In my previous article, I gave an overview of the Guardian Alert radar system, disassembled one of the modules, and walked through a series of photographs as I described how the device operates. The most "interesting" part of the design, from an electrical engineering standpoint, is the microwave radar board. It contains an oscillator, the operation of which is described in U.S. Patent 6,064,276, a mixer, constructed from a diode pack, and a number of interconnections along with assorted fins, ground lines, and other bizarre shapes, all of which has some function at the 10.5 GHz operating frequency of the radar. This article focuses on the design of the fins used to isolate the microwave frequencies.
At low frequencies, and even into the radio frequencies, the lumped circuit model is widely used by electrical engineers to analyze analog circuitry. Circuit elements are represented by individual, discrete "lumps", mainly resistors, capacitors, inductors, and current or voltage sources, each behaving as an ideal component and interconnected by ideal wires. Complex devices such as transistors are modeled as a collection of ideal components. Even at UHF frequencies, the lumped model can still be used through careful placement of decoupling capacitors to isolate the power supply and bypass feedback paths, and the addition of additional circuit elements to model stray capacitances that would be swamped out at lower frequencies. SPICE and its varients is the most importance software tool for analyzing lumped circuit designs.
Around roughtly 1 GHz, though, the lumped circuit model becomes unusable. At 1 GHz, a wavelength in free space is 30 cm. In the typical PC board, with a dielectric constant of 2-5, the wavelength might only be 10 cm. Circuit elements on the order of centimeters now become a significant fraction of the wavelength. For example, on a circuit operating at 1 GHz, with a 10 cm effective wavelength in the PC board dielectric, moving 2.5 cm down a trace is equivalent to 90 degree phase shift in the signal. Corners, edges, and protruding fins produce more complex effects. Not only can these effects no longer be brushed away by careful board layout, but the clever microwave engineer learns to take advantage of them, implementing filters using the PC board's copper trace.
Towards the end of the twentieth century, the Finite-Difference Time-Domain (FDTD) method has emerged as most popular simulation technique for microwave circuitry. FDTD was originally proposed by Kane S. Yee in 1966, but only in recent years, as computers have become increasingly powerful, that it has emerged as the method of choice. FDTD is mathematically simple, based on a straightforward approximation of Maxwell's equations, and operates by "throwing CPU cycles" at the problem. It numerically solves Maxwell's equations for the entire simulated circuit, finding the electric and magnetic fields, as well as the charge distribution, to an arbitrary level of precision at each moment in a time series.
The FDTD approximation is based on the differential vector formulation of Maxwell's equations: