Electronics is an engineering discipline that involves the design and analysis ofelectronic of electronic circuits. 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 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. schools . FORMULAS FOR THE BASIC CIRCUIT COMPONENTS IMPEDANCE CIRCUIT ELEMENT
absolute value
VOLT-AMP EQUATIONS
comple instantaneou x s form values
RMS values for sinusoidal signals
ENERGY (dissipated on R or stored in L, C)
RESISTANC E
R
R
v=i×R
Vrms=Irms×R
E=Irms2R×t
INDUCTANC E
2πfL
jωL
v=L×di/dt
Vrms=Irms×2πfL
E=Li2 /2
CAPACITAN CE
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 - angu angula larr frequ frequenc ency; y; 2 j - imaginary unit ( j =-1 ) Euler's formula: e jx=cosx+jsinx
EQUATIONS FOR SERIES AND PARALLEL CONNECTIONS CIRCUIT
SERIES
PARALLEL
ELEMENT
CONNECTION
CONNECTION
Rseries= R1+R2+...
Rparallel= 1/ (1/R1+1/R2+.. .)
INDUCTANC E
Lseries= L1+L2+...
Lparallel= 1/ (1/L1+1/L2+... )
CAPACITAN CE
Cseries= 1/ (1/C1+1/C2+ ...)
Cparallel= C1+C2+...
RESISTANC E
CALCULATIONS OF EQUIVALENT RLC IMPEDANCES CIRCUIT CONNECTION
COMPLEX FORM
ABSOLUTE VALUE
Z=R+jωL+1/jωC Series
Z= 1/(1/R+1/jωL+jωC) Parallel 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 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 I B 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's behavior varies with the gate voltage Vg. When VgVth 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.
Voltage: Enter the source nominal voltage. Use the larger voltage of the system. Example: For a 120/240V Use 240V Square Footage: Measure the total square footage of the occupancy using the outside dimensions. Do not include open porches, unused or unfinished spaces not adaptable for future use. Small Appliance Branch Circuits: Enter the number of small appliance branch circuits. At least 2 are required for dwelling units.210-11(c)(1) Appliance Branch Circuit - A branch circuit that supplies energy to one or more outlets to which appliances are to be connected, and that has no permanently connected lighting fixtures that are not part of an appliance. Laundry Branch Circuits: Enter the number of laundry branch circuits. At least 1 is required for dwelling units. 210-11(c)(2) Fastened In Place Appliances: Use Volt Amps or Watts. These are appliances you can not pick up and carry out of the house without using some kind of tool. Examples of fastened in place appliances: electric water heater, attic fan, disposal, trash compactor and dish washer. Do not include electric ranges, air conditioners, clothes dryers or space heaters. Use the nameplate ratings. Horse power ratings should be converted to Amps using T430.148, then converted to VA by multiplying by the rated voltage (i.e. 120 volts) Clothes Dryers:(optional) Enter the rating in volt-amps. A clothes dryer is not required. If there w ill be no clothes dryers then enter a zero. The minimum rating is 5000va so, use 5000va or the name plate rating which ever is larger. If your rating is listed in kW then multiply that rating by 1000. for example 6kW = 6000va. The neutral load will be calculated at 70% of the dryer load. Household Cooking Appliances:(optional) Enter in kilo-watts the household cooking appliances rated over 1.75kW. Examples of Household cooking appliances are Ranges, Ovens, Cooktops rated over 1.75kW. If there will be no household cooking appliances over 1.75kw then skip this section. The neutral load will be calculated at 70% of the total calculated load. Heating or Air Conditioning: Enter in volt-amps the larger of either the ac or heating loads. For example you have central system comprising of an AC compressor(4000va), condenser fan(240va), air ha ndler(345va) and heat coils(15000va). You also have a space heater(3500va). Now what is the largest load that will be running at any time? Will it be when you run the heating or the AC? You can eliminate one since you will not be using both at the same time. When the AC is being used the compressor, condenser, and air handler will be running. This gives us a total AC load of 4585va.
The total heating load is the sum of the heat coils, air handler and the space heater which in this case is 18845va. I would enter 18845 and select the Heater button. If your compressor also serves as a heat pump it should be added to the heating load. Heating or Air Conditioning Neutral: Enter the neutral load in Volt Amps. This is the same as the 120V load. Example: An AC system usually consists of a condenser fan motor(208-240V), compressor motor(208-240V) and a blower motor(120V). In this case I only need the Volt-Amps of the blower motor. Use the nameplate ratings. Horse power ratings should be con verted to Amps using T430.148, then converted to VA by multiplying by the rated voltage (ie 120 volts). A 1/2 horse motor is a large common blower motor. The same is true with heating find all the 120V loads in the system and add them up. For this calculation Watts are the same as Volt-Amps. Largest Motor: Enter in volt-amps the larges motor. In most cases this will be the AC compressor. If this motor is only listed in horse power it should be converted to Amps using T430.148, then converted to VA by multiplying by the rated voltage (ie 120 volts). If this is a 120V motor check the neutral box.
MAGNETIC UNITS CONVERSION DEFINITIONS, ONLINE CALCULATORS, EQUATIONS IN SI AND CGS
Magnetic field is one of two components of the electromagnetic field. It is a region where forces acting on moving electric charges can be detected. Magnetic fields are created by moving electric charges or variable electric field. The charge movement that creates magnetic field may be macroscopic (currents in conductors), or microscopic (associated with spin and orbital motion of electrons, resulting in "magnetic materials"). The SI unit for magnetic flux is the weber (Wb). If the magnetic flux changes by 1 Wb over a time of 1s, then a voltage of 1 V is induced in a conductive loop encircling it: 1 Wb = 1 Vs. The SI unit for magnetic flux density (magnetic induction) B is tesla (T): 1 T = 1 Wb/m2 = 1 Vs/m2. Magnetic field with density of 1 T generates one newton of force per ampere of current per meter of conductor. When the magnetic fields generated by currents pass through some materials they produce magnetization in the direction of the applied field. In ferromagnetics it results in increased total field B. Quantity called magnetic field strength (or magnetizing force) H is a measure of the applied magnetic field from external currents, independent of the material's magnetic response. Quantity called magnetisation M defines the material's response- it is magnetic moment per unit volume of material. Flux density (magnetic induction) B describes the resulting field in the material. In power electronics it is the main magnetic quantity used in calculation of the minimum required crosssectional area of power transformer cores for given voltage and frequency (see also: engineering reference info on power transformer design ). The table below provides magnetic formulas in both SI and CGS systems and conversion factors of magnetic units.
MAGNETIC FLUX DENSITY UNIT CONVERSION CALCULATOR
MAGNETIC FIELD STRENG CONVERSION CALCULA
Top of Form
Top of Form
tesla [T]:
ampere/meter [A/m]:
gauss [Gs, G]:
oersted [Oe]:
weber/square meter:
Bottom of Form
weber/square centimeter: maxwell/square meter: maxwell/sq. centimeter: line/square centimeter: gamma: Bottom of Form
Calculators' data are courtesy of www.unitconversion.org
QUANTITY
SYMBO L
SI UNIT
SI EQUATION
CGS UNIT
CGS EQUATION
Magnetic induction
B
tesla (T)
B=µo(H+M)
gauss (G)
B = H+4πM
Magnetic field strength
H
ampere/meter (A/m)
H = N×I/lc ( lc - magnetic path, m)
oersted (Oe)
H = 0.4πN×I/lc (lc - magnetic path, cm)
Magnetic flux
Φ
weber (Wb)
Φ = B×Ac (Ac - area, m 2 )
maxwell (M)
Φ = B×Ac (Ac - area, cm 2 )
emu/cm3
M=m/V (m- total magnetic moment, V- volume, cm3 )
1
-
Magnetization
M
ampere/meter (A/m)
M=m/V (m- total magnetic moment, V- volume, m 3 )
Magnetic permeability of vacuum
µo
newton/ampere2
µo= 4π×10-7
henry
L=0.4πμN2Ac/lc×10-8 (Ac-area, cm2, lc - magnetic path, cm)
volt
V=-10-8N×dΦ/dt
Inductance
L
henry
L=μoμN2Ac/lc (Ac- area, m2, lc - magnetic path, m)
Emf (voltage)
V
volt
V=-N×dΦ/dt
Note: in the above equations: N- turns, I - current (in amps)
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CONTACT US
DISCLAIMER and TE
UNDERSTANDING ELECTRONIC CIRCUITS
CURRENT AND VOLTAGE
It has been found experimentally that the intensity of various electrical effects is related to the amount of ele charge that passes by a certain region per unit time. Therefore this quantity I=Q/t, which is called the el current, presents a special interest in EE. Sponsor
In practice, the flow of the current is controlled by various electronic components. A network of interconn components that can accomplish a certain task is referred to as electronic circuit. The circuits can be us processing signals, information, or energy. A current can be measured by an instrument called an ammeter. current to flow continuously, the circuit should have an energy source and a closed path. When a charged particle is placed in an electrical field, it experiences a force that depends on its position. particle therefore has a potential energy associated with this position. When a particle moves from one po another, the amount of work done by the electrical field equals the drop in its electrical energy, which is converted into other forms of energy, such as mechanical motion, heat and light. The change in the ele energy of a particle per unit charge as it moves from one point to another is defined as voltage or pot difference between these two points: V=ΔE/q. The power transfer is then equals to: P=ΔE/t=V×q/t=V×I. Not
only voltage differences rather than absolute voltages have direct physical meaning. The voltage betwee points can be measured by an instrument called a voltmeter. A voltmeter can be just an ammeter with a s connected high-value resistor through which the current proportional to the measured voltage is forced to For hobbyist electronic projects there are inexpensive digital multimeters that can measure voltage, current resistance.
IMPEDANCE
The V/I relationships for energy storage components (inductors and capacitors) are described by differ equations. In practical cases the handling of these equations quickly becomes unmanageable. That's wh analysis of the networks with sinusoidal signals usually uses complex exponentialsmethod. With this me voltages, currents and impedances are represented by complex exponential functions ( phasors) based on relationship ejx=cosx+jsinx, where j is imaginary unit. The lenght of the phasor is proportional to the magn of the quantity it represents, and its angle represents a phase shift relative to some reference signal. This a turning differential equations into algebraic equations. In linear AC networks with single-frequency sinu voltage sources impedance Z is defined as the ratio of voltage phasor to the current phasor: Z=V/ magnitude is the ratio of the voltage amplitude to the current amplitude, and phase is the phase shift betwee current and the voltage.
Impedance in general is a complex number that can be calculat using formulas for series and parallel connections. With known complex impedance, current phasor is Ĩ =V/Z. pie chart ("wheel") illustrates relationships between voltage, current, impedance and power in linear network a sinusoidal input. These formulas are adaptations of Ohm's law and Joule's law for AC signals. In this "p wheel": V - rms voltage (volts); I - rms current (amps); Z - magnitude of impedance (ohms); S - apparent power (volt-amps).
By knowing any two values of V, I, Z or S, you can find the values of the remaining quantities. For a pure resistor Z=R, I=V/R, and S=P, where R - resistance, P - active power. For impedance calculations and I-V relationships between basic electrical parts see Electrical Formulas.
DESIGN AND ANALYSIS
Every circuit design involves the development of a schematic. A schematic diagram is a drawing components are represented by graphical symbols and that can communicate information about a circ theory, the processes in electronic circuits could be described by Maxwell's equations and the physics describing properties of materials. However, in practical design and analysis engineers consider ide elements that reflect some essential aspects of the operation of the real devices. This allows describin operation of the circuit with simplified equations that use circuit theory terms. The basis for most circuit analysis technique is Kirchoff's current and voltage laws in conjunction with Ohm' extended for AC. There are also a number of network theorems and methods (such as Thevenin, N Superposition, Y-Delta transform) that are derived from these three laws. The circuit design typically includes computer simulation, breadboarding and prototyping. Electronic devices are normally assembled on printed circuit boards (PCBs) that mechanically support electrically interconnect parts by using conductive traces, etched from copper sheets laminated onto an isol substrate.
REFERENCE INFORMATION
EDUCATION AND CAREER RESOURCES
R, L and C impedances and voltamp relationships
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Electrical Engineering reference, basic circuit theorems, online textbooks
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BASIC ELECTRONIC CIRCUIT DESIGN AND ANALYSIS
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ELECTRICAL ENGINEERING REFERENCE INFORMATION ELECTRICITY AND MAGNETISM BASICS, CIRCUIT THEOREMS AND EQUATIONS
Electrical engineering (EE) is a discipline that deals with electricity, magnetism and their applications. EE applications include electronics, power conversion, data communications, computer science, information technologies, and other. The term EE usually encompasses electronic engineering or electronics. Electronics involves the design and analysis of electronic circuits. In academia and electronic industry, the terms electrical and electronics engineer often are used interchangeably. Find Science and Engineering Degree Program Online
In other industries, the term electrical engineer may refer to those who deal with utility and industrial power systems and other electric equipment. In any case, both disciplines are overlapping. The theoretical foundation for EE is electromagnetism. The theory of classical electromagnetism is based on Maxwell's equations (see below), which provide a unified description of the behavior of electric and magnetic fields as well as their interactions with matter. In practice however, circuit designers normally use simplified equations of electricity and magnetism and theorems that use circuit theory terms, such as Ohm's law modified for AC circuits, voltage and current Kirchoff's laws, and power relationships. This webpage is for those who already learned EE and needs a quick reference. Here you
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MAXWELL'S EQUATIONS IN FREE SPACE (in SI units) LAW Gauss' law for electricity
Gauss' law for magnetis m
Faraday's law of induction
Ampere's law
DIFFERENTIAL FORM
INTEGRAL FORM
NOTES: E - electric field, ρ - charge density, ε0 ≈ 8.85×10-12 - electric permittivity of free space, π ≈ 3.14159, k - Boltzmann's constant, q - charge, B - magnetic induction, Φ - magnetic flux, J - current density, i electric current, c ≈ 299 792 458 m/s - the speed of light, µ0 = 4π×10-7 - magnetic permeability of free space, - del operator (ifV is a vector function, then
.
V is divergence of V,
×V is the curl of V).
BASIC ELECTRICAL THEOREMS AND CIRCUIT ANALYSIS LAWS THE LAW
w extended for AC circuits le frequency sinusoidal
RELATIONSHIP TO OTHER
DEFINITION
LAWS
V=Z× Ĩ, where V and Ĩ - voltage and current phasors, Z - complex impedance (for resistive circuits: Z=R and V=R×I )
Lorentz force law and Drude model for resistors
's Current Law (KCL)
The sum of electric currents which flow into any junction in a circuit is equal to the sum of currents Conservation of electric charge which flow out
's Voltage Law (KVL)
The sum of the voltages around a closed circuit must be zero
Conservation of energy
that Kirchhoff's laws can be derived from Maxwell's equations under static conditions, although historically they ded Maxwell's equations. an download a reference sheet with the above equations in a pdf file.
ELECTRICAL NETWORK THEOREMS FOR AC CIRCUITS THE THEOREM
DEFINITION
CALCULATION
Thevenin's Theorem
Any combination of a single frequency sinusoidal AC sources and impedances with two terminals can be replaced by a single voltage source V in series with an impedance Z.
V - open-circuit voltage phasor original circuit; Z - impedance between the tw terminals with all voltage sour shorted and all current source opened.
Any combination of a single frequency sinusoidal AC sources and impedances with two terminals A and B can be replaced by a single current source I in parallel with an impedance Z.
I - short-circuit current phasor original circuit; Z - impedance between the tw terminals with all voltage sour shorted and all current source opened.
Superposition Theorem
The current (voltage) phasor in any part of a linear circuit equals the algebraic sum of the current (voltage) phasors produced by each source separately.
To find an individual current (v from each source, short all oth voltage sources and open all o current sources.
Maximum Power Transfer Theorem
A voltage source delivers maximum power to a adjustable when the source and the load impedances are complex conjugates of each other
Active components of the sour load impedances should be eq and reactive components sho have equal magnitude but opp sign.
A delta network of three impedances can be transformed into a star (Y) network of three impedances
Za = ZcaZab / (Zab+Zbc+Zca) Zb = ZabZbc / (Zab+Zbc+Zca) Zc = ZbcZca / (Zab+Zbc+Zca)
A star (Y) network of three impedances can be transformed into a delta network of three impedances
Zab = Za + Zb + (ZaZb / Zc) Zbc = Zb + Zc + (ZbZc / Za) Zca = Zc + Za + (ZcZa / Zb)
Norton's Theorem
Delta to Wye Transformation
Star-Delta Transformation
ECTRONICS REFERENCE
ELECTRICITY AND MAGNETISM ONLINE TEXTBOOKS, HANDBOOKS and COURSES
electrical engineering las and circuit calculations
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Classical Electromagnetismrelationships: Maxwell's equations, energy, relativity
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Power supply design and other analog circuit design jobs
