Richards' theorem (original) (raw)

Richards' theorem is a mathematical result due to Paul I. Richards in 1947. The theorem states that for, if is a positive-real function (PRF) then is a PRF for all real, positive values of . The theorem has applications in electrical network synthesis. The PRF property of an impedance function determines whether or not a passive network can be realised having that impedance. Richards' theorem led to a new method of realising such networks in the 1940s.