تحليل الشبكات (دوائر كهربائية)

تحليل خطي للشبكات
العناصر

المكونات

دوائر التوالي والتوازي

تحويلات المعاوقة

مبرهنات المولد	مبرهنات الشبكة

أساليب تحليل الشبكات

Two-port parameters

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الشبكة، في مجال الإلكترونيات، هي مجموعة من المكونات المترابطة. تحليل الشبكات، عملية إيجاد the voltages across, and the currents through, every component in the network. ويوجد تقنيات مختلفة لتحقيق ذلك. However, for the most part, they assume that the components of the network are all linear. The methods described in this article are only applicable to linear network analysis except where explicitly stated.

تعريفات

Component	A device with two or more terminals into which, or out of which, charge may flow.
Node	A point at which terminals of more than two components are joined. A conductor with a substantially zero resistance is considered to be a node for the purpose of analysis.
Branch	The component(s) joining two nodes.
Mesh	A group of branches within a network joined so as to form a complete loop.
Port	Two terminals where the current into one is identical to the current out of the other.
Circuit	A current from one terminal of a generator, through load component(s) and back into the other terminal. A circuit is, in this sense, a one-port network and is a trivial case to analyse. If there is any connection to any other circuits then a non-trivial network has been formed and at least two ports must exist. Often, "circuit" and "network" are used interchangeably, but many analysts reserve "network" to mean an idealised model consisting of ideal components.^[1]
Transfer function	The relationship of the currents and/or voltages between two ports. Most often, an input port and an output port are discussed and the transfer function is described as gain or attenuation.
Component transfer function	For a two-terminal component (i.e. one-port component), the current and voltage are taken as the input and output and the transfer function will have units of impedance or admittance (it is usually a matter of arbitrary convenience whether voltage or current is considered the input). A three (or more) terminal component effectively has two (or more) ports and the transfer function cannot be expressed as a single impedance. The usual approach is to express the transfer function as a matrix of parameters. These parameters can be impedances, but there is a large number of other approaches, see two-port network.

دوائر متكافئة

معاوقة كهربائية مزدوجة

Impedances in series: $Z_{e q} = Z_{1} + Z_{2} + \dots + Z_{n} .$

Impedances in parallel: $\frac{1}{Z_{e q}} = \frac{1}{Z_{1}} + \frac{1}{Z_{2}} + \dots + \frac{1}{Z_{n}} .$

The above simplified for only two impedances in parallel:

Z_{e q} = \frac{Z_{1} Z_{2}}{Z_{1} + Z_{2}} .

Delta-wye transformation

Delta-to-star transformation equations

R_{a} = \frac{R_{a c} R_{a b}}{R_{a c} + R_{a b} + R_{b c}}

R_{b} = \frac{R_{a b} R_{b c}}{R_{a c} + R_{a b} + R_{b c}}

R_{c} = \frac{R_{b c} R_{a c}}{R_{a c} + R_{a b} + R_{b c}}

Star-to-delta transformation equations

R_{a c} = \frac{R_{a} R_{b} + R_{b} R_{c} + R_{c} R_{a}}{R_{b}}

R_{a b} = \frac{R_{a} R_{b} + R_{b} R_{c} + R_{c} R_{a}}{R_{c}}

R_{b c} = \frac{R_{a} R_{b} + R_{b} R_{c} + R_{c} R_{a}}{R_{a}}

General form of network node elimination

R_{x y} = R_{x} R_{y} \sum_{i = 1}^{N} \frac{1}{R_{i}}

For a star-to-delta ( $N = 3$ ) this reduces to:

R_{a b} = R_{a} R_{b} ({\frac{1}{R}}_{a} + {\frac{1}{R}}_{b} + {\frac{1}{R}}_{c}) = \frac{R_{a} R_{b} (R_{a} R_{b} + R_{a} R_{c} + R_{b} R_{c})}{R_{a} R_{b} R_{c}} = \frac{R_{a} R_{b} + R_{b} R_{c} + R_{c} R_{a}}{R_{c}}

For a series reduction ( $N = 2$ ) this reduces to:

R_{a b} = R_{a} R_{b} ({\frac{1}{R}}_{a} + {\frac{1}{R}}_{b}) = \frac{R_{a} R_{b} (R_{a} + R_{b})}{R_{a} R_{b}} = R_{a} + R_{b}

For a dangling resistor ( $N = 1$ ) it results in the elimination of the resistor because $(\binom{1}{2}) = 0$ .

Source transformation

V_{s} = R I_{s}

or

I_{s} = \frac{V_{s}}{R}

الشبكات البسيطة

Voltage division of series components

V_{i} = Z_{i} I = (\frac{Z_{i}}{Z_{1} + Z_{2} + \dots + Z_{n}}) V

Current division of parallel components

I_{i} = (\frac{(\frac{1}{Z_{i}})}{(\frac{1}{Z_{1}}) + (\frac{1}{Z_{2}}) + \dots + (\frac{1}{Z_{n}})}) I

for $i = 1, 2, . . ., n .$

Special case: Current division of two parallel components

I_{1} = (\frac{Z_{2}}{Z_{1} + Z_{2}}) I

I_{2} = (\frac{Z_{1}}{Z_{1} + Z_{2}}) I

Nodal analysis

Mesh analysis

Superposition

اختيار الطريقة

Transfer function

Two terminal component transfer functions

Resistor	$Z (s) = R$
Inductor	$Z (s) = s L$
Capacitor	$Z (s) = \frac{1}{s C}$

Resistor	$Z (j ω) = R$
Inductor	$Z (j ω) = j ω L$
Capacitor	$Z (j ω) = \frac{1}{j ω C}$

Resistor	$Z = R$
Inductor	$Z = 0$
Capacitor	$Z = \infty$

Two port network transfer function

$A (j ω) = \frac{V_{o}}{V_{i}}$

$A (ω) = | \frac{V_{o}}{V_{i}} |$

Two port parameters

$[\begin{matrix} V_{1} \\ V_{0} \end{matrix}] = [\begin{matrix} z (j ω)_{11} & z (j ω)_{12} \\ z (j ω)_{21} & z (j ω)_{22} \end{matrix}] [\begin{matrix} I_{1} \\ I_{0} \end{matrix}]$

$[z (j ω)]$ or just $[z]$

Distributed components

تحليل الصورة

Non-linear networks

i = I_{o} (e^{\frac{v}{V_{T}}} - 1)

Constitutive equations

f (v, i) = 0

f (v, φ) = 0

f (v, q) = 0

Boolean analysis of switching networks

Separation of bias and signal analyses

Graphical method of dc analysis

Small signal equivalent circuit

Piecewise linear method

Time-varying components

انظر أيضا

المصادر

^ Belevitch V (1962). "Summary of the history of circuit theory". Proceedings of the IRE. 50 (5): 849. doi:10.1109/JRPROC.1962.288301. {{cite journal}}: Unknown parameter |month= ignored (help) cites "IRE Standards on Circuits: Definitions of Terms for Linear Passive Reciprocal Time Invariant Networks, 1960". Proceedings of the IRE. 48 (9): 1609. 1960. doi:10.1109/JRPROC.1960.287676. {{cite journal}}: Unknown parameter |month= ignored (help)to justify this definition.
Sidney Darlington Darlington S (1984). "A history of network synthesis and filter theory for circuits composed of resistors, inductors, and capacitors". IEEE Trans. Circuits and Systems. 31 (1): 4.
follows Belevitch but notes there are now also many colloquial uses of "network".

وصلات خارجية

Circuit Analysis Techniques — includes node/mesh analysis, superposition, and thevenin/norton transformation
Nodal Analysis of Op Amp Circuits
Analysis of Resistive Circuits
Circuit Analysis Related Laws, Examples and Solutions
Solved problems in electrical circuits

[1] Belevitch V (1962). "Summary of the history of circuit theory". Proceedings of the IRE. 50 (5): 849. doi:10.1109/JRPROC.1962.288301. {{cite journal}}: Unknown parameter |month= ignored (help) cites "IRE Standards on Circuits: Definitions of Terms for Linear Passive Reciprocal Time Invariant Networks, 1960". Proceedings of the IRE. 48 (9): 1609. 1960. doi:10.1109/JRPROC.1960.287676. {{cite journal}}: Unknown parameter |month= ignored (help)to justify this definition.
Sidney Darlington Darlington S (1984). "A history of network synthesis and filter theory for circuits composed of resistors, inductors, and capacitors". IEEE Trans. Circuits and Systems. 31 (1): 4.
follows Belevitch but notes there are now also many colloquial uses of "network".

[1]