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Active Elements: Network Theory
When a network element or circuit element has the ability to deliver electrical energy or to produce power gain in the circuit, the element is called an active element. In other words, a circuit element for which the slope of its characteristic curve at any point is negative, or which can supply power to the rest of the network under some operating condition, is an active element. Active elements are therefore the network elements that deliver power to other elements present in an electric circuit. Active elements are commonly realized as sources of voltage or current.
Types of Sources
Sources that provide voltage or current in circuits are classified into two broad categories: Independent Sources Dependent (Controlled) Sources
Independent Sources
Independent sources produce a fixed value of voltage or current which does not depend on any other voltage or current in the circuit. Independent sources are of two main kinds. Independent Voltage Sources Independent Current Sources
Independent Voltage Sources
An independent voltage source produces a constant voltage across its two terminals; this voltage is independent of the current flowing through the source.
The V-I characteristic of an ideal independent voltage source is a
constant (flat) line: the terminal voltage equals the source voltage for any value of current. For an ideal voltage source, the internal (series) resistance is zero.
Practical voltage sources differ from the ideal case because they have a
non-zero internal (series) resistance; therefore, the terminal voltage falls
when the output current increases due to the drop across the internal resistance.
Independent Current Sources
An independent current source produces a constant current through its
terminals; this current is independent of the voltage across the source.
The V-I characteristic of an ideal independent current source is a
constant line: the source current is the same regardless of the terminal voltage. For an ideal current source, the internal (shunt) resistance is infinite. Practical current sources include a finite shunt resistance, so the actual current delivered can vary slightly with the terminal voltage due to currents through the internal resistance. There is a deviation in the V-I characteristic of a practical current source from the ideal characteristic because some portion of the current may flow through the internal shunt resistance.
Dependent (Controlled) Sources
Dependent sources produce a voltage or current whose magnitude depends on some other voltage or current in the circuit. They are also called controlled sources. Dependent sources are useful for modelling active devices (for example, transistors, op-amps) in circuit analysis. Dependent sources are grouped into two main categories: Dependent Voltage Sources
Dependent (controlled) sources appear naturally in the equivalent circuit models of transistors and operational amplifiers; they allow linear circuit analysis techniques to model device behaviour.
Source Transformation Technique
Often in circuit analysis it is convenient to convert a practical voltage source (an ideal voltage source in series with a resistance) into an equivalent practical current source (an ideal current source in parallel with the same resistance), or vice versa. This conversion is valid only from the point of view of the external terminals: the two forms are equivalent as seen by the rest of the circuit. Transform a practical voltage source into a practical current source. Transform a practical current source into a practical voltage source.
Practical Current Source into a Practical Voltage Source
A practical current source consists of an ideal current source IS in parallel with a shunt resistance RS. The equivalent practical voltage source consists of an ideal voltage source VS in series with the same resistance RS. The value of the equivalent voltage source is the product of the source current and the resistance:
Practical Voltage Source into a Practical Current Source
A practical voltage source consists of an ideal voltage source VS in series with a series resistance RS. The equivalent practical current source consists of an ideal current source IS in parallel with the same resistance RS.
The numerical relation between the voltage source, the current source and the resistance is: 𝐼 (^) 𝑆 = 𝑉 (^) 𝑆 / 𝑅 (^) 𝑆 Summary An active element is any circuit element that can deliver power to the network. Active elements are principally classified into independent sources (fixed voltage or current) and dependent (controlled) sources (output depends on some other circuit variable). Ideal voltage sources have zero internal resistance; ideal current sources have infinite internal resistance. Practical sources include series or shunt resistance and can be transformed into each other using the source transformation relations.
