Dependent and Independent Sources

Understanding Electrical Sources

An electrical source is any element that supplies electrical energy to a circuit. It provides the necessary voltage or current that drives the flow of charge through components.

Independent vs. Dependent Sources

Sources are classified based on how their values are determined.

Independent Sources

An independent source supplies a voltage or current whose value does not depend on any other voltage or current in the circuit. The value is set externally and remains fixed regardless of the surrounding network.

Independent sources are drawn as circles in circuit diagrams.

Dependent (Controlled) Sources

A dependent source provides a voltage or current that is controlled by another variable elsewhere in the circuit. Its value is a function of that controlling variable.

Dependent sources are represented by a diamond-shaped symbol, not a circle.

Key Differences Summarized

• Independent: Value set independently; symbol is a circle.
• Dependent: Value controlled by another variable; symbol is a diamond.

Common Types of Dependent Sources

Dependent sources are further categorized by the nature of their controlling variable (voltage or current) and their output (voltage or current). The four standard types are:

1. VCVS – Voltage‑Controlled Voltage Source: The output voltage is proportional to a controlling voltage.
2. VCCS – Voltage‑Controlled Current Source: The output current is proportional to a controlling voltage. The governing equation is in = g·vn, where g is the transconductance measured in Siemens (S).
3. CCVS – Current‑Controlled Voltage Source: The output voltage is proportional to a controlling current. Its equation can be expressed as vn = r·in, where r is the transresistance.
4. CCCS – Current‑Controlled Current Source: The output current is proportional to a controlling current, often written as β·in, where β denotes the current gain.

VCVS vs. VCCS

Both VCVS and VCCS are voltage‑controlled, but they differ in what they produce:

• VCVS: Produces a voltage output that follows the controlling voltage.
• VCCS: Produces a current output that follows the controlling voltage.

CCVS Example

In a CCVS, the output voltage is directly proportional to a controlling current. The relationship vn = r·in shows that the proportionality constant r (transresistance) determines how much voltage appears for a given current.

CCCS Example

A CCCS outputs a current that is β·in times the controlling current, where β is the current gain factor.

Units and Truth Statements

• The unit of transconductance (g) is Siemens (S). This statement is true.
• A diamond symbol indicates a dependent source; a circle indicates an independent source. The claim that a dependent source is represented by a circle is false.
• A 12 V battery qualifies as an independent voltage source only when its voltage is specified independently of other circuit variables. This condition is true.

Practical Implications

When analyzing circuits, recognizing the type of source is crucial for applying the correct equations and for correctly interpreting the schematic symbols. Independent sources provide fixed references, while dependent sources introduce relationships that must be accounted for in circuit equations, such as Kirchhoff’s laws or nodal analysis.

For example, in a circuit containing a VCCS, the current contributed by the source will be in = g·vn. If the controlling voltage vn changes, the source current changes proportionally, affecting the overall node currents and potentially the operating point of the circuit.

Similarly, a CCVS will affect voltage drops across elements connected to its terminals, because its output voltage depends on a controlling current elsewhere in the network.

Summary Table

Conclusion

Distinguishing between independent and dependent sources, recognizing their symbols, and understanding the four primary dependent‑source types are foundational skills for anyone studying electrical circuits. Mastery of these concepts enables accurate circuit analysis and design, ensuring that the influence of each source is correctly incorporated into calculations.