An Exact Method using Quantum Theory to Calculate the Noise Figure in a Low Noise Amplifier

In this article, a low noise amplifier is quantum mechanically analyzed to study the behavior of the noise figure. The analysis view is changed from the classic to quantum, because using quantum theory produces some degrees of freedom, which may be ignored when a circuit is analyzed using a classical theory. For this reason, the associated Lagrangian is initially derived for the circuit and then using Legendre transformation and canonical quantization procedure the classical and quantum Hamiltonian are derived, respectively. Consequently, the dynamic equation of motion of the circuit is introduced by which all of the circuit measurable observations such as voltage and current fluctuations are calculated. As an interesting point of this study, the low noise amplifier is deliberately supposed as two oscillators connecting to each other sharing the mutual specifications and accordingly the voltage and current are expressed in terms of the oscillators photon number. As a result, one can analyze the critical quantity such as the noise figure in terms of the oscillators photon number and also the photons coupling between oscillators. The latter mentioning term is considered as a factor to engineering the amplifier critical quantities. Additionally, the considered circuit is designed and classically simulated to testify the derived results using the quantum theory.