THE RX HALF-PLANE

Recall the quarter-planes for resistance R and inductive reactance X_L from the preceding sections. This is the same as the upper-right quadrant of the complex-number plane. Similarly, the quarter-plane for resistance R and capacitive reactance X_C is the same as the lower-right quadrant of the complex-number plane. Resistances are represented by nonnegative real numbers. Reactances, whether they are inductive (positive) or capacitive (negative), correspond to imaginary numbers.
There is no such thing, strictly speaking, as negative resistance. That is to say, one cannot have anything better than a perfect conductor. In some cases, a source of dc, such as a battery, can be treated as a negative resistance; in other cases, a device can behave as if its resistance were negative under certain changing conditions. Generally, however, in the RX (resistancereactance) half-plane, the resistance value is nonnegative (Fig. 1).

Fig. 1. The RX impedance half-plane showing some points for specific complex-number impedances.