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P. Vanassche
| Speaker: |
Piet Vanassche (Katholieke Universiteit Leuven, ESAT-MICAS)
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| Date: |
Wednesday June 25, 2003 |
| Title: |
The Geometry of Radio-Frequent Circuit Behavior
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Abstract
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Many radio-frequent (RF) circuits exhibit a mixture
of fast- and slow-varying behavior.
They produce output signals that contain high-frequent oscillations. The
characteristics of these oscillations, e.g. their amplitude and phase, vary
at a rate well below the oscillation frequency. This mixture of fast- and
slow-varying behavior renders traditional (polynomial-based) circuit simulation
very inefficient. The presence of fast-varying signal components forces these
simulators to use a small integration time step. The slow-varying signal components
imply a large overall simulation time interval. Envelope algorithms, e.g.
circuit envelope and envelope following, try to cope with the widely separated
signal time constants by representing all waveforms as a sum of slowly modulated
carriers. With the fast-varying oscillations taken into account a priori
(as part of the signal model), only the slow-varying envelopes need to be
solved for. Theoretically, this can be accomplished using a large integration
time step. However, the equations that govern the envelopes turn out to be
stiff. This complicates solving them.
This talk focuses on an alternative method for dealing with widely separated
time constants. The method partitions the circuit equations into a core system
and a set of pertubation terms. The core system contains that part of the
circuit equations generating the fast-varying oscillations. The slow-varying
system behavior is induced by the small perturbation terms that “push the
core system around”. Key to the method is the characterization of the core
system’s behavior. Typically, the collection of all its steady state solutions
makes up a stable manifold that quickly attracts the core system’s behavior.
This manifold can be subdivided into a number of layers, i.e. submanifolds
that are invariant with respect to the equations that model the core system.
The set of all layers provides a geometric characterization of the RF circuit’s
core. Given the geometry of its core system, the slow-varying dynamics of
an RF circuit can easily be interpreted as the perturbation terms that make
the circuit “change layers” and “slip around on a particular layer”. This
point of view is put to work by means of perturbation analysis and averaging.
It yields a compact set of equations that capture the essence of the RF circuit’s
dynamics.
The method that is subject to this talk offers a good understanding of the
mechanisms that govern RF circuit behavior. Although it seems like highly
abstract, the theory above is applicable to many circuits occurring in design
practice. In this talk, we illustrate its use to capture harmonic oscillator
and phase-locked loop behavior.
References
[1] P. Vanassche, G. Gielen andW. Sansen, “Behavioral
Modeling of (Coupled) Harmonic Oscillators”,
In IEEE Trans. on Computer-Aided Design, vol. 22, no.
8, August 2003
[2] P. Vanassche, G. Gielen and W. Sansen, “Analyzing
Slowly Modulated Oscillator Behavior”, In
Proc. IEEE ProRISC, pp. 507-515, Veldhoven, 2002
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