Applications of Knowledge-Based Artificial Neural Network Modeling to Microwave Components P. M. Watson, 1 K. C. Gupta, 2 R. L. Mahajan 2 1 Air Force Research Laboratory, Sensors Directorate, Wright-Patterson Air Force Base, Ohio; e-mail: watson@el.wpafb.af.mil 2 Center for Advanced Manufacturing and Packaging of Microwave, Optical, and Digital Electronics ( ) CAMPmode , University of Colorado at Boulder, Boulder, Colorado 80309 Recei  ed 8 August 1998; re ised 4 December 1998 ABSTRACT: This paper expands upon reported methods for utilizing prior knowledge for reducing complexity of input–output relationships that an ANN must learn. Previously, two simple methods, difference method and prior knowledge input method, were demonstrated for new model developments. This paper utilizes knowledge-based modeling techniques for novel microwave modeling applications.  1999 John Wiley & Sons, Inc. Int J RF and Mi- crowave CAE 9: 254260, 1999. Keywords: artificial neural network; knowledge based; computer-aided design; modeling; microwave I. INTRODUCTION Accurate and efficient models for circuit compo- nents are essential for cost-effective circuit design at RF, microwave, and higher frequencies. Mod- els are generally developed using analytical, elec- tromagnetic simulation, andor measurement-  based methods 1 . Analytical models, when they exist, are generally based on assumptions that are valid only over a certain limited range of opera- Ž . tion. Electromagnetic models EM can provide accurate responses. However, the computational expense required does not make practical, inter- active circuit design using EM simulations feasi- ble. This is especially true when a component must be optimized, by altering the physical struc- ture, in order to provide the desired response. Measurement-based models are developed by measuring the S-parameter characteristics of the element, requiring costly mask designs, fabrica- tion, and testing. Although this method can be Correspondence to: P. M. Watson accurate, it is generally limited to the specific structures that were fabricated and measured. In recent years, empirical models for mi- crowave components based on artificial neural Ž . networks ANNs have received much attention   2  8 as an alternative to standard empirical mod- eling techniques, such as polynomial fitting and look-up tables. ANN models provide a general framework for modeling complex input  output mappings between multiple inputs and outputs. ANN models can be much faster than original EM models, more accurate than polynomial fitted and other empirical models, allow more input dimensions than look-up table models, and are easier to develop when a new component  tech-  nology is introduced 9 . A potential drawback of ANN modeling is the amount of training data that needs to be provided in order to obtain an accurate model. Training data must be provided to characterize the compo- nent to be modeled over a desired range of oper- ation and for different combinations of geometri- cal and physical model inputs. The difficulty arises  1999 John Wiley & Sons, Inc. CCC 1096-429099030254-07 254