Practical Voltage Source

 Practical Voltage Source

An Ideal Voltage Source can't be a Practical Voltage Source, it's not practical possible. there's no source which may maintain its terminal voltage constant when its terminals are shot-circuited.

It could do so, it would mean that it can supply an infinite amount of power to a short circuit. This is not possible. Hence, an Ideal voltage source does not exist in practice. However, the concept of an ideal voltage source is very helpful in understanding the circuits containing a practical voltage source.

A practical voltage source can be considered to consist of an ideal voltage source in series with an impedance. This impedance is called the internal impedance of the source.

 

A practical voltage source can be considered to consist of an ideal voltage source in series with an impedance. This impedance is called the internal impedance of the source.

The symbolic representation of practical voltage sources are shown in the following figure. :

It is not possible to reach any other terminal except A and B. These are the terminals available for making external connections. In the DC source, since the upper terminal of the ideal voltage source is marked positive, The terminal A will be positive with respect to terminal B. In the AC

source in the above figure, the upper terminal of the ideal voltage source is marked as positive and lower as negative. The marking of the positive and negative on an ac source does not mean the same thing as the markings on a DC source. 

Here (In AC), it means that the upper terminal (terminal A) of the ideal voltage source is positive with respect to the lower terminal at that instant.

In the next half-cycle of AC, the lower terminal will be the positive and the upper is negative. Thus, the positive and negative markings on an AC source indicate the polarities at a given instant of time.

Characteristics of a Practical Voltage Source

Characteristics of a Practical Voltage Source : 

The question arises naturally: What should be the characteristics of a source so that it may be considered a good  constant practical voltage source ?

An Ideal Voltage Source must have zero internal impedance. In Practice, no source can be an ideal one. Therefore, it is necessary to determine how much the value of the internal impedance Z_S should be, so that it can be called a practical voltage source. 

Let us an example. A DC source has an open circuit voltage of 2V, and internal resistance of only 1 Ω. It is connected to a load resistance R_L  as shown in figure below. 

The load resistance can assume any value between 1 Ω to 10 Ω. Let us now find the variation in the terminal voltage of the source.

When the load resistance R_L is 1 Ω, the total resistance in the circuit is 1+1 = 2 Ω. 

The current in the circuit is :  

 

 V_I = V_s/(R_s + R_L)

 = 2/(1+1) = 1 A

The terminal voltage is then

V_T1 = I₁ * R_L1 = (V_S/(R_S + R_L1) * R_L1 )

 = (2/(1+1) *1 )= 1.0V

 

When the load resistance becomes 10Ω, the total resistance in the circuit becomes 10+1 = 11Ω. We can again find the terminal voltage as 

V_T2 = (V_S/(R_S + R_L2) * R_L2 )

= (2/(1+10) *10 )= 1.818V

Thus, we find that the maximum voltage available across the terminals of the source is 1.818V. When the load resistance varies between its extreme limits- from 1Ω to 10Ω

The terminal voltage varies from 1 V to 1.818V. This is certainly a large variation. The variation in the terminal voltage is more than 40 % of the maximum voltage.

 

Let us consider another example, A 600-Ω, 2-V ac source is connected to a variable load as shown in figure below :

The load impedance Z_L can vary from 50kΩ to 500kΩ, again a variation having the same ratio 1:10, as in the case of the first example. We can find the variation in the terminal voltage of the source. When the load impedance is 50kΩ, The terminal voltage is :

V_T1 = (V_S/ (Z_S + Z_L1 )) * Z_L1

 = (2/(600+50 000))*50 000

= 1.976V

When the load impedance is 500kΩ, The terminal voltage is

 

V_T2 = (V_S/ (Z_S + Z_L2)) * Z_L2

= (2/(600+500 000))*500 000

= 1.997V

With respect to the maximum value, the percentage variation in terminal voltage

 

=  (1.997-1.976/(1.997))*100

= 1.05%

We can now compare the two examples. In the first example, although the internal resistance of the dc source is only 1Ω, yet it is not justified to call it a constant voltage source. Its terminal voltages varies by more than 40%. In the second example, although the internal impedance of the ac source is 600Ω, it may still be called a practical constant voltage source, since the variation in its terminal voltage is quit small( only 1.05%).

Thus, we conclude that it is not the absolute value of the internal impedance that decides whether a source is a good constant voltage source or not. It is the value of the internal impedance relative to the load impedance that is important.

 

The lesser the ratio of Z_S/Z_L , the better is the source as a constant voltage source.

No practical voltage source can be an ideal voltage source. Thus, no practical voltage source can have the V-I Characteristics as shown below .

 When the load current is increases, the terminal voltage of a practical voltage source decreases. The characteristics are then modified to that shown above (2 fig).It is sometime preferred to take voltage on the x-axis and current on the y-axis.