Twisted pair cable

When two wires are twisted inside the cable, they are called a twisted pair. By twisting the wires, the electromagnetic interference caused by the electrical current is greatly reduced. Most LAN cabling uses two twisted pairs – one for transmitting and one for receiving.

Linear and Non-Linear Inductors

An ideal inductor would have zero capacitance and zero resistance.

The Figure below shows a graph of inductive reactance X_{L} versus frequency f. Inductive reactance increases linearly with frequency.

Figure: Inductive reactance X_{L} vs frequency f (ideal inductor)

A real inductor can be modeled by the following elements:

  • a series inductor L
  • a series resistor R_{DC} or R_{S}
  • a parallel capacitor C_{P} or C_{d}: It is the distributed capacitance between the turns of the wire and is derived from the Self Resonant Frequency (f_{o}).
  • a parallel resistor R_{P}: It represents the magnetic core loss of the inductor core.

The figure below shows a real-life impedance vs frequency graph.

Figure: Inductive reactance X_{L} vs frequency f (real inductor)

Self-Resonant Frequency (SRF) or f_{o} in Hz: This is the frequency at which the inductance of the inductor L resonates with the inductor’s distributed capacitance C_{P}. Increasing L or C lowers f_{o}. Decreasing L or C raises f_{o}.

f_{o} = \frac{1}{2 \pi \sqrt{LC}}

At f_{o}

  • the inductor will act as a pure resistor,
  • the input impedance is at its peak,
  • the Quality factor of the inductor is zero,
  • the reactance of the inductor X_{L} is zero,
  • the capacitance is given by C_{P} = \frac {1}{(2 \pi f_{o})^2L_{o}}

At frequencies below f_{o} the reactance is inductive and increases as the frequency increases.

At frequencies above f_{o} the reactance is capacitive and decreases as the frequency increases.

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Закон за пълния ток (Ampere’s Law)

Законът обвързва циркулацията на вектора на интензитета на магнитното поле H по произволен затворен контур G с пълния ток I_{\Sigma}, който преминава през ограничената от контура повърхност. За избраната посока на обхождане на G, I_{\Sigma} = i_{1} - i_{2} - i_{k}.

Когато контурът G обхвъща навивките на намотка с N навивки, през които протича ток i, пълният ток I_{\Sigma} = Ni=F_{m}, където величината F_{m}=Ni се нарича магнитодвижещо напрежение (magnetomotive force).

Ако пространството през което минава контурът G се раздели на M участъка, всеки с дължина l_{k}, сечение S_{k}, и магнитна проницаемост \mu_{k}, такива, че във всеки участък интензитета на полето  H_{k} има постоянна стойност, законът за пълния ток приема вида:

С използване на известните връзки между интензитета на магнитното поле H, неговата индукция B и създадения магнитен поток \Phi, магнитодвижещото напрежение на източника F_{m} се представя с израза: