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switched_circuit_response_Spice

# switched_circuit_response_Spice - Proceedings of the 5th...

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Evaluation of Various Approaches to Frequency Response Calculation of Switched Circuits in Spice JAN BICAK, JIRI HOSPODKA Department of Circuit Theory, Faculty of Electrical Engineering, Czech Technical University, Technicka 2, 166 27 Prague, CZECH REPUBLIC, Abstract: – This paper is a presentation of frequency response calculation of switched circuits in Spice program. Evaluated methods are based on transient analysis of circuits followed by Fourier transformation of the computed time response. Three types of circuit excitation are taken into account – pulse, set of harmonic signals and the same set but with Sample and Hold circuit. Fourier transformation is computed either by DFT or by numerical calculation of Fourier integral. Key-Words: – Analysis of switched circuits, Switched capacitors, Fourier Transformation, Spice 1 Introduction There are several methods for computing frequency response of switched circuit. The basic method is charge equations method for switched capacitor (SC) circuits [2, 3] or nodal equations method modiﬁed for switched currents (SI) circuits [6, 3]. This method is applicable only for idealized circuits. For linear switched circuits with parasitical effects we can solve general linear differential equation of a circuit by a method based on the Fourier transformation [4] or the Laplace transformation [5], see section 5. The third one is general solution of the circuit by transient analysis using program like SPICE. The frequency re- sponse is obtained consecutively by Discrete Fourier Transformation (DFT) of output signal samples [7, 9]. The comparison of this method was shortly described in [1]. The main motivation of this contribution is to ﬁnd conditions for reliable analysis of frequency re- sponse of switched circuit which is excited by a pulse in comparison with excitation by sinusoidal signals. This paper is focused on the third method using Spice. Compared to [1] there are used more types of exciting signals and alternative method of DFT com- puting based on [8], besides of spec command of Winspice. The frequency response of switched circuit is ob- tained from computed output signal spectrum. How- ever the excitation signal type affects the output spec- trum, specially for real dissipation circuit and for cir- cuit, where the part of input signal comes to output by direct (“non-swithed”) way. 2 Exciting Signals There are used three different signals for exciting the circuit. The ﬁrst signal is sinusoidal or set of sinu- soidal signals as was used in [1]. The set includes all frequencies in which frequency response will be calculated. The conditions mentioned in [1] must be kept. The circuit can be also excited through a sample and hold circuit with same results of magnitude response in case of idealized switched circuit (without parasiti- cal capacitors and resistors) and where any part of in- put signal does not pass directly to output. The high- est frequency of exciting signal must be less than half of clock frequency f c / 2 . However the frequency re-

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switched_circuit_response_Spice - Proceedings of the 5th...

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