The concave resistor

          The concave resistor is composed by a linear two terminal resistor, an independent DC voltage source, and an ideal diode (Fig. 1.1). It is a piecewise-linear, voltage-controlled resistor which is uniquely specified by two parameters: G, the slope of the linear segment, and E, the breakpoint voltage (Fig. 1.2). Its symbol is shown in Fig. 1.3.

The v-i characteristic of a concave resistor can be specified by

i = (G/2)[|v - E| + (v - E)]         (1)

In fact, let us consider Fig 2.1 where i = (G/2)(v - E) is plotted. In Fig 2.2, we plot its absolute value, i.e., i = (G/2)|v - E|. Adding the two, we obtain the characteristic of the concave resistor shown in Fig 1.2.

Alternatively, we consider directly Eq.(1) which states

i = G(v - E)         for v - E > 0 This is precisely the characteristic of the one-port in Fig 1.1 when the diode is conducting. Now Eq.(1) also states i = 0         for v - E < 0 This is the characteristic of the same one-port when the diode is reversed biased.