Electrical element

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The concept of electrical elements is used in the analysis of electrical networks. Any electrical network can be modeled by decomposing it down to multiple, interconnected electrical elements in a schematic diagram or circuit diagram. Each electrical element affects the voltage in the network or current through the network in a particular way. By analyzing the way a network is affected by its individual elements, it is possible to estimate how a real network will behave on a macro scale.

Contents 1 Elements vs. components 2 The elements 3 Examples 4 References 5 See also

[edit] Elements vs. components

There is a distinction between real, physical electrical or electronic components and the ideal electrical elements by which they are represented.

• Electrical elements do not exist physically, and are assumed to have ideal properties according to a lumped element model.
• Conversely, components do exist, have less than ideal properties, their values always have a degree of uncertainty, they always include some degree of nonlinearity and typically require a combination of multiple electrical elements to approximate their functions.

Circuit analysis using electric elements is useful for understanding many practical electrical networks using components.

[edit] The elements

The four fundamental circuit variables are current, I; voltage, V, charge, Q; and magnetic flux, Φ_m. Only 6 elements, produced by manipulating these four variables, are required to represent any component or network:

• Two sources:
  • Current source, measured in amperes - produces a current in a conductor. Affects charge according to the relation dQ = − Idt.
  • Voltage source, measured in volts - produces a potential difference between two points. Affects magnetic flux according to the relation dΦ_m = Vdt.

• Four 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 = RdI.
  • 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 = CdV.
  • Inductance L, measured in henries - produces a voltage proportional to the rate of change of current through the element. Relates flux and current according to the relation dΦ_m = LdI.
  • Memristance M – produces a current such that the rate of change of current is proportional to the rate of change of voltage across the element. Relates flux and charge according to the relation dΦ_m = MdQ.

• 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 with respect to a specified gain, used to model Field Effect Transistors and vacuum tubes (has infinite input impedance and infinite output impedance).
  • Current Controlled Voltage Source (CCVS) Generates a voltage based on an input current with respect to a specified gain. (has zero input impedance and zero output impedance).
  • 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).

The fourth element, the memristor, was theorized 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.^[1][2][3][4] With the advent of the memristor, each pairing of the four variables can now be related. Memristors are able to store one bit of non-volatile memory. They may see application in programmable logic, signal processing, neural networks, and control systems, among other fields. Because memristors are time-variant by definition, they are not included in linear time-invariant (LTI) circuit models.

[edit] 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 voltage.

[edit] References

[edit] See also

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• Electrical or electronic component