ACTIVE AND PASSIVE CIRCUIT ELEMENTS

An electric circuit is simply an interconnection of the element. Circuit analysis is the process of determining the current through the elements or voltages across the elements of the circuit.
There are two types of elements found in electric circuits :- Active element and Passive elements, by considering the energy delivered to or by them.
A circuit element is said to be passive if the total energy delivered to it from the rest of the circuit is always non-negative i.e.

w=∫p dt=∫v.i dt ≥ 0

Of course, an active element is one that is not passive. That is equation (1.10) does not hold good for all time. In general, an active element is capable of generating energy while a passive element is not. Examples of passive elements are resistors, inductors, and capacitors. Examples of active elements are generators, batteries, and operational amplifiers.
The most important active elements are voltage or current sources that generally delivers power to the circuit connected to them. There are two types of sources :- Independent and Dependent sources.

An independent voltage source is a two-terminal element that maintains a specified voltage between its terminals. The voltage is completely independent of current through the element. Physical sources such as generator and batteries may be regarded as approximations to ideal voltage source. 

Note that both symbols of above figure can be used to represent DC voltage source, but the symbol of figure(a) can be used for a time varying voltage source.

 An independent current source is a two-terminal element that provides a specified current completely independent of the voltage across the source.

Independent sources are usually meant to deliver power to the external circuit. Symbol above is true for both DC and AC current source. For example i=2Amp is DC current source and i=2sin(100Πt) is AC current source.



Dependent sources are usually designated by diamond-shaped symbols.

A dependent or controlled voltage source is similar to an independent source expect that the voltage across the source terminals is a function of other voltage or currents in the circuit.

A voltage-controlled voltage source is a voltage source having a voltage equal to a constant times the voltage across a pair of terminals elsewhere in the network. This is shown in figure (c).
A current-controlled voltage source is a voltage source having a voltage equal to a constant times the current through some other element in the circuit. This is shown in figure (d). The factor multiplying the current is called the gain parameters.
The current flowing through a dependent current source is determined by a current or voltage elsewhere in the circuit. Two example of current controlled current sources are shown below :-

A current-controlled current source is shown in figure (e). In this case it is assumed that current through the source is 2-times the value of iₓ. A voltage-controlled current source is shown in figure (f). The current through the source is 3-times the voltage vₓ. The factor multiplying the voltage is called the gain parameter.
Controlled-voltage sources and controlled-current sources are useful in constructing circuit models for many types of real-world devices, such as transistor,transformers,electrical machines and electronics amplifiers.
In summary, there are four kinds of controlled sources,

1. Voltage-Controlled Voltage Sources (VCVS)
2. Current-Controlled Voltage Sources (CCVS)
3. Current-Controlled Current Sources (CCCS)
4. Voltage-Controlled Current Sources (VCCS)