Phase structure of NJL model with weak renormalization group

We analyze the chiral phase structure of the Nambu--Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential $V(\sigma;t)$ is given as a partial differential equation, where $\sigma:=\bar \psi\psi$ and $t$ is a dimensionless RG scale. When the dynamical chiral symmetry breaking (D$\chi$SB) occurs at a certain scale $t_c$, $V(\sigma;t)$ has singularities originated from the phase transitions, and then one cannot follow RG flows after $t_c$. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the D$\chi$SB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.Comment: 32 pages, 12 figures; Version published in Nuclear Physics

A 2.4-GHz, 2.2-W, 2-V fully-integrated CMOS circular-geometry active-transformer power amplifier

A 2.4-GHz, 2.2-W, 2-V fully integrated circular geometry power amplifier with 50 Ω input and output matching is fabricated using 2.5V, 0.35 pm CMOS transistors. It can also produce 450mW using a 1V supply. Harmonic suppression is 64dB or better. An on-chip circular-geometry active-transformer is used to combine several push-pull low-voltage amplifiers efficiently to produce a larger output power while maintaining a 50 Ω match. This new on-chip power combining and impedance matching method uses virtual ac grounds and magnetic couplings extensively to eliminate the need for any off-chip component such as wirebonds. It also desensitizes the operation of the amplifier to the inductance of bonding wires and makes the design more reproducible. This new topology makes possible a fully-integrated 2.2W, 2.4GHz, low voltage CMOS power amplifier for the first time

The Class-E/F Family of ZVS Switching Amplifiers

A new family of switching amplifiers, each member having some of the features of both class E and inverse F, is introduced. These class-E/F amplifiers have class-E features such as incorporation of the transistor parasitic capacitance into the circuit, exact truly switching time-domain solutions, and allowance for zero-voltage-switching operation. Additionally, some number of harmonics may be tuned in the fashion of inverse class F in order to achieve more desirable voltage and current waveforms for improved performance. Operational waveforms for several implementations are presented, and efficiency estimates are compared to class-E