simple time-domain analysis based on time-varying waveforms on an oscilloscope is usually sufficient.
The second type of circuit is the continuously varying output type, which can be a complex closed-loop state circuit or a simple RC or RLC circuit. The output is usually required to vary continuously with the input, and is a predictable, stable response that meets certain accuracy requirements. At this point, simple time domain analysis is no longer sufficient to analyze the circuit. We need to enter another perspective to analyze the circuit, that is, the frequency domain. For the vast majority of hardware circuit engineers, there is actually no way to avoid the second type of circuit and unknowingly perform some of the necessary frequency domain analysis.
The second type of circuit is what we often refer to as an analog circuit. For analog circuits, one of the difficulties is to learn and master the complex characteristics of various electronic components, and the other is to learn and master the method of analyzing analog circuits. With these two foundations, it is possible to enter the analog world and design analog circuits, rather than being in a state of fog and ignorance.
The analysis methods involved in analog circuits are supported by a complete set of theoretical foundations: LTI systems, convolution, Fourier transform, Laplace transform, transfer functions, time domain analysis, frequency response, stability analysis, frequency domain compensation, and so on. In this course, we will focus on the analysis of analog circuits, with the aim of mastering the necessary time domain and frequency domain analysis methods. However, it is not only limited to these two clear objectives, but also to tell more contents behind these two analysis methods, so that the students can better understand the circuit they are facing and can go farther in analog circuits.
