# Circuit Idea/Formulas

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Why Formulas Cannot Explain Circuits[nb 1]

A tip: Understand, explain and invent circuits by qualitative means; compute circuits by quantitative means.

{\begin{aligned}\\{\frac {{\frac {R_{G}\cdot R_{F}}{R_{G}+R_{F}}}\cdot \left({\frac {R_{G}\cdot R_{i3}}{R_{G}+R_{i3}}}+R_{F}\right)}{{\frac {R_{G}\cdot R_{i3}}{R_{G}+R_{i3}}}\cdot \left({\frac {R_{G}\cdot R_{F}}{R_{G}+R_{F}}}+R_{i3}\right)}}=-G_{3}\\\\{\frac {{\frac {{\cancel {R_{G}}}\cdot R_{F}}{\cancel {R_{G}+R_{F}}}}\cdot {\frac {\cancel {R_{G}\cdot R_{i3}+R_{G}\cdot R_{F}+R_{F}\cdot R_{i3}}}{\cancel {R_{G}+R_{i3}}}}}{{\frac {{\cancel {R_{G}}}\cdot R_{i3}}{\cancel {R_{G}+R_{i3}}}}\cdot {\frac {\cancel {R_{G}\cdot R_{F}+R_{G}\cdot R_{i3}}}{\cancel {R_{G}+R_{F}}}}}}=-G_{3}\\{}\end{aligned}} What can and what cannot formulas?

## Formulas reign in electronics

Formal approach reigning in technical education and publishing is based on formal analysis of ready-made circuit solutions. If we turn over the pages of classical books on analog electronics, we will find out formulas, definitions and formal analyses. By means of these quantitative means authors try to explain qualitative things. Similarly, if we peek into classrooms, we will see how lecturers juggle skillfully with formal methods trying to explain without success circuit phenomena.

In this story, we will try to find out the answers to the questions, "What can and what cannot formulas do? When do we use them and when not? Where do we place them?" We will illustrate our assertions by some examples written in italic.

## What formulas can do

Math is an excellent tool for analyzing circuits as it

• helps us to define the magnitudes of the component parameters - resistance, capacitance, etc.,
• reveals the relationship between the electrical attributes inside a circuit; thus, it helps us to define the magnitudes of electrical attributes in any circuit point including inputs and outputs,
• enables us to analyze unfamiliar circuits without requiring scrutinizing about circuit operation,
• can present the essential data about circuits in a compact and suitable for manipulation form.

In addition, math gives an excellent opportunity:) for poor university lecturers having no technical sense, abilities and vocation

• to work in technical departments,
• to write excellent (pseudo-)scientific articles, books and dissertations, in order to climb up the ladder (promoting of rank an assistant, associate and full professor),
• to build "brilliant" courses and to carry out "striking" lections where to analyze circuits by applying sophisticated formal methods... without understanding circuit phenomena at all (figuratively speaking, in education formulas serve like wide-spectrum antibiotics in medicine:).

Similarly, math gives a unique chance:) to students that are averse to technics

• to enter technical universities at the expense of those having a technical vocation (e.g., students graduating mathematical, philological, trading and other non-technical schools can enter Technical university of Sofia by solving a few mathematical problems),
• to graduate successfully from universities.
• Math has even changed whole parts of science as mechanics and electricity transmuting them actually into mathematical mechanics and mathematical electricity :) Today, students are compelled rather to solve boring differential equations in classrooms than to carry out interesting and exciting experiments in laboratories.
• Math helps poor scientists to create apparently solid reports on projects that say nothing essential.
• Generally speaking, math has the unique opportunity:) to hide human mediocrity: in technical area, formulas help poor technicians to hide their mediocrity as in medicine, the Latin language help poor physicians to hide their mediocrity. In this way, math gives an opportunity to professionals to easily manipulate ordinary people...

## What formulas cannot do

Math is wonderful; only, it cannot

• tell us how to connect circuit elements (what the circuit structure is),
• show where currents flow through and voltages appear across the circuit elements,
• tell us what points inside circuits are inputs and what - outputs,
• provoke our human imagination and fancy and inspire us to create new circuits,
• show causality between the electrical quantities in the circuit (e.g., it is not clear in Ohm's law what quantity is an input and what quantity is an output, only, we human beings need to know; that is why, in a voltage-to-current converter we suppose that voltage causes current while in a current-to-voltage converter we assume that current causes voltage),
• tell us what actually the circuit idea is.

## Where to place formulas

People do not think in terms of mathematics when understand, explain and invent circuits. So, the place of formulas is at the end of the circuit design after the intuitive explanations. We have first to explain qualitative things by qualitative means; then, to compute quantitative things by quantitative means. We have first to build and reinvent circuits by using human intuition, imagination and emotions; then, to define exactly the circuit parameters and to analyze thoroughly the circuit operation by using formal methods.