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,
[email protected], [email protected]
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.
KeyWords:
– 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 (“nonswithed”) 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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 Spring '09
 Gounot
 Fourier Series

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