"We duplicate what we simulate"....how is it done? Simulation is the art and science of computing the actual characteristics of a particular filter or component, while that component is embedded in its operating environment. Most engineers are familiar with the theoretical performance of a Chebychev or Butterworth filter, synthesized for performance in a 50 ohm environment. However, what happens to the filter when it sees the "real world" terminations of an amplifier or mixer or antenna? What about the internal "leakages" within the filter which always are present due to imperfect components? Under those terminating conditions, many filters will not perform anywhere near their idealized models. The resulting deviations from expected performance can spell the difference between success and failure in a particular system implementation. For the system designer, it is better to know the problems in advance. As was said "pay me now or pay me later".....
To predict the performance of a design under any conditions requires that an accurate model of the filter be available. Such models can include lumped-element, distributed element, electromagnetic coupling modules, or all of the above. At RS Microwave, we use the approach wherein electromagnetic coupling is taken into account between the physical portions of the theoretically synthesized circuit. Using optimization, we derive lumped element equivalents which enable representation of the circuit, including the non-idealized internal leakages, as simple linear lumped element models with great accuracy over the frequency range applicable to the design in question. Thus, the process of simulation involves four separate, but related steps:
1. Synthesis and analysis of a theoretical network compliant to specification, under idealized terminating conditions and with idealized construction.
2. Representation of the synthesized network by an appropriate set of very accurate lumped elements. For any circuit, this involves modeling the physical structure and computing the lumped elements which best represent the actual, electromagnetic structure (i.e. solving Maxwell's equations inside the proposed filter structure).
3. Optimizing the filter response with the stipulated terminating impedances (i.e. the complex source and load impedance), using the representation of the circuit as computed in Step 2.
4. Revising the physical structure, if required, by iterating the analysis portion of Step 1.
The solutions to Maxwell's equations which allow for derivation of the lumped equivalents requires the comparison of a set of scattering parameters which will describe the physical structure (computed using E-M) to a set which will describe the characteristics of an assumed lumped element topology (computed using linear simulation). The difference between the two sets is reduced using optimization (see Refs. [1], [2]). The data set is stored, and is used in an iterative manner as described in Step 4. All physical structures can be described by a set of lumped elements of arbiratry complexity. Unfortunately, not every set of lumped parameters describes a physically realizable structure, so care must be taken to assume a "realizable" lumped circuit topology. This is where the "art" of simulation comes into prominence.
RS Microwave can perform the above analyses quickly and efficiently due to custom "in-house" models and programming. We can e-mail ASCII data sets to you, the customer, so that you can embed the results into your system simulator and make sure that your overall design will be stable and compliant to your requirements. We can include the effects of amplifiers, circulators, switches, mixers, etc., either from in-house" models or using sets of parameters supplied by you, our valued customer. We are constantly improving our models and programming with one goal: build and supply filters which truly are duplicates of our simulations...we will truly "duplicate what we simulate".
Reference:
1. Snyder, R.V., "Embedded Resonator Filters", Proceedings - ESA Workshop of Filters, November, 1995, Noordvyck, Netherlands.
2. Snyder, R.V., "Inverted Resonator Evanescent Bandpass Filters", Proceedings -1996 MTT-S International Symposium, San Francisco.