This paper addresses the problem of anisotropy in substrate materials for microwave integrated-circuit applications. It is shown that in modeling the circuit characteristics, a serious error is incurred which becomes larger with increasing frequency when the substrate anisotropy is neglected. Quasi-static, dynamic, and empirical methods employed to obtain the propagation characteristics of microstrip, coplanar waveguides, and slotlines on anisotropic substrates are presented. Numerical solutions such as the method of moments and the transmission-line matrix technique are outlined. The modified Wiener-Hopf, the Fourier series techniques, and the method of lines are also discussed. A critique of the aforementioned methods and suggestions for future research directions are presented. The paper includes new results as well as a review of established methods.

Integrated-Circuit Structures on Anisotropic Substrates

We report on a time-domain analog to the spatial far-field Fraunhofer diffraction using microstrip lines with chirped distributed Bragg coupling between the fundamental microstrip mode and the same but counter-propagating mode. The chirping of the microstrip impedance yields to linear group delays within the reflected bandwidth. Under the condition of a temporal equivalent of the spatial Fraunhofer inequality, the distortion of a frequency-limited pulse results in an output reflected signal whose complex envelope is, except a phase factor, proportional to the Fourier Transform of the input pulse envelope. This has important temporal applications and, in particular, the devices designed in this paper work as real-time energy spectral density analyzers.

Real-Time Spectrum Analysis in Microstrip Technology

A simple model for the propagation of high-frequency signals on coplanar striplines with lossy semiconductor substrates is proposed and demonstrated. This model incorporates the effect of a conductive substrate through the loss tangent in a distributed-circuit analysis extended to high frequencies. Very strong attenuation and dispersion due to the substrate are observed even when the GaAs conductance is only 1 mho/cm, corresponding to a doping density of around 10/sup 15/ cm/sup -3/. The accuracy of this model is tested with a direct comparison to experimental data of picosecond pulse propagation on a doped GaAs coplanar stripline (CPS) measured in the time domain using the electro-optic (EO) sampling technique. Good agreement is found in terms of the attenuation and phase velocity of the distorted pulses at four propagation distances up to 300 mu m. The pulse propagation on a multiple modulation-doped layer is also studied experimentally as a prototype of high-frequency signal propagation on the gate of a modulation-doped field-effect transistor (MODFET). The attenuation shows linear frequency dependence up to 1.0 THz, contrary to the cubic or quadratic dependence of coplanar transmission lines on low-loss substrates. >

Picosecond pulse propagation on coplanar striplines fabricated on lossy semiconductor substrates: modeling and experiments

The eigenmode problem for the open microstrip line is analyzed in the space domain starting from the calculation of a dyadic Green's function in the spectral domain. The transverse and the longitudinal current are discretized using the method of moments. A point-matching technique is used to impose the boundary condition, i.e., zero tangential electric field, on the strip. The edge conditions at the end points of the strip are explicitly incorporated and special care is taken to accurately retain the static behavior of the field on and near the strip. Special attention is given to the variation of the current distribution as a function of frequency. >

Rigorous full-wave space-domain solution for dispersive microstrip lines

A method for determining the modal dispersion of gigahertz-bandwidth pulses on microstrip transmission lines is described. We have investigated the evolution of temporal waveforms propagating on microstrips, with very good agreement noted between experimental pulse shapes and numerical simulations. The resulting pulse distortion contributed to a pulse-shaping application where 100-ps rise times were stretched to the nanosecond durations necessary to control the shape of high-energy optical pulses used in fusion research. The tunability of the shape of the rising edge was investigated through variation of the stripline geometry and the substrate material. Additional effects due to high-frequency attenuation in several dipolar liquid dielectrics were substantiated experimentally, and the relevance of the results has been discussed.

Pulse Dispersion and Shaping in Microstrip Lines

A simple approximate formula for the CAD of the dispersion property of microstrip lines is reported in this paper which well fits the calculated curves based on a rigorous method.

An Approximate Dispersion Formula of Microstrip Lines for Computer Aided Design of Microwave Integrated Circuits

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An Approximate Dispersion Formula of Microstrip Lines for Computer Aided Design of Microwave Integrated Circuits