Admittance, , is a quantity which is used in analysing electronic circuits. A typical expression for admittance is
where can be thought of as representing frequency. To predict the behaviour of the circuit it is often necessary to express the admittance as the sum of its partial fractions and find the effect of each part separately. Express in partial fractions.
The fraction is proper. The denominator contains an irreducible quadratic factor, which cannot be factorised further, and also a linear factor. Thus
Multiplying both sides of Equation (1) by we obtain
To find the constant we let in Equation (2) to eliminate and .
Equating coefficients of in Equation (2) we find
so that .
Equating constant terms in Equation (2) gives
which can be written as
Express each of the following as the sum of its partial fractions.