Mathematics Yoshio Sep 8th, 2023 at 8:00 PM 8 0
電子學 Microelectronics
電子學 MicroelectronicsElectronics is a general term for the field of science that involves managing electric currents through circuits. Microelectronics is one of the sub-categories of electronics. Microelectronics specifically relates to manufacture of very small electronic circuits.
Impedance
Impedance is a combination of Resistance and Reactance.
Impedance, denoted Z, is an expression of the opposition that an electronic component, circuit, or system offers to alternating and/or direct electric current. Impedance is a Complex (two-dimensional) quantity consisting of two independent scalar (one-dimensional) phenomena: Resistance and Reactance.
阻抗（Impedance）又稱電阻抗，是電路中電阻、電感、電容對交流電的阻礙作用的統稱。阻抗是一個複數，實部稱為電阻（Resistance），虛部稱為電抗（Reactance）。
Reactance
Reactance is a property that opposes a change in current and is found in both inductors and capacitors. Because it only affects changing current, reactance is specific to AC power and depends on the frequency of the current. When reactance is present, it creates a 90 degree phase shift between voltage and current, with the direction of the shift depending on whether the component is an inductor or a capacitor.
Inductor
Reactance that occurs in an inductor is known as inductive reactance. When inductive reactance is present, energy is stored in the form of a changing magnetic field, and the current waveform lags the voltage waveform by 90 degrees. Inductive reactance is caused by devices in which wire is wound circularly — such as coils (including line reactors), chokes, and transformers.
\(X_L=2\mathrm{πfL}\)
X_{L} = inductive reactance (ohms)
f = frequency (Hz)
L = inductance (henrys)
Capacitor
Reactance that occurs in a capacitor is known as capacitive reactance. Capacitive reactance stores energy in the form of a changing electrical field and causes current to lead voltage by 90 degrees. Capacitance is created when two conducting plates are placed parallel to one another with a small distance between them, filled with a dielectric material (insulator).
\(X_C=\frac1{2\mathrm{πfC}}\)
X_{C} = capacitive reactance (ohms)
C = capacitance (farads)
電容器兩端的電壓滯後於通過電容器的電流，兩者之間的相位差為 \(\pi/2\) ；電感器兩端的電壓超前於通過電感器的電流，兩者之間的相位差為 \(\pi/2\) 。由於電壓與電流的振幅相等，阻抗的大小為 \( 1\).
Individual Voltage Vectors for a Series RLC Circuit
Admittance
Admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance, analogous to how conductance and resistance are defined.
Admittance, denoted Y, is an expression of the ease with which alternating current ( AC ) flows through a complex circuit or system. Admittance is a two-dimensional Complex quantity comprised of two independent Scalar phenomena: Conductance(G) and Susceptance(B).
導納（Admittance）用來描述交流電通過電路或系統時的容許程度。導納是一個複數，實部稱為電導（Conductance），虛部稱為電納（Susceptance）。
Electrical Parameter |
Measuring Unit |
Symbol | Description |
---|---|---|---|
Voltage | Volt | V or E |
Unit of Electrical Potential V = I × R |
Current | Ampere | I or i |
Unit of Electrical Current I = V ÷ R |
Resistance | Ohm | R or Ω |
Unit of DC Resistance R = V ÷ I |
Conductance | Siemens | G or ℧ |
Reciprocal of Resistance G = 1 ÷ R |
Capacitance | Farad | C |
Unit of Capacitance C = Q ÷ V |
Charge | Coulomb | Q |
Unit of Electrical Charge Q = C × V |
Inductance | Henry | L or H |
Unit of Inductance V_{L} = -L(di/dt) |
Power | Watts | W |
Unit of Power P = V × I or I^{2} × R |
Impedance | Ohm | Z |
Unit of AC Resistance Z^{2} = R^{2} + X^{2} |
Frequency | Hertz | Hz |
Unit of Frequency ƒ = 1 ÷ T |
Magnetic Flux | Weber | Wb |
Unit of magnetic flux \(Φ_B\) |
Electric Flux | Coulomb | C |
Unit of electric flux \(Φ_E\) |
Magnetic Flux Density | Tesla | T |
Unit of magnetic flux density \(Φ_B\) |
時間常數 \((τ )\) Time constant
The time constant – usually denoted by the Greek letter τ (tau) – is used in physics and engineering to characterize the response to a step input of a first-order, linear time-invariant (LTI) control system. The time constant is the main characteristic unit of a first-order LTI system.
Time constant, denoted as \(τ\), is a crucial concept in electrical engineering, measuring the response time of a system to a step input. In an RC circuit, \(τ = RC\), and in an RL circuit, \(τ = L/R\).