Microwave circuits containing lumped as well as distributed sub-circuits are investigated by a method combining circuit simulation with system identification models. The signal transmission behaviour of the distributed sub-circuits is computed in the time domain using the transmission line matrix (TLM) method. Applying system identification methods to the TLM results compact circuit models are generated. By this way efficient circuit simulation is achieved. I IntroductionIn this paper microwave circuits are investigated by combining the TLM method with system identification. In many cases microwave circuits can be separated into linear distributed sub circuits and lumped subcircuits containing linear and nonlinear elements, active devices and input sources. The linear distributed subcircuits are modelled field-theoretically whereas network-oriented methods are applied to the lumped element sub-circuits. We use the TLM method for the simulation of the distributed sub-circuits. System identification methods have emerged as a powerful tool in recent years [1][2][3][4][5]. Prony's method allows to match a deterministic model of the circuit to the data obtained by electromagnetic field simulation [1]. Mostly it has been used in combination with full-wave analysis for reducing the computational effort in time domain analysis [2][3][4]. Time domain circuit simulation of complex distributed circuits may exhaust the available computing resources. In this case time domain diakoptics allows to subdivide the task of circuit modelling. However time domain diakoptics still needs large computer storage for the time responses and considerable computing time, especially if the circuits contain sub-circuits exhibiting long time responses. Prony's method may also be used to determine the poles for the generation of canonical equivalent circuit models [7,8]. However, in general it is difficult to find lumped equivalent circuit models for distributed subcircuits. In our approach we introduce a mathematical model based on the residues and poles description of the time responses obtained by system identification methods from TLM data. By this way efficient circui simulation is enabled avoiding the conventional convolution approach and the results of time consuming field analysis are made easily accessible for network analysis. TheoryIn the first step the distributed sub-circuits are characterized by time responses obtained by TLM method. The general interface technique introduced in [6] is used for field excitation as well as the extraction of currents and voltages at the ports. Then we apply system identification methods for the generation of compact circuit models for the distributed sub-circuits. Prony's method attempts the approximation of a time series x(n) by a linear superposition of complex exponentials.The extended Prony's method utilizes two leastsquares steps with two data sets of the length N for determination of the complex parameters Zk and hk [21. This method limits also the number of poles to half of the total number 2N...