4.2.5. Conversion circuits with the ideal voltage and current sources

So as a voltage source and current source are sources of energy, they can be converted into each other. So for the real voltage source (fig. 1.4,b) and real current source (Fig.1.6.b) if the same currents ‘’ I ’’ and voltages "u", expressing the current from the relation (1.32), we get

(4.58)

and equating it (1.33), we obtain

(4.59)

Expressing voltage from the ratio (1.33)

(4.60)

and equating it to (1.32), we obtain

(4.61)

There are also methods for transferring an ideal voltagу source and current source. Let us consider Fig. 4.9. Compile equations of Kirchhoff's laws for the network on Fig. 4.9, а

Fig. 4.9

Compile equations of Kirchhoff's laws for the network of Fig. 4.9.a

For the nodes A and b we get:

(4.62)

Or, in short we obtain

(4.63)

For the loops I – IV we get:

(4.64)

(4.65)

(4.66)

(4.67)

Make an equation for the circuit of Fig. 4.9.b

For the node A we get:

(4.68)

For the nodes I – IV we obtain:

(4.69)

(4.70)

(4.71)

(4.72)

Hence we see the equations (4.63) and (4.68), (4.64) - (4.67) and (4.69) - (4.72) are identical. That is the networks of Fig. 4.9.a and Fig. 4.9.b are equivalent. As a result we can conclude: if an ideal voltage source is included between two nodes, it can be transferred to all branches growing from one of the nodes.

Fig.4.10

Let us consider Fig. 4.10,a. According to the Kirchhoff's law for the current for nodes A, B, C we get

(4.73)

(4.74)

(4.75)

For the network of Fig. 4.10,b we can write down for the nodes A, B, C

(4.76)

(4.77)

(4.78)

Hence we see the equations (4.73) - (4.75 and (4.76) - (4.78) are identical. Therefore the networks of Fig. 4.10 and Fig.. 4.10,b are equivalent. As a result of a conclusion can be made: if an ideal current source is included between two nodes, it can be moved in parallel all branches, forming a path between these nodes.