Cauer introduced two forms of circuit realization from the network function. These are known as

Cauer 1^{st} Form of network/circuit realization :

The network function used for realization is such that of n>m,where n is the degree of numerator (P(s)) polynomial and m is the degree of the denominator polynomial. This leads to a pole at ω=0 producing inductor as the first element. This form of circuit realization produces ladder type of circuit realization with 1^{st} element as an inductor and the parallel element is a capacitor and this way a ladder is formed.

Also to note that id the degree of denominator is more than the degree of numerator by one i.e. m>n then a zero appears at ω=∞ producing the 1^{st} parallel element as a capacitor.

These driving point immitance for Cauer 1st form is:

Cauer 2nd Form of Realization:

In the 2nd form of Cauer, arranger the polynomial in ascending order.

Cauer 2^{nd} Form of network/circuit realization: This form also produces a ladder type of circuit with the 1^{st} element as the capacitor and parallel elements are the inductor and following that way a ladder is formed.

when the degree of the lowest order term of denominator polynomial is higher than the degree of the lowest order term numerator polynomial, then the realization produces first element as series capacitor and then a series capacitor.

The driving point immitance according to cauer 1st Form is obtained as: