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We give a new decomposition of derangements, which gives a direct interpretation of a formula for their generating function. This decomposition also works for counting derangements by number of excedances.
This paper presents the realization of a linear polar transmitter supporting multistandard applications. The harmonic-tuned class-AB biased (class-AB/F) power amplifier (PA) with the novel envelope shaping method linearly amplifies the input signal with high efficiency. The hybrid switching supply modulator with programmable hysteretic comparator enables… (More)
This paper describes the analysis of an optimized envelope shaping function for the envelope tracking power amplifier (ET PA) and its implementation. The proposed shaping function, which is sweet spot tracking with crest factor reduction, improves the efficiency and output power of the power amplifier (PA), as well as its linearity. For an accurate… (More)
This paper presents a gallium nitride (GaN)-based hybrid current-mode class-S (CMCS) power amplifier (PA) using a bandpass delta-sigma modulator (BPDSM) for a 955-MHz LTE signal. To enhance the drain efficiency of the CMCS PA, the chip-on-board (COB) technique, which can reduce the external parasitic components of the packaged transistor and allow fast… (More)
A quarter-wavelength impedance transformer as well as a number of other factors limit the bandwidth (BW) of Doherty power amplifiers (PAs). We utilize the lower Q of a quarter-wave length transformer and propose a phase compensation circuit and an additional offset line to be incorporated into the matching net works for an enhanced BW of the Doherty PA. The… (More)
A multimode/multiband power amplifier (PA) with a boosted supply modulator is developed for handset applications. A linear broadband class-F amplifier is designed to have a constant fundamental impedance across 1.7-2 GHz and its second and third harmonic impedances are located at the high-efficiency area. To reduce the circuit size for handset application,… (More)
An envelope-tracking (ET) CMOS power amplifier (PA) is fabricated using a 0.18- μm CMOS process. The module containing the supply modulator, the PA, and the output transformer is implemented on a printed circuit board (PCB). The CMOS PA employs the second and third harmonic controls at the input and the second harmonic short at the output for… (More)
This paper presents a dual power-mode and multi-band power amplifier (PA) for handset applications that improves the efficiency in low-power regions. This PA operates in two modes through path control by a shunt switched capacitor. The proposed control method provides efficient mode control without any efficiency degrading and bandwidth (BW) limiting. The… (More)
A combinatorial bijection between k-edge colored trees and colored Prüfer codes for labelled trees is established. This bijection gives a simple combinatorial proof for the number k(n − 2)! nk−n n−2 of k-edge colored trees with n vertices.