Accurate method to calculate noise figure in a low noise amplifier: Quantum theory analysis

Abstract

In this study, a low-noise amplifier is quantum-mechanically analyzed to study the behavior of the noise figure. The analysis view has been changed from classic to quantum, because using quantum theory produces some degrees of freedom, which may be ignored when a circuit is analyzed using classical theory. For this purpose, the Lagrangian is initially derived by considering the related nonlinearity of the transistor, and then using the Legendre transformation and canonical quantization procedure, the quantum Hamiltonian is derived. As an interesting point of this study, the low-noise amplifier is deliberately considered as two oscillators connecting to each other to share the photonic modes between them; accordingly, the voltage and current as measurable observations and the noise figure as a critical quantity in a low-noise amplifier are theoretically expressed in terms of the oscillator's mean photon number. The main goal of this work is to study quantities such as the noise figure in a sufficient detail using quantum theory. In addition, as an advantage of this theory, one can control and manipulate the noise figure only by manipulation of the oscillator's mean photon number and coupling it between two oscillators. Finally, the circuit is classically designed and simulated to verify the derived results using quantum theory. The comparison results show that there is a partial consistency between the two approaches; as the frequency increases, the noise figure becomes minimized at a particular frequency.