Independent Current Source

Dependent Voltage & Current Source

Ideal Voltage Source

Ideal Current Source

Current Source to Voltage Source Conversion

There are several **voltage sources** as well as **current sources** encountered in our daily life. Batteries , DC generator or alternator all are very common examples of **voltage source**. There are also some **current sources** encountered in our everyday life, such as photo electric cells, metadyne generator etc.

The sources can be categorized into two different types – independent source and dependent source.

## Independent Voltage Source

Output of an independent source does not depend upon the voltage or electric current of any other part of the network. When terminal voltage of a **voltage source** is not affected by the current or voltage of any other part of the network, then the source is said to be an **independent voltage source **. This type of sources may be referred as constant source or time variant source. When terminal voltage of an independent source remains constant throughout its operation, it is referred as time–invariant or constant **independent voltage source **.

Again independent voltage source can be time–variant type, where the output terminal voltage of the source changes with time. Here, the terminal voltage of the source does not vary with change of voltage or electric current of any other part of the network but it varies with time.

## Independent Current Source

Similarly, output electric current of independent current source does not depend upon the voltage or electric current of any other part of the network. It is also categorized as independent time-invariant and time-variant current source .

Symbolic representations of independent time-invariant and time-variant voltage and current source s are shown below.

Now we will discuss about dependent voltage or **current source**. Dependent voltage source is one that's output voltage is the function of voltage or current of any other part of the circuit. Similarly, dependent **current source** is one that's output current is the function of electric current or voltage of any other parts of the circuit. The amplifier is an ideal example of dependent source where the output signal depends upon the signal given to the input circuit of the amplifier.

## Dependent Voltage Source & Dependent Current Source

There are four possible dependent sources as are represented below,

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- Voltage dependent voltage source .
- Current dependent voltage source .
- Voltage dependent current source .
- Current dependent current source .

Dependent voltage source s and dependent current sources can also be time variant or time invariant. That means, when the output voltage or current of a dependent source is varied with time, referred as time invariant dependent current or voltage source and if not varied with time, it is referred as time variant.

## Ideal Voltage Source

Now we will discuss about **ideal voltage source **.

In every practical voltage source , there is some electrical resistance inside it. This resistance is called internal resistance of the source. When the terminal of the source is open circuited, there is no current flowing through it; hence there is no voltage drop inside the source but when load is connected with the source, current starts flowing through the load as well as the source itself. Due to the resistance inside the voltage source , there will be some voltage drop across the source. Now if any one measures the terminal voltage of the source, he or she will get the voltage between its terminals which is reduced by the amount of internal voltage drop of the source. So there will be always a difference between no-load (when source terminals are open) and load voltages of a practical voltage source . But in **ideal voltage source ** this difference is considered as zero that means there would not be any voltage drop in it when current flows through it and this implies that the internal resistance of an ideal source must be zero. This can be concluded that, voltage across the source remains constant for all values of load current.

The V-I characteristics of an ideal voltage source is shown below.

There is no as such example of ideal voltage source but a lead acid battery or a dry cell can be considered an example when the electric current drawn is below a certain limit.

## Ideal Current Source

**Ideal current source s** are those sources that supply constant electric current to the load irrespective of their impedance. That means, whatever may be the load impedance; ideal current source always gives same electric current through it. Even if the load has infinite impedance or load, is open circuited to the **ideal current source ** that gives the same electric current through it. So naturally from definition, it is clear that this type of current source is not practically possible.

## Current Source to Voltage Source Conversion

All sources of electrical energy give both electric current as well as voltage. This is not practically possible to distinguish between voltage source and current source . Any electrical source can be represented as voltage source as well as current source . It merely depends upon the operating condition. If the load impedance is much higher than internal impedance of the source, then it is preferable to consider the source as a voltage source on the other hand if the load impedance is much lower than internal impedance of the source; it is preferable to consider the source as a current source . Current source to voltage source conversion or voltage source to current source conversion is always possible.

Now we will discuss how to convert a current source into voltage source and vice-versa.

Let us consider a voltage source which has no load terminal voltage or source voltage V and internal resistance r. Now we have to convert this to an equivalent current source . For that, first we have to calculate the electric current which might be flowing through the source if the terminal A and B of the voltage source were short circuited. That would be nothing but I = V / r. This electric current will be supplied by the equivalent current source and that source will have the same resistance connected across it.

Similarly a current source of output electric current I in parallel with resistance r can be converted into an equivalent voltage source of voltage V = Ir and resistance r connected in series with it.