Transpose Return Relation Method for Designing Low Noise Oscillators

Abstract

Abstract-In this paper, a new linear method for optimizing compact low noise oscillators for RF/MW applications will be presented. The first part of this paper makes an overview of Leeson's model. It is pointed out, and it is demonstrates that the phase noise is always the same inside the oscillator loop. It is presented a general phase noise optimization method for reference plane oscillators. The new method uses Transpose Return Relations (RR T ) as true loop gain functions for obtaining the optimum values of the elements of the oscillator, whatever scheme it has. With this method, oscillator topologies that have been designed and optimized using negative resistance, negative conductance or reflection coefficient methods, until now, can be studied like a loop gain method. Subsequently, the main disadvantage of Leeson's model is overcome, and now it is not only valid for loop gain methods, but it is valid for any oscillator topology. The last section of this paper lists the steps to be performed to use this method for proper noise optimization during the linear design process and before the final non-linear optimization. The power of the proposed RR T method is shown with its use for optimizing a common oscillator, which is later simulated using Harmonic Balance (HB) and manufactured. Then, the comparison of the linear, HB and measurements of the phase noise are compared.

Stability, Mounting, and Measurement Considerations for High-Power GaN MMIC Amplifiers

“…In our opinion, the NDF is a modern version of the return ratio (RR). Furthermore, it has successfully been used to design oscillators [13,14], showing its agreement with Bode's RR. However, the NDF criterion is difficult to apply and requires that the software be prepared for its use.…”

“…In Table 1, V D is the drain bias voltage; f lower − f upper are the lower ( f lower ) and upper ( f upper ) cutoff frequencies of the bandwidth (BW (13)), respectively; f o is the center frequency (14); ∆ f o is the percentage bandwidth (15); P out is the output power; PAE is the power-added efficiency; CW stands for continuous wave; NA stands for not applicable; and Time/Duty is the pulse width of the modulating or pulsed signal with respect to one duty cycle. BW = f upper − f lower (13) f o = f upper + f lower 2 ( 14)…”

Classic Linear Methods Provisos Verification for Oscillator Design Using NDF and Its Use as Oscillators Design Tool

“…Other useful characteristics of the NDF are that it can predict the oscillation frequency without transistor compression (g m ) for Kurokawa's first harmonic approximation; and that it is suitable for the calculus of the Q L of the circuit because it is directly related with the RR T [8]. These characteristics make it suitable to use it as an optimization tool for low noise oscillators [12]. In the same way it is also suitable for estimating the start-up time.…”

A compact low-phase noise oscillator with superior harmonic suppression characteristics based on novel nested split-ring resonator (NSRR)

“…Oscillator is one of the important signal sources. At present, there has been increasing demand on oscillators with low-phase noise, because it determines the overall performance of radar and communication systems [1]. Besides, other factors of oscillators such as output power, harmonic suppression, DC–RF conversion efficiency and physical dimension, also play an important role.…”