ELECTRICAL and ELECTRONICS REFERENCE



BASIC FORMULAS, THEOREMS, CIRCUIT DESIGN AND ANALYSIS,
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Electronic engineering or electronics is an engineering discipline that involves the design and analysis of electronic circuits. Originally, this subject was referred to as radio engineering. An electronic circuit is a collection of components through which electrical current can flow or which use electromagnetic fields in their operation.

The electronic circuit design and analysis rests primarily on two Kirchoff's laws in conjunction with 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 voltage and current are usually represented as complex-valued functions called phasors. Practical circuit design and analysis also requires a comprehensive understanding of semiconductor devices, integrated circuits and magnetics.

Here you will also find electricity and magnetism reference, basic electrical engineering formulas, calculators, and other related information.

Also see:
Electrical Engineering Reference: circuit laws and theorems;
Search online degree programs and courses from accredited schools;
The guides to distance learning and online schools.

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
RESISTANCE resistance series connection Rseries=
R1+R2+...
Resistor parallel connection Rparallel=
1/
(1/R1+1/R2+...)
INDUCTANCE inductance series connection Lseries=
L1+L2+...
Inductance parallel connection Lparallel=
1/(1/L1+1/L2+...)
CAPACITANCE Capacitance series conection Cseries=
1/
(1/C1+1/C2+...)
Capacitor parallel connection 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 a pdf file.

TRANSISTORS AND DIODES: THE BASICS


The properties of semiconductor devices are subject to college courses. The introduction to the circuits including operation of diodes and transistors and their basic formulas can be found in various textbooks or handbooks such as The Art of Electronics. Below are 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 resistance in the collector circuit, the transistor is saturated.

MOSFET's 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 a limit determined by an external circuit, it remains fixed and MOSFET acts as a constant resistance. In this mode Vds≈Id×Rdson, where Rdson - the ON-state channel's resistance specified in data sheets. Power MOSFETs are usually used as switching devices which operate in either ON or OFF state.


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