معاوقة كهربائية مزدوجة

تحليل خطي للشبكات
العناصر
المكونات
دوائر التوالي والتوازي
تحويلات المعاوقة
مبرهنات المولد	مبرهنات الشبكة
أساليب تحليل الشبكات
Two-port parameters

المعاوقة المزدوجة والشبكة المزدوجة، هي مصطلحات تستخدم في مجال شبكات التحليل الإلكترونية. ازدواج المقاومة $Z$هو المعكوس الجبري لها $Z^{\prime }=\frac{1}{Z}$. لاحظ أن $Z$ و$Z^{\prime }$ مزدوج لكل منهما that is, they are reciprocal. For this reason the dual impedance is also called the inverse impedance. The dual of a network of impedances is that network whose impedance is $Z^{\prime }$. In the case of a network with more than one port the impedance looking into each of the ports must simultaneously be dual.

Another way of stating this is that the dual of $Z$ is the admittance $Y=Z$.

This is consistent with the definition of dual as being that circuit whose voltages and currents are interchanged since $Z=\frac{V}{I}$ and $Z^{\prime }=\frac{1}{Z}=\frac{I}{V}$

Scaled and normalised duals

$\frac{Z^{\prime }}{Z_0}=\frac{Z_0}{Z}$

ازدواج عناصر الدائرة الأساسية

العنصر	Z	الازدواح	Z'
Resistor R	$R$	Conductor G = R	$\frac{1}{R}$
Conductor G	$\frac{1}{G}$	Resistor R = G	$G$
Inductor L	$i\omega L$	Capacitor C = L	$\frac{1}{i\omega L}$
Capacitor C	$\frac{1}{i\omega C}$	Inductor L = C	$i\omega C$
Series impedances Z = Z1 + Z2	$Z_1+Z_2$	Parallel admittances Y = Z1 + Z2	$\frac{1}{Z_1+Z_2}$
Parallel impedances 1/Z = 1/Z1 + 1/Z2	$Z=\frac{Z_1{Z}_2}{Z_1+Z_2}$	Series admittances 1/Y = 1/Z1 + 1/Z2	$\frac{1}{Z_1}+\frac{1}{Z_2}$
Voltage generator V		Current generator I = V
Current generator I		Voltage generator V = I

طريقة بيانية

مثال - شبكة نجمية

A star network of inductors, such as might be found on a three-phase transformer

Attaching generators to the three ports

Nodes of the dual network

Components of the dual network

The dual network with the original removed and slightly redrawn to make the topology clearer

The dual network with the notional generators removed

مثال- شبكة كوير

A low-pass filter implemented in Cauer topology

Attaching generators to the input and output ports

Nodes of the dual network

Components of the dual network

The dual network with the original removed and slightly redrawn to make the topology clearer

المصادر

• Ghosh, Smarajit, Network Theory: Analysis and Synthesis, Prentice Hall of India