In this paper we present a new approach towards global passive approximation in order to find a passive transfer function G(s) that is nearest in some well-defined matrix norm sense to a non-passive transfer function H(s). It is based on existing solutions to pertinent matrix nearness problems. It is shown that the key point in constructing the nearest passive transfer function, is to find a good rational approximation of the well-known ramp function over an interval defined by the minimum and maximum dissipation of H(s). The proposed algorithms rely on the stable anti-stable projection of a given transfer function. Pertinent examples are given to show the scope and accuracy of the proposed algorithms.