Stability Analysis of Power Amplifiers Under Output Mismatch Effects

Abstract

1 Abstract -Novel criteria are presented for small-and large-signal stability analysis of microwave circuits under output mismatch effects. They are based on concepts from bifurcation theory, which enable the derivation of general equations for the stability boundaries that depend on the termination load. The boundary calculation does not require any optimization of the circuit parameters. Instead, it is based on the direct calculation of an admittance function obtained through circuit linearization about either the dc solution, in the small-signal stability analysis, or the periodic solution, in the large-signal one, with low computational cost. As will be demonstrated both with homotopy and bifurcation concepts, the Hopf locus obtained in this way delimits a stable region and a potentially unstable one. In a large-signal stability analysis, the sidebands that influence the stability properties are identified, which depend on the particular amplifier topology and its filtering effects. The stability boundaries are then calculated with the conversion matrix approach for all load impedance values at the relevant harmonic and sideband frequencies. For the derivation of absolute stability conditions, a new scattering type matrix is proposed describing the circuit response from the output reference plane with respect to the two sidebands about the input carrier. The new methodologies and formulations have been validated by independent simulations using pole-zero identification, and by measurements.

Pole-Zero Identification: Unveiling the Critical Dynamics of Microwave Circuits Beyond Stability Analysis

“…From a general perspective, this is an incommensurable multidimensional problem because, for each input power P in , negative resistance at frequency f s will depend on load terminations at Kf in and at side bands Kf in ± f s , with K being the number of relevant harmonics and f in the fundamental frequency of the input signal. A rigorous generalization of the Rollet stability criterion to largesignal periodic regimes under output mismatch effects is given in [49]- [50]. It is applied to practical cases in which the output filter of the amplifier allows the consideration of only two (or three at most) relevant sidebands at the load termination port.…”

Prediction of odd-mode instabilities under output mismatch effects

“…To guarantee a reliable operation in a variety of conditions, some applications impose stable operation even under highly reflective loads [3]. This stability analysis must be carried out under unknown values of the load impedance, which will be different from 50 V. Due to its frequency dependence, this impedance will be different at the fundamental frequency f in and its various harmonic components, mf in , and sideband frequencies, mf in + f, where m is an integer and f is a perturbation frequency, to be swept in the stability analysis [4,5]. Even-and odd-mode instabilities can be distinguished, which, as described next, require different analysis procedures.…”

Generalized Stability Criteria for Power Amplifiers Under Mismatch Effects

“…Taking all the above into account, the approach in [9]- [11] assumes a bandpass filtering action of the PA output network, such that the particular values of the load impedances at frequencies other than the fundamental frequency in f f f , at which the termination impedances may take any value. Then, a two-tier conversion matrix analysis is carried out [10]- [11]. The outer-tier system is based on a 2×2 scattering-type matrix at the two mismatched sideband frequencies ports, which has enabled the extension of the Rollet stability criteria [24]- [25] to large-signal operation under output mismatch effects [10].…”

“…Then, a two-tier conversion matrix analysis is carried out [10]- [11]. The outer-tier system is based on a 2×2 scattering-type matrix at the two mismatched sideband frequencies ports, which has enabled the extension of the Rollet stability criteria [24]- [25] to large-signal operation under output mismatch effects [10]. However, [10] assumed a particular (matched) termination condition  o = 0 at the fundamental frequency f in .…”

“…The outer-tier system is based on a 2×2 scattering-type matrix at the two mismatched sideband frequencies ports, which has enabled the extension of the Rollet stability criteria [24]- [25] to large-signal operation under output mismatch effects [10]. However, [10] assumed a particular (matched) termination condition  o = 0 at the fundamental frequency f in . The generalization to arbitrary  o terminations implies some analysis difficulties, since any change of  o leads to a different steady-state solution, which must be calculated with harmonic balance (HB).…”