The planar-circuit approach to the analysis and design of microwave integrated circuits (MIC's), with specific reference to microstrip circuits, is reviewed. The planar approach overcomes the limitations inherent to the more conventional transmission-line approach. As the operating frequency is increased and/or Iow-impedence levels are required, in fact, the transverse dimensions of the circuit elements become comparable with the wavelength and/or the longitudinal dimensions. In such cases, one-dimensional analyses give inaccurate or even erroneous results. The analysis of planar elements is formulated in terms of an N-port circuit and results in a generalized impedance-matrix description. Analysis techniques for simple geometries, such as the resonant mode expansion, and for more complicated planar configurations, such as the segmentation method, are discussed along with planar models for accounting for fringing fields effects and radiation loss.

Planar Circuits, Waveguide Models, and Segmentation Method

The port admittance matrix of a planar network is formulated in terms of certain harmonic functions related to the port voltages and the network geometry, together with the natural modes of the network with all ports shorted. The necessary harmonic functions and eigenfunctions are found using a finite element technique, for which general-purpose computer programs already exist. An advantage of the method is that the admittance matrix appears in partial-fraction form with geometric data separated from frequency, leading to inexpensive computations where recalculation at various frequencies is required.

Finite Element Analysis of Planar Microwave Networks

The ferrite planar circuit to be discussed in this paper is a general planar circuit using ferrite substrates magnetized perpendicular to the ground conductors. The main subject of this paper is the analysis of an arbitrarily shaped triplate ferrite planar circuit. In particular, the circuit parameters of the equivalent multiport are determined. To analyze ferrite planar circuits in general, two approaches are possible. One approach is based upon a contour-integral solution of the wave equation. In the other approach the fields in the circuit are expanded in terms of orthonormal eigenfunctions. Examples of the application of such analyses are described.

Ferrite Planar Circuits in Microwave Integrated Circuits

An adaptive scheme is proposed to generate the spectral response of waveguide junctions in minimum computation time The procedure uses the newly developed transfinite element method to determine the fields in junctions at a, few adaptively selected frequencies and then employs these solutions to generate the spectral response throughout the frequency range of interest In typical problems, the method converges in five or six iterations to the full spectral response evaluated at 100 points We show by solving example problems that the new procedure is orders of magnitude faster than the alternatives

An Adaptive Spectral Response Modeling Procedure for Multiport Microwave Circuits

A broad-band equivalent circuit of a generic microwave planar network is derived in terms of lumped constant elements. Contrary to previously proposed equivalent circuits, whose elements are strongly frequency dependent, the elements of the new one show only a smooth dependence on the frequency, because of the dispersion properties of microstrip structures. The equivalent circuit proposed is therefore easy to handle and is shown to be a useful basis for direct synthesis of planar structures. Good agreement with the theory is demonstrated by experiments performed on structures with different geometries up to 12.5 Ghz, by using equivalent circuits whose elements are assumed to be constant with the frequency.

Wide-Band Equivalent Circuits of Microwave Planar Networks

The port impedance and admittance matrices of threelayer structures of linear, passive, isotropic materials are defined and their properties briefly investigated. Discrete equivalent circuit representations are given, together with two examples.

P. Civalleri

Papers

Impedance and admittance matrices of distributed three-layer N-ports