Instabilities diagnosis and the role of K in microwave circuits

Provisos for Classic Linear Oscillator Design Methods. New Linear Oscillator Design Based on the NDF/RRT

“…The Q L can be calculated with Equation (18) from the HB simulation of the phase noise, Figure 18. The Q L is similar to the one estimated by the NDF/RR T method with Equation (17), which is shown in Figure 16. …”

“…It is also necessary that the I o /I numerator does not have any visible or hidden poles in the RHP. The best way to verify this condition is to analyze the circuit in Figure 2 with both ports Z 0 loaded with the NDF [17,18]. This condition assures the correct solution of the CF Nyquist analysis but is not remarked by Randall and Hock [1].…”

“…From the works of some authors [15,[17][18][19] it is possible to define the additional conditions for the correct use of these methods for stability analysis. The additional conditions for the right and left sub-circuits for the Z, Y and Γ methods are defined in the following sections.…”

“…It is important to remember that the NDF/RR T method estimates the first harmonic approximation oscillation frequency, and it is not necessary to compress the g m of the transistor as with the reference plane and loop-gain methods. With the NDF/RR T method is possible to calculate the Q L of the circuit, Equation (17). As it is possible to estimate Q L , the phase noise of the oscillator can be approximated with the Lesson expression [27], or the Everard improved one [28,29].…”

“…The poles frequency is 1.27 GHz. The Q L is calculated from the RR T plot using Equation (17) and shown in Figure 22. The Q L at the oscillation frequency has a value of 18. This oscillator has been manufactured and shown in the photo in Figure 23.…”