Utente:Superspritz/Componente elettrico

Un componente ideale è un'astrazione concettuale che rappresenta in modo ideale dispositivi elettrici elementari come resistenze, condensatori e induttori per l'analisi teorica dei circuiti elettrici. Ogni circuito elettrico può essere rappresentato e analizzato sotto forma di collegamenti tra componenti multipli; se il componente corrisponde grosso modo anche al dispositivo fisico reale, la rappresentazione costituisce uno schema elettrico a parametri concentrati. In altri casi, come ad esempio per modellare le linee trasmissive i componenti rappresentano elementi infinitesimali (schema a parametri distribuiti).

I componenti ideali, pur rappresentando dispositivi fisici reali, non hanno un corrispettivo reale dato che si assume che le loro proprietà siano ideali, mentre i componenti reali hanno proprietà non ideali, valori reali caratterizzati da tolleranza rispetto al valore nominale e possiedono un determinato grado di non linearità. Per questo motivo, per poter modellare e approssimare il funzionamento di un componente reale tenendo conto degli aspetti non ideali può essere necessario rappresentarlo combinando tra loro più componenti ideali differenti. Per esempio, un induttore ideale è caratterizzato dalla sola induttanza e non presenta né resistenza né capacità mentre un induttore fisico reale, come ad esempio una bobina, presenta anche un valore di resistenza e quindi la sua rappresentazione in uno schema a componenti ideali è costituita da un induttore ideale collegato in serie a un resistore ideale.

L'analisi dei circuiti basata sui componenti ideali è utile per comprendere il funzionamento pratico dei circuiti elettrici reali: analizzando e combinando gli effetti risultanti generati dai componenti ideali è possibile stimare il comportamento effettivo reale.

Tipi

I componenti si possono classificare in diverse categorie; una di queste si basa sul numero di terminali disponibili per i collegamenti con gli altri componenti:

• Bipolari  – sono i più semplici e presentano per il collegamento solo due terminali. Esempi sono le resistenze, i condensatori, le induttanze e i diodi
• Multipolari  – che si collegano agli altri dispositivi tramite coppie di terminali. Ogni coppia di terminali costituisce un "porta". Per esempio, un trasformatore a tre avvolgimenti è dotato di sei terminali e viene rappresentato in maniera ideale come un elemento a tre porte, ciascuna composta da una coppia. Gli elementi più comuni di questo tipo sono i componenti a due porte, caratterizzati da due coppie di terminali.

I componenti si possono suddividere anche tra:

• Componenti attivi o generatori  – sono elementi in grado di generare potenza elettrica, come i generatori di tensione o i generatori di corrente. Tipicamente si usano per modellare batterie e alimentatori. A questa categoria appartengono i
  • generatori controllati  – in cui la tensione o la corrente generate sono proporzionali alla tensione o alla corrente applicata a un'altra coppia di terminali. Si uano per modellare amplificatori come i transistor, le valvole termoioniche e gli amplificatori operazionali.
• Componenti passivi  – sono elementi che non sono in grado di generare autonomamente energica, come ad esempio le resistenze, le capacitanze e le induttanze.

Un'ulteriore distinzione classifica tra:

• componenti lineari  – in cui la relazione tra tensione e corrente è una funzione lineare e si può applicare il principio della sovrapposizione degli effetti. Esempi di componenti lineari sono le resistenze, le capacitanze, le induttanze e i generatori controllari lineari. I circuiti composti da soli componenti lineari, detti anche circuiti lineari, non presentano fenomeni come l'intermodulazione e possono essere analizzati tramite techniche matematiche potenti come la trasformata di Laplace.
• componenti non lineari  – in cui la relazione tra tensione e corrente è esprimibile tramite una funzione non lineare. Un esempio è il diodo, in cui la corrente è una funzione esponenziale della tensione. I circuiti che comprendono componenti non lineari sono più complessi da analizzare e da progettare e spesso è necessario ricorrere a programmi di simulazione come per esempio SPICE.

One-port elements

Only nine types of element (memristor not included), five passive and four active, are required to model any electrical component or circuit. Each element is defined by a relation between the state variables of the network: current, $I$; voltage, $V$, charge, $Q$; and magnetic flux, $\Phi$.

• Two sources:
  • Current source, measured in amperes – produces a current in a conductor. Affects charge according to the relation $dQ=-I\,dt$.
  • Voltage source, measured in volts – produces a potential difference between two points. Affects magnetic flux according to the relation $d\Phi =V\,dt$.

$\Phi$ in this relationship does not necessarily represent anything physically meaningful. In the case of the current generator, $Q$, the time integral of current, represents the quantity of electric charge physically delivered by the generator. Here $\Phi$ is the time integral of voltage but whether or not that represents a physical quantity depends on the nature of the voltage source. For a voltage generated by magnetic induction it is meaningful, but for an electrochemical source, or a voltage that is the output of another circuit, no physical meaning is attached to it.

Both these elements are necessarily non-linear elements. See #Non-linear elements below.

• Three passive elements:
  • Resistance $R$, measured in ohms – produces a voltage proportional to the current flowing through the element. Relates voltage and current according to the relation $dV=R\,dI$.
  • Capacitance $C$, measured in farads – produces a current proportional to the rate of change of voltage across the element. Relates charge and voltage according to the relation $dQ=C\,dV$.
  • Inductance $L$, measured in henries – produces the magnetic flux proportional to the rate of change of current through the element. Relates flux and current according to the relation $d\Phi =L\,dI$.
• Four abstract active elements:
  • Voltage-controlled voltage source (VCVS) Generates a voltage based on another voltage with respect to a specified gain. (has infinite input impedance and zero output impedance).
  • Voltage-controlled current source (VCCS) Generates a current based on a voltage elsewhere in the circuit, with respect to a specified gain, used to model field-effect transistors and vacuum tubes (has infinite input impedance and infinite output impedance). The gain is characterised by a transfer conductance which will have units of siemens.
  • Current-controlled voltage source (CCVS) Generates a voltage based on an input current elsewhere in the circuit with respect to a specified gain. (has zero input impedance and zero output impedance). Used to model trancitors. The gain is characterised by a transfer impedance which will have units of ohms.
  • Current-controlled current source (CCCS) Generates a current based on an input current and a specified gain. Used to model bipolar junction transistors. (Has zero input impedance and infinite output impedance).

These four elements are examples of two-port elements.

Non-linear elements

Conceptual symmetries of resistor, capacitor, inductor, and memristor.

In reality, all circuit components are non-linear and can only be approximated to linear over a certain range. To more exactly describe the passive elements, their constitutive relation is used instead of simple proportionality. From any two of the circuit variables there are six constitutive relations that can be formed. From this it is supposed that there is a theoretical fourth passive element since there are only five elements in total (not including the various dependent sources) found in linear network analysis. This additional element is called memristor. It only has any meaning as a time-dependent non-linear element; as a time-independent linear element it reduces to a regular resistor. Hence, it is not included in linear time-invariant (LTI) circuit models. The constitutive relations of the passive elements are given by;

• Resistance: constitutive relation defined as $f(V,I)=0$.
• Capacitance: constitutive relation defined as $f(V,Q)=0$.
• Inductance: constitutive relation defined as $f(\Phi ,I)=0$.
• Memristance: constitutive relation defined as $f(\Phi ,Q)=0$.

where $f(x,y)$ is an arbitrary function of two variables.

In some special cases the constitutive relation simplifies to a function of one variable. This is the case for all linear elements, but also for example, an ideal diode, which in circuit theory terms is a non-linear resistor, has a constitutive relation of the form $V=f(I)$. Both independent voltage, and independent current sources can be considered non-linear resistors under this definition.

The fourth passive element, the memristor, was proposed by Leon Chua in a 1971 paper, but a physical component demonstrating memristance was not created until thirty-seven years later. It was reported on April 30, 2008, that a working memristor had been developed by a team at HP Labs led by scientist R. Stanley Williams. With the advent of the memristor, each pairing of the four variables can now be related.

There are also two special non-linear elements which are sometimes used in analysis but which are not the ideal counterpart of any real component:

• Nullator: defined as $V=I=0$
• Norator: defined as an element which places no restrictions on voltage and current whatsoever.

These are sometimes used in models of components with more than two terminals: transistors for instance.

==Two-port elements== ... All the above are two-terminal, or one-port, elements with the exception of the dependent sources. There are two lossless, passive, linear two-port elements that are normally introduced into network analysis. Their constitutive relations in matrix notation are;

Transformer

${\begin{bmatrix}V_{1}\\I_{2}\end{bmatrix}}={\begin{bmatrix}0&n\\-n&0\end{bmatrix}}{\begin{bmatrix}I_{1}\\V_{2}\end{bmatrix}}$

Gyrator

${\begin{bmatrix}V_{1}\\V_{2}\end{bmatrix}}={\begin{bmatrix}0&-r\\r&0\end{bmatrix}}{\begin{bmatrix}I_{1}\\I_{2}\end{bmatrix}}$

The transformer maps a voltage at one port to a voltage at the other in a ratio of n. The current between the same two port is mapped by 1/n. The gyrator, on the other hand, maps a voltage at one port to a current at the other. Likewise, currents are mapped to voltages. The quantity r in the matrix is in units of resistance. The gyrator is a necessary element in analysis because it is not reciprocal. Networks built from the basic linear elements only are obliged to be reciprocal and so cannot be used by themselves to represent a non-reciprocal system. It is not essential, however, to have both the transformer and gyrator. Two gyrators in cascade are equivalent to a transformer but the transformer is usually retained for convenience. Introduction of the gyrator also makes either capacitance or inductance non-essential since a gyrator terminated with one of these at port 2 will be equivalent to the other at port 1. However, transformer, capacitance and inductance are normally retained in analysis because they are the ideal properties of the basic physical components transformer, inductor and capacitor whereas a practical gyrator must be constructed as an active circuit.

Examples

The following are examples of representation of components by way of electrical elements.

• On a first degree of approximation, a battery is represented by a voltage source. A more refined model also includes a resistance in series with the voltage source, to represent the battery's internal resistance (which results in the battery heating and the voltage dropping when in use). A current source in parallel may be added to represent its leakage (which discharges the battery over a long period of time).
• On a first degree of approximation, a resistor is represented by a resistance. A more refined model also includes a series inductance, to represent the effects of its lead inductance (resistors constructed as a spiral have more significant inductance). A capacitance in parallel may be added to represent the capacitive effect of the proximity of the resistor leads to each other. A wire can be represented as a low-value resistor
• Current sources are more often used when representing semiconductors. For example, on a first degree of approximation, a bipolar transistor may be represented by a variable current source that is controlled by the input current.

See also

• Transmission line