Practical Electronics/Inductors

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Inductor[edit]

This device generates a magnetic field as current passes through it similar to the magnetic field of a magnet. An inductor stores electrical energy in the form of a magnetic field.

Inductor's Symbol[edit]

The symbol for inductance is L and is measured in Henry which has the symbol H.

Coil.gif

Inductor's Construction[edit]

An inductor is a device made from a wire conductor with several turns that has the dimensiion permability, length of inductor, and number of turns and inversely proportional to cross-sectional area.

L = \frac{B}{I} = μN^2\frac{A}{l}

Characteristics[edit]

Inductance[edit]

Inductance is the ability to generartes Magnetic Field B for a given Current

L = \frac{B}{I}

Magnetic Field[edit]

When a voltage is applied across the inductor, current generates Electric Field . Change of Electric Field in the turns generates Magnetic Field perpendicular to Electric Field

B = I L

Voltage[edit]

V_L = L \frac{dI}{dt} = \frac{dB}{dt}

Current[edit]

I_L = \frac{1}{L} \int V dt

Reactance[edit]

Reactance is defined as the ratio of Voltage over current

X_L = \frac {L \frac{dI}{dt}}{I}
X_L = \omega L \ang 90^\circ
X_L = j \omega L
X_L = s L

Impedance[edit]

Impedance is defined as the sum of Reactance and Resistance of Inductor . Since all conductor has Resistance

Z_L = R_L + X_L
Z_L = \sqrt{R_L^2 + (\omega L)^2} \ang \arctan ( \omega \frac{L}{R} )
Z_L = R_L + j \omega L
Z_L = R_L + s L

Frequency Respond[edit]

Inductor is a device depends on frequency \omega

  • \omega = 0  , X_L = 0, Inductor Closed circuit, I ≠ 0
  • \omega = \infty , X_L = \infty, Inductor Opened circuit, I = 0
  • \omega = \frac{R_L}{L}
X_L = R_L ,
Z_L = [(RL]⅓</math> ,
V_L = \frac {V}{2}
I_L = \frac {V}{2R_L}

With the value of I at three frequency points ω = 0, \infty , 1 / CRC I - f curve can be drawn to give a picture of current in the inductor over time

Phase Angle[edit]

When a Voltage is applied across inductor , current generates magnetic field . Change in curent generate change in magnetic field which generate voltage across inductor . Therefore, current will lead voltage

For ideal losses inductor which has no internal resistance, Current will lead Voltage an angle 90 . For Non - Ideal inductor which has an internal resistance, Current will lead Voltage an angle θ

Tanθ =  \omega {L}{R_L} = 2π f \frac{L}{R_L}

Phase angle relates to time frequecy or time and the value of R and L . When there is a change in phase angle Time and frequency also change

f = \frac{Tan\theta}{2\pi}\frac{R_L}{L}
 t =\frac{2\pi}{Tan\theta}\frac{L}{R_L}

Induced Voltage[edit]

Induced Voltage is defined as the voltage of the turns which oppose the current flow


-ξ = N \frac{dB}{dt} = \frac{d\phi}{dt} where Φ = NB

Từ Dung[edit]

Từ Dung là tính chất Vật lý của Cuộn Từ đại diện cho Từ Lượng sinh ra bởi một Dòng Điện trên Cuộn Từ . Từ Dung đo bằng đơn vị Henry H và có ký hiệu mạch điện L

L = \frac{B}{I}

Cuộn Từ tạo từ một cộng dây dẩn điện có kích thứớc Chiều dài , l , Điện tích , A , với vài vòng quấn N . Khi mắc với điện

L = \mu N^2 \frac{l}{A}

Độ Dẩn Từ của vật liệu

\mu = \frac{B}{I} \frac{A}{l} \frac{1}{N^2}


Construction Formula Dimensions
Cylyndrical Coil [1] L=\frac{\mu_0KN^2A}{l}
  • L = inductance in henries (H)
  • μ0 = permeability of free space = 4\pi × 10-7 H/m
  • K = Nagaoka coefficient[1]
  • N = number of turns
  • A = area of cross-section of the coil in square metres (m2)
  • l = length of coil in metres (m)
Straight wire conductor L = l\left(\ln\frac{4l}{d}-1\right) \cdot 200 \times 10^{-9}
  • L = inductance (H)
  • l = length of conductor (m)
  • d = diameter of conductor (m)
L = 5.08 \cdot l\left(\ln\frac{4l}{d}-1\right)
  • L = inductance (nH)
  • l = length of conductor (in)
  • d = diameter of conductor (in)
Short air-core cylindrical coil L=\frac{r^2N^2}{9r+10l}
  • L = inductance (µH)
  • r = outer radius of coil (in)
  • l = length of coil (in)
  • N = number of turns
Multilayer air-core coil L = \frac{0.8r^2N^2}{6r+9l+10d}
  • L = inductance (µH)
  • r = mean radius of coil (in)
  • l = physical length of coil winding (in)
  • N = number of turns
  • d = depth of coil (outer radius minus inner radius) (in)
Flat spiral air-core coil L=\frac{r^2N^2}{(2r+2.8d) \times 10^5}
  • L = inductance (H)
  • r = mean radius of coil (m)
  • N = number of turns
  • d = depth of coil (outer radius minus inner radius) (m)
L=\frac{r^2N^2}{8r+11d}
  • L = inductance (µH)
  • r = mean radius of coil (in)
  • N = number of turns
  • d = depth of coil (outer radius minus inner radius) (in)
Toroidal core (circular cross-section) L=\mu_0\mu_r\frac{N^2r^2}{D}
  • L = inductance (H)
  • μ0 = permeability of free space = 4\pi × 10-7 H/m
  • μr = relative permeability of core material
  • N = number of turns
  • r = radius of coil winding (m)
  • D = overall diameter of toroid (m)

Network[edit]

Inductors can be connected in series to increase inductance or in parallel to decrease inductance

Parallel Connection[edit]

A diagram of several inductors, side by side, both leads of each connected to the same wires
 \frac{1}{L_\mathrm{eq}} = \frac{1}{L_1} + \frac{1}{L_2} + \cdots +  \frac{1}{L_n}


Series Connection[edit]

A diagram of several inductors, connected end to end, with the same amount of current going through each
 L_\mathrm{eq} = L_1  + L_2 + \cdots + L_n \,\!


References[edit]

  1. a b Nagaoka, Hantaro. The Inductance Coefficients of Solenoids[1]. 27. Journal of the College of Science, Imperial University, Tokyo, Japan. p. 18.