Impedance Combinations

Impedance Combinations


Consider the N series-connected impedances shown in Fig. 9.18. The same current I flows through the impedances. Applying KVL around the loop gives


V = V1 +V2 +···+VN = I(Z1 +Z2 +···+ZN)


The equivalent impedance at the input terminals is

Zeq =V/I = Z1 +Z2 +···+ZN

showing that the total or equivalent impedance of series-connected impedances is the sum of the individual impedances. This is similar to the series connection of resistances.

IfN = 2, as shown in Fig., the current through the impedances is

In the same manner, we can obtain the equivalent impedance or admittance of the N parallel-connected impedances shown in Fig. 9.20. The voltage across each impedance is the same. Applying KCL at the top node,

I = I1 +I2 +···+IN = V ( 1/Z1 + 1/Z2 +···+ 1/ZN )

The equivalent impedance is

1 /Zeq =I /V =1 /Z1 +1 /Z2 +···+1/ ZN

and the equivalent admittance is

Yeq = Y1 +Y2 +···+YN

This indicates that the equivalent admittance of a parallel connection of admittances is the sum of the individual admittances

.