- Independent Voltage and Current Sources Definition: Independent sources are defined as sources whose output is fixed by their characteristics, not dependent on other circuit elements.
- Independent Voltage Source: Maintains a specific voltage across its terminals regardless of current flow, such as in batteries or generators.
- Independent Current Source: Maintains a specific current through its terminals regardless of voltage, as seen in photovoltaic cells.
- Ideal Sources: These theoretical sources have no internal resistance and provide infinite power, used for simplifying circuit analysis.
- Source Conversion: Voltage sources can be converted to current sources and vice versa by finding equivalent currents and resistances, essential for circuit design.
A voltage source sets a specified electric potential difference across its terminals. A current source sets a specified electric current through its branch. The current drawn from a voltage source and the voltage across a current source depend on the rest of the circuit.
Sources are classified as independent or dependent according to what sets their specified value. A separate distinction identifies whether a source is an ideal circuit element or a practical device with limits.
What is an Independent Voltage or Current Source?
An independent source has a specified voltage or current that is not controlled by another voltage or current in the circuit. Its value may be constant or may follow a stated function of time.
An ideal independent voltage source maintains its specified terminal voltage while the circuit determines its current. An ideal independent current source maintains its specified branch current while the circuit determines its terminal voltage.
A DC source has a constant specified value. A time-varying source follows a defined waveform such as a sinusoidal wave, pulse or ramp. A source can therefore be independent without being constant.
The symbols below use a circle for an independent source. An arrow inside a current-source symbol shows the reference direction of current. Plus and minus signs on a voltage-source symbol show the reference polarity of voltage.
Batteries, solar cells, generators and alternators are practical devices, not ideal sources. A battery or generator can approximate an independent voltage source over a stated load range. An illuminated solar cell is often represented by a light-dependent current source as one part of its equivalent circuit.
What is a Dependent Voltage or Current Source?
A dependent source has an output voltage or current set by another voltage or current elsewhere in the circuit. It is also called a controlled source. The controlling variable and the source output must both be identified.
A voltage-controlled source responds to a measured circuit voltage. A current-controlled source responds to a measured circuit current. The control variable does not need a direct wire connection to the output branch in the circuit model.
The four linear types are a voltage-controlled voltage source, current-controlled voltage source, voltage-controlled current source and current-controlled current source. Their output equals the control variable multiplied by a voltage gain, transresistance, transconductance or current gain.
A diamond identifies a dependent source. An arrow gives the reference direction for a dependent current source, while plus and minus signs give the reference polarity for a dependent voltage source. The controlling voltage or current is labelled elsewhere in the circuit.
Dependent sources are used in circuit models of amplifiers, transistors and operational amplifiers. The source element represents a controlled relationship within the model; the physical device is usually more complex.
The output of a dependent source follows its controlling quantity. A linear source is proportional to that quantity, while a nonlinear controlled-source model may use a more complex function.
What is an Ideal Voltage or Current Source?
An ideal source is a circuit model with an exact voltage-current characteristic. An ideal voltage source has zero series output resistance or impedance. An ideal current source has infinite parallel output resistance or impedance. Neither model includes a built-in power limit.
An ideal voltage source keeps its specified voltage for any current demanded by a compatible circuit. An ideal current source keeps its specified current for any resulting terminal voltage. Real sources depart from these characteristics because of internal impedance, current limits, voltage limits, heating and stored-energy limits.
Ideal independent sources use the same circle, arrow and polarity marks described above. A practical source model adds the relevant series or parallel internal impedance and any operating limits.
No physical source is ideal. A battery can approximate an ideal voltage source when its series resistance causes little voltage drop at the required current. A photovoltaic cell can approximate a current source over part of its operating range when shunt resistance is high, series loss is small and illumination is stable.
How to Convert Between Voltage and Current Sources?
A linear two-terminal source can be written in Thévenin form as a voltage source in series with an impedance, or in Norton form as a current source in parallel with the same impedance. The two forms produce the same terminal voltage and current for every connected load within the model.
To convert a voltage source Vs in series with resistance R, replace it with a current source Is = Vs/R in parallel with R. Keep the source direction consistent with the original voltage polarity.
The Norton current Is equals the short-circuit current of the Thévenin form. With the terminals shorted, the source voltage Vs appears across R, so Ohm’s law gives Is = Vs/R.
The resistance value does not change during conversion. The series resistance in the voltage-source form becomes the parallel resistance in the current-source form. It is also the equivalent resistance seen at the terminals, linking the open-circuit voltage to the short-circuit current under the usual linear-network rules.
To convert a current source Is in parallel with resistance R, replace it with a voltage source Vs = IsR in series with R. Choose the voltage polarity to match the current-source direction.
The Thévenin voltage Vs equals the open-circuit voltage of the Norton form. With no external load, source current Is flows through the parallel resistance R, so Vs = IsR.
The parallel resistance in the current-source form becomes the series resistance in the voltage-source form. It is the same equivalent resistance, not a separate short-circuit resistance.
These source conversions apply to linear two-terminal behaviour where Ohm’s law describes the source resistance or impedance. Other independent sources do not invalidate the method. If a network contains dependent sources, keep them active and use a test source when needed to find the equivalent resistance.
Conclusion
Independent and dependent describe what sets a source value. Ideal and practical describe how closely a source holds its specified voltage or current as the load changes. Keeping these classifications separate prevents common circuit-analysis errors.
Main points to remember are:
- An independent source value is not controlled by another voltage or current in the circuit.
- A dependent source output is controlled by another circuit voltage or current.
- An ideal voltage source has zero output impedance, while an ideal current source has infinite output impedance.
- Practical sources have finite impedance plus current, voltage, power and temperature limits.
- A voltage source Vs in series with R converts to a current source Vs/R in parallel with R.
- A current source Is in parallel with R converts to a voltage source IsR in series with R.
The equivalent voltage-source and current-source forms are interchangeable at their two external terminals, even though current and voltage inside the two models are not the same.
