BASIC ELECTRICAL and ELECTRONICS ENGINEERING FORMULAS



EE REFERENCE, THEOREMS, CIRCUIT DESIGN AND ANALYSIS,
ELECTRIC CALCULATIONS

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Let's start with quick definitions. Electronics is an engineering discipline that involves the design and analysis of electronic circuits. Originally, this subject was referred to as radio engineering. The circuit is a collection of components through which electrical current can flow or which use electromagnetic fields in their operation.

Circuit design and analysis rests primarily on two Kirchoff's laws, Ohm's law modified for AC circuits, and power relationships. There are also a number of network theorems and methods (such as Thevenin, Norton, Superposition, Y-Delta transform) that are consequences of these three laws. In order to simplify calculations in AC circuits, sinusoidal voltages and currents are usually represented as complex-valued functions called phasors. With phasors we need to solve algebraic equations instead of differential equations (see below). In general, practical circuit design and analysis also requires an understanding of semiconductor devices, integrated circuits and magnetics.


Below you will find electricity and magnetism reference, basic electrical engineering formulas, calculators, and other related information. Also see:
Electrical engineering reference: electric network laws and theorems;
The guide to accredited online schools: search distance learning programs and courses.

FORMULAS FOR THE BASIC CIRCUIT COMPONENTS
CIRCUIT
ELEMENT		 IMPEDANCE VOLT-AMP EQUATIONS ENERGY
(dissipated on R or stored in L, C)
absolute value complex
form		 instantaneous
values		 RMS values for sinusoidal signals
RESISTANCE R R v=i×R Vrms=Irms×R E=Irms2R×t
INDUCTANCE 2πfL
 jωL v=L×di/dt Vrms=Irms×2πfL E=Li2/2
CAPACITANCE 1/(2πfC) 1/jωC i=C×dv/dt Vrms=Irms/(2πfC) E=Cv2/2
Notes:
R- resistance in ohms, L- inductance in henrys, C- capacitance in farads, f - frequency in hertz, t- time in seconds, π≈3.14159;
ω=2πf - angular frequency;
j - imaginary unit ( j2=-1 )
Euler's formula: ejx=cosx+jsinx






EQUATIONS FOR SERIES AND PARALLEL CONNECTIONS
CIRCUIT
ELEMENT		 SERIES
CONNECTION		 PARALLEL
CONNECTION
RESISTORS Series connection circuits Rseries=
R1+R2+...		 Parallel connection circuits Rparallel=
1/
(1/R1+1/R2+...)


INDUCTORS


 Lseries=
L1+L2+...		 Lparallel=
1/(1/L1+1/L2+...)
CAPACITORS Cseries=
1/
(1/C1+1/C2+...)		 Cparallel=
C1+C2+...

CALCULATIONS OF EQUIVALENT RLC IMPEDANCES

CIRCUIT CONNECTION COMPLEX FORM ABSOLUTE VALUE
Series RLC series circuit Z=R+jωL+1/jωC series rlc formula
Parallel RLC parallel circuit Z=
1/(1/R+1/jωL+jωC)		 parallel rlc formula
Note: you can download a reference sheet with these and other formulas in pdf file.

TRANSISTORS AND DIODES: THE BASICS


The properties of semiconductor devices are studied in college courses. The introduction to the circuits including operation of diodes and transistors and basic formulas can be found in various textbooks or handbooks, such as The Art of Electronics. Below are just some highlights.

The I-V characteristic of a diode is approximated by the Shockley equation:
I=Is×(enVd/Vt-1),
where Is - the reverse bias saturation current (~10−15 to 10−12 A for Silicon); Vd - voltage drop in volts; Vt - the thermal voltage (~0.026V at room temperature), n - the "ideality factor" (from 1 to 2).
At a fixed current I, forward voltage drop changes by about -2 mV/oC.

In a bipolar transistor collector current Ic in a linear mode is related to the base-emitter voltage by the same Shockley (also called Ebers-Moll) equation, except for n=1. The collector current relates to the base current IB by Ic=IB×h21, where h21 - static current gain (typically 20-1000). When Ic reaches a limit determined by the supply voltage and the net external impedance in the collector circuit, the transistor is saturated.



MOSFET behavior varies with the gate voltage Vg. When Vg<Vth, where Vth - gate threshold voltage, the MOSFET is in OFF state with drain current Id≈0. When Vg>Vth and the external load is such that Vd>Vg-Vth, the MOSFET is in an active region, in which Id is proportional to the (Vg-Vth)2 and practically does not depend on the Vd. Once Id reaches certain limit determined by an external circuit, MOSFET start acting as a nearly constant resistance. In this mode Vds≈Id×Rdson, where Rdson - the ON-state channel's resistance specified in data sheets as a function primarily of temperature and gate voltage. Power MOSFETs are usually used as switching devices which operate in either ON or OFF state.



ELECTRICITY AND MAGNETISM

Classical electromagnetism reference: Maxwell's equations, electrical formulas, theorems, tutorials

Basic Electronics- free ebooks and online tutorials with simulations and troubleshooting

ELECTRONICS REFERENCE

Basic electronic circuit design and analysis

Electronic components - cross reference and parts' search

Recommended books on electronics and circuit design

ELECTRIC CALCULATION PROGRAMS

A collection of electrical engineering software and other tools

Online scientific calculator

Metric to U.S. calculator online