TABLE OF CONTENTS Asymptotic waveform evaluation (AWE) is an efficient frequency-domain analysis approach and was proposed in 1990 by L.Pileggi [91, 92]. It basically combines the fast recursive moment computation methods presented in Subsection 2.2.1 with Pade approximation to compute the poles and residues of the order truncated transfer functions. We first present the Pade approximation method.
The idea of Pade approximation is to approximate a transfer function H (s) by an order-limited rational function H q (s), where q is the order.
Specifically, after the moments are generated, a general multi-input multi-output (MIMO) transfer function H (s) is represented as a Taylor series expansion form or the block moment form
where m i is the ith block moment of the circuit, and
where x i is the ith order state block moment vector. Once the moment expansion is available, a Pade approximation is calculated. For a qth order approximation, 2 q moments must be computed.
Without losing generality, we consider a single-input single-output transfer function. Consider the transfer function at entry (p, q) and let m i= m i,pq for i= 0, 1, 2, , the scalar moment expansion then can be written as
Then we can use a qth Pade approximation rational function H q (s) to match H(s),
such that they agree on the first 2 q terms in the moment form, i.e.,
To compute...
