What is Dependent Voltage Source?

The dependent voltage source is a four terminal device whose output voltage is controlled either by circuit current or voltage. The output voltage is dependent on the input voltage or current flowing in the circuit. The output voltage increase or decrease linearly with increase/decresae in the input voltage or circuit current.Therefore, the dependent voltage source is also called controlled voltage source.

The symbol of the dependent voltage source is as given below.

An ideal voltage source has its output constant irrespective of the whatever magnitude of the current flowing in the circuit. on contrary the output voltage of the dependent voltage source depends on the magnitude of the circuit current.Thus, the output voltage of dependent or controlled voltage source can not remain constant.

The output voltage of the dependent volatge source depends on the magnitude of the current and the input voltage. Based on this, the dependent voltage source can be classified into two categories.

• Voltage controlled voltage source(VCVS)
• Current controlled voltage source(CCVS)

The voltage source whose output depends on the input voltage is called voltage controlled voltage source(VCVS).

The voltage source whose output depends on the current flowing in the circuit is called current controlled voltage source(CCVS).

Voltage Controlled Voltage Source(VCVS)

The output voltage of dependent voltage source is scalar multiples of the input voltage. If the input voltage is 5 volts the output voltage can not be equal to the input voltage and the output voltage is equal to the input voltage multiplying by a constant. A multiplying constant is called the dependency factor or scaling factor of the dependent voltage source.

The output voltage V_out of dependent voltage source is dependent on the input voltage V_in. The output voltage V_out is  μ times of the input voltage V_in . Here  is the constant known as dependency factor or the scaling factor.

Thus the dependency factor μ is dimensionless quantity. The example of VCVS is an ideal transformer. The output voltage V₂ linearly increase or decrease with increase or decrease of the voltage V₁ at the primary side of the transformer. This happens because the voltage drop does not take place in an ideal transformer. The secondary voltage  V₂ is function of the primary voltage V₁, and the magnitude of the secondary voltage depends on the voltage transformation ratio of the transformer. 

Using transformation ratio,

In an ideal transformer, the secondary voltage has linear relationship with the input voltage. An ideal transformer is thus an example of dependent voltage source.

Current Controlled Voltage Source(CCVS)

The magnitude of the input voltage depends on the multiplying constant times the controlling current input generated elsewhere within the connecetd circuit. This dependency of the output voltage on the value of the input current makes it a dependent current source and this is the reason the voltage source is called current controlled voltage source(CCVS).

It can be seen from the above diagram that the output voltage of CCVS has linear relationship with the input current. I_i determines the magnitude of the output voltage. The output voltage V_out is equal to the product of the input current I_i and dependency constant ρ. Thus the output voltage V_out is equal to:

V_{out =} ρ I<sub>i

ρ =</sub> V_{out /} I_i

The unit of the dependency constant is Ohm(Ω) and unit of the dependency constant is Volts/ amperes.

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