UNDERSTANDING ELECTRONIC CIRCUITS
CURRENT AND VOLTAGE
It has been found experimentally that the intensity of various electrical effects is related to the amount of electrical charge that passes by a certain region per unit time. Therefore this quantity I=Q/t, which is called the electric current, presents a special interest in engineering.
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In practice, the flow of the current is controlled by various
electronic components. A network of interconnected components that can
accomplish a certain task is referred to as electronic circuit.
The circuits can be used for processing signals, information, or
energy. A current can be measured by an instrument called an ampmeter. For a
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. Such particle therefore has a potential energy associated with this position. When a particle moves from one point to another, the amount of work done by the electrical field equals the drop in its electrical energy, which is being converted into other forms of energy, such as mechanical motion, heat and light. The change in the electrical energy of a particle per unit charge as it moves from one point to another is defined as voltage or potential difference between these two points: V=ΔE/q. The power transfer is then equals to: P=ΔE/t=V×q/t=V×I. Note that only voltage differences rather than absolute voltages have direct physical meaning. The voltage between two points can be measured by an instrument called a voltmeter. A voltmeter can be just an ammeter with a series-connected high-value resistor through which the current proportional to the measured voltage is forced to flow. For hobbyist electronic projects there are inexpensive digital multimeters that can measure voltage, current, and resistance.
IMPEDANCE
The V/I relationships for energy storage components (inductors and capacitors) are described by differential equations. In practical cases the handling of these equations quickly becomes unmanageable. That's why the analysis of the networks with sinusoidal signals usually uses complex exponentials method. With this method, voltages, currents and impedances are represented by complex exponential functions (phasors) based on Euler relationship ejx=cosx+jsinx, where j is imaginary unit. The lenght of the phasor is proportional to the magnitude of the quantity it represents, and its angle represents a phase shift relative to some reference signal. This allows turning differential equations into algebraic equations. In linear AC networks with single-frequency sinusoidal voltage sources impedance Z is defined as the ratio of voltage phasor to the current phasor: Z=V/Ĩ . Its magnitude is the ratio of the voltage amplitude to the current amplitude, and phase is the phase shift between the current and the voltage.
Impedance in general is a complex
number that can be calculated by using formulas for series and parallel
connections. With known complex impedance, current phasor is Ĩ=V/Z. This pie
chart ("wheel") illustrates relationships between voltage, current,
impedance and power in linear networks with a sinusoidal input. These
formulas are adaptations of Ohm's law and Joule's law for AC signals.
In this "power 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 where components are represented by graphical symbols and that can communicate information about a circuit. In theory, the processes in electronic circuits could be described by Maxwell's equations and the physics laws describing properties of materials. However, in practical design and analysis engineers consider idealized elements that reflect some essential aspects of the operation of the real devices. This allows describing the 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's law extended for AC. There are also a number of network theorems and methods (such as Thevenin, Norton, 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 and electrically interconnect parts by using conductive traces, etched from copper sheets laminated onto an isolating substrate.
REFERENCE
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Handbook of operational amplifier applications and OpAmp circuit collection Digital Logic basics The DSP Guide: ADC & DAC basics, sampling theorem, Fourier Transform, FFT |
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