This paper presents high efficiency Class-E and compact Doherty power amplifiers (PAs) with novel harmonics termination for handset applications using a GaAs/InGaP heterojunction bipolar transistor (HBT) process. The novel harmonics termination circuit effectively reduces the insertion loss of the matching circuit, allowing a device with a compact size. The Doherty PA uses a lumped-element transformer which consists of metal-insulator-metal (MIM) capacitors on an IC substrate, a bonding-wire inductor and short micro-strip lines on a printed circuit board (PCB). The fabricated Class-E PA exhibits a power added efficiency (PAE) as high as 69.0% at 1.95GHz and as high as 67.6% at 2.535GHz. The fabricated Doherty PA exhibits an average output power of 25.5dBm and a PAE as high as 50.1% under a 10-MHz band width quadrature phase shift keying (QPSK) 6.16-dB peak-to-average-power-ratio (PAPR) LTE signal at 1.95GHz. The fabricated chip size is smaller than 1mm2. The input and output Doherty transformer areas are 0.5mm by 1.0mm and 0.7mm by 0.7mm, respectively.

Spectral graph theory, based on the adjacency matrix or the Laplacian matrix that represents the network topology and link weights, provides a useful approach for analyzing network structure. However, in large scale and complex social networks, since it is difficult to completely know the network topology and link weights, we cannot determine the components of these matrices directly. To solve this problem, we propose a method for indirectly determining the Laplacian matrix by estimating its eigenvalues and eigenvectors using the resonance of oscillation dynamics on networks.