Appendix 10 - Analytical study of oscillator phase noise

Summary

A study of phase noise

In this section we look into how phase noise arises from noise currents in an oscillator, using an analytic power series model. An analysis is conducted based on this power series model, and this is used to predict the phase noise of an oscillator. This circuit is then made to oscillate with transient simulation and is studied for its phase noise performance with the harmonic balance method using a proprietary simulator (ADS). The results are then compared. The basis of this study will be a half circuit test bench of a Colpitts oscillator as in Figure 10.14(a) and Figure 10.41 of Chapter 10, but with a HBT instead of a MOSFET.

The topic of phase noise was introduced in Section 10.1.4 of Chapter 10. Equation (10.15) simply assumed a phase noise existing at a frequency offset from the fundamental oscillation frequency, but does not explain how this phase noise arises from real physical noise current sources (e.g. resistors, lossy inductors, transistor shot noise, etc.) present inside the oscillator circuit. The latter is studied in more detail in this Appendix using a one-port equivalent circuit for the oscillator, as shown in Figure A10.1.

The inductor, L_pt, is assumed in parallel with a resistor R_pt, at the base input of the transistor. (An equivalent series L-R representation is also possible.) One end of this inductor is placed at the desired DC base bias voltage of the transistor. The value of R_pt is calculated based on the assumed Q of an actual linear inductor, at the oscillation frequency. The resistor R_pt is shown inside the “one-port” as illustrated in Figure A10.1. When this assembly is in steady-state oscillation, the input to the one-port must by definition be purely capacitive because the net negative resistance created inside the oscillator must balance any sources of positive resistance. Note that in the Colpitts oscillator the transistor inside the one-port does not have its emitter connected to ground, so the subsequent analysis of the one-port is of the prototype structure of this oscillator, not just of the proprietary device models included in it.