while (38) implies that  2 Ͼ 0 since the term in the square bracket can be shown to be always nonnegative. Upon dropping the denominator and taking the square root, we arrive atTo prove in the opposite direction, one can simply interchange the indexes in the foregoing symmetrical procedure. These same steps are also applicable for showing the mutual implications in the input and output planes. Hence, it has been explicitly justified that (31) N (32) and (33) N (34). The justifications above have also proved 1 Ͼ 1 N 2 Ͼ 1 in a concise and clear-cut manner.
CONCLUSIONThis paper has presented a simple derivation of the single-parameter geometrical stability criteria for linear two-ports. The derivation has been carried out based on the classical constraints familiar to most circuit designers with regard to stability circles and stable regions. It has been shown that the combination of one geometrical constraint on the stability circle in the source, load, input plane, or output plane, together with one auxiliary condition, allows one to deduce the geometrical stability parameters directly. A straightforward proof of the mutual implications of various geometrical stability criteria, including the dual geometrical and auxiliary conditions as well as the single-parameter geometrical conditions, has also been provided in a concise and explicit manner. A piecewise curve-fitting predistorter for a given power amplifier transfer characteristic has been reported in [5,6]. One approach uses a nonmonotonic function generator and consists of a combination of operational amplifiers and resistors [5], however, this approach is not viable for RF applications. Another approach consists of an independent amplitude and phase predistorter [6]. The main disadvantage of this predistorter is its complexity.We propose an RF curve-fitting predistorter which uses a reflection-type diode based on the amplitude modulation to amplitude modulation (AM-AM) and amplitude modulation to phase modulation (AM-PM) transfer function characteristics in order to extend the linearized dynamic range of the power amplifier. The advantages of the proposed predistorter are its simplicity and stable configuration, using shunt diodes instead of series diodes.
OPERATION PRINCIPLE OF RF CURVE-FITTING PREDISTORTERThe curve-fitting predistorter uses a single diode, as shown in Figure 1(a), to approximate one segment of the predistortion transfer characteristic and achieve IMD cancellation at a fixed point [see Fig. 1(c)]. The transfer function characteristic of the predistorter can be closely matched by the selection of a sufficient number of diodes [ Fig. 1(b)]. However, increasing the number of diodes gives rise to higher insertion loss and greater complexity of parameter adjustment. The linearized dynamic range can be extended by more than 10 dB using a three-diode predistorter, as shown in Figure 1(c). Figure 2 shows a block diagram and equivalent circuit of the proposed RF curve-fitting predistorter. It consists of a -type attenuator for input/output match...