Piecewise linear approximations to electronic non-linear circuits and devices have many attractive features. For example [1], a piecewise linear approximation to a pn diode may be made from a controlled switch, and linear capacitors and resistors. When used as a model for SPICE simulation, or when built from discrete components, this approximate circuit behaves chaotically in combination with an inductor in a very similar manner to the RL-diode arrangement. It is also possible to make a piecewise linear bipolar junction transistor (BJT) model [2] which performs similarly. In principle, piecewise linear circuits are more amenable (than are circuits containing continuously turning nonlinearities) to analytic investigations; the motions can be reduced to quadrature and the equations of motion can be integrated in the linear regions and the initial values matched at the breakpoints to calculate the entire trajectory. Thus a kind of return map linking the initial values at one piecewise-linear section to the initial values at the next section may be derived analytically; as was demonstrated in [3] for the offset impact oscillator this allows one to calulate the bifurcation boundaries analytically for such a system.
Normally, a piecewise linear circuit needs a comparator
and a controlled switch to implement the breakpoints
in the piecewise linear characteristic. Here we start
from a piecewise linear restoring force which is
zero at 
and has a discontinuity at the origin.
Such a system represents a double potential well harmonic
oscillator with the cusp of potential at the origin.
To implement such a circuit electronically the
offsets are obtained from a comparator
driving a Zener diode clamping ladder, and fed from
the voltage in a two-integrator loop oscillator
circuit which models displacement.
In this paper, we describe the properties of such a circuit; we show that it is very similar to the offset impact oscillator previously analysed [3], and that a simple modification makes it into an extended offset impact oscillator with phase portrait extending either side of the wall; a crossing of the trajectory from one side to the other corresponds to an impact in the offset impact oscillator. We describe the circuits; we describe the results of experiments and simulations; we introduce the concept of traps to describe the sudden cessation of chaotic transient behaviour; we describe observations of noisy trapping [4] behaviour in a simulation; and we discuss analytic methods for obtaining the bifurcation behaviour.