Using Mathcad, Matlab and Pspice for Electronics Simulations

During the conception and development phases of complex designs, electronics engineers usually need development tools that make the design faster and avoid breadboarding. Mathcad® and MATLAB® are among the most commonly used mathematical tools while PSpice® is certainly the most popular electronics simulator. This paper is not intended to be a tutorial; it only presents a few examples that illustrate how these programs have been used to ease designs. INTRODUCTION Constrained by increased project complexity and shorter design cycles, engineers rely ever more on analytical and simulation results before committing designs to hardware. A few examples will show the use of Mathcad® [1] and PSpice® [2] for electronics developments and MATLAB® [3] for beam data analysis. USING MATHCAD Mathcad lets engineers simultaneously design and document their projects, using a comprehensive set of mathematical functions. It is an efficient tool that integrates calculation results, graphs and text in a single worksheet, improving work verification and engineering collaboration. Mathcad is used in these examples to calculate the main parameters of some Beam Position Monitors (BPM) and plot their transfer functions. Button type BPM The button is an electrostatic monitor that uses the charge induced by the image current of a circulating beam. It generates a signal proportional to the beam intensity Ib and inversely proportional to the distance of the beam from the button. Its response can be evaluated using the “Spice” equivalent circuit of Fig. 1, where Z∞ is the coupling impedance, Ce is the electrode capacity and Rl is the load impedance. Figure 1: Simplified button equivalent circuit and actual view of the LHC button BPM. On Fig. 2, the main parameters of the button are calculated using Mathcad and the worksheet can be modified easily to fit the same kind of BPM with different dimensions. Depending on its size, the electrode capacity usually ranges from less than 1pF to a few pF and the corresponding low frequency cut-off extends from some hundreds of MHz to several GHz. Figure 2: Mathcad worksheet for the LHC button showing the main parameters and the frequency responses. The same approach can be applied to other button type electrodes, such as a High Frequency (HF) button where the electrode is simply the central conductor of a vacuum feedthrough. Its capacitance is about 0.6pF and the low frequency cut-off of this BPM is about 5GHz. Its transfer impedance is about 0.7Ω compared to the 1.4Ω obtained for the LHC button. The LHC coupler Couplers are devices that use the electromagnetic field of the beam to generate signals on strip-line structures. The amplitude response, versus frequency, is periodic and it depends on the strip-line dimensions. The maximum is obtained for a frequency corresponding to f0 = c/4l and the minimum for fmin = c/2l, where l is the coupler length. Fig. 3 presents both the LHC coupler parameters and the frequency response. Figure 3: Mathcad worksheet showing the LHC coupler parameters and its frequency response. SIMULATION WITH PSPICE PSpice provides a complete simulation environment with schematic capture and plotting facilities. Analogue or digital models are available from many manufacturers. The “Optimizer” is an interesting feature that is presented here to improve the input matching of a filter.