LearnTronics
Math
The mathematics used in electronics
This is not intended to be a complete mathematics course. Its purpose is simpler: to explain the mathematical ideas, symbols, and operations that appear in electronics well enough that they do not become a barrier to understanding the electronics.
Whenever possible, the examples here will connect directly to familiar electrical ideas such as voltage, current, resistance, frequency, phase, charging time, gain, power, and waveforms.
A useful RPN calculator
This is an older Windows RPN (Reverse Polish Notation) calculator from Syntillium Software. It includes scientific, trigonometric, logarithmic, binary/hexadecimal, and other functions useful when working with electronics.
Click the ? twice for instructions on using it. RPN stands for Reverse Polish Notation and is a bit different from most other calculators. As you enter a number, click Enter and it stacks in the display. Hitting another key such as + then performs the operation on the top numbers in the stack.
For example, to add 1 plus 2, type: 1 Enter 2 Enter +
Download RPN Calculator — ZIP file
The ZIP contains the original Windows executable, RPNCALC.EXE. Because this is older software, modern Windows or security software may display a warning before allowing it to run.
Numbers, operations, and notation
- Arithmetic — addition, subtraction, multiplication, division, fractions, decimals, and percentages.
- Powers and roots — squares, square roots, exponents, and why they appear in electrical formulas.
- Scientific notation — a practical way to work with very large and very small quantities.
- Metric prefixes — pico, nano, micro, milli, kilo, mega, and the powers of ten behind them.
- Order of operations — knowing which part of a formula is evaluated first.
Equations and algebra
- Variables — letters used to stand for quantities such as V, I, R, C, L, and f.
- Rearranging formulas — for example, changing V = IR into I = V/R or R = V/I.
- Ratios and proportions — voltage dividers, transformer ratios, gain, and scaling.
- Exponents and logarithms — useful in RC curves, decibels, filters, and frequency calculations.
- Boolean algebra — the special algebra of TRUE/FALSE and 1/0 used by digital logic.
Geometry
- Angles — degrees, turns, and the geometry behind phase.
- Triangles — especially right triangles and the Pythagorean relationship.
- Circles — radius, diameter, circumference, and why a rotating circle helps explain AC.
- Vectors — quantities that have both magnitude and direction, useful when discussing AC voltage and current.
Trigonometry — especially important in AC work
A technician or electrician does not need to become a mathematician to understand sine waves. But it is very useful to understand what sine, cosine, an angle, and a phase angle actually mean.
We will connect a point rotating around a circle with the familiar sine-wave shape. That gives a visual meaning to expressions such as sin(θ), and makes it much easier to understand why two AC waveforms can have the same frequency but still be 30°, 90°, or 180° out of phase.
This section can also connect phase angle to practical subjects such as resistance, capacitance, inductance, impedance, power factor, filters, and oscillators.
Calculus — removing the mystery
Calculus is used much more heavily by engineers than by most electronics technicians, but its notation appears often enough that it is worth knowing what the symbols mean. We do not need to begin with formal proofs.
- Rate of change — a derivative describes how quickly something is changing.
- dV/dt — simply asks how quickly voltage is changing with time.
- dI/dt — asks how quickly current is changing with time.
- The integral sign ∫ — represents adding up many very small contributions.
- Slope and area — visual ideas that make derivatives and integrals much less mysterious.
Possible first Math pages
- Numbers, powers, scientific notation, and metric prefixes
- Reading and rearranging formulas
- Ratios, proportions, and voltage dividers
- Angles, circles, and degrees
- Trigonometry without the mystery
- How a rotating circle becomes a sine wave
- Phase angle — what “90 degrees out of phase” means
- Exponents, logarithms, and decibels
- Calculus notation for electronics technicians
- Boolean algebra as the mathematics of logic