What oscillator simulation can show: a brief overview

created: Jul. 2021

While simulating the oscillator in the time domain may be useful when designing a simple ON-OFF-Keying (OOK) transmitter because one is interested in knowing the time needed to reach the final frequency & amplitude, but it is of little relevance to receiving systems.

Fortunately, there are oscillator simulation techniques which can benefit radio receivers. We will introduce the conceptually simplest first and then move on to progressively more complicated techniques. 

The 2-port, open loop technique championed by Rhea among others, is suitable for oscillators which have a low impedance node in the feedback path, such as Colpitts, Clapp or Hartley [1-2]. Opening the loop at the low Z node enables simulation of the transmission magnitude |S21| and phase (fig. 1). Reliable oscillation occurs at the frequency where phase S21 crosses 0 degree and the gain exceeds 3 dB (or 1.4 times). The simulated results show 0 deg. phase at 40 MHz and an associated gain of 3.1 or 9.8 dB (fig. 2). If the inductor is very lossy - low unloaded Q (Qul) - the gain  |S21| can drop below 1.4x or 3 dB which is considered as the minimum threshold for reliable starting. On the other hand, if the gain is > 8 dB, one can trade off some gain for better phase noise via the capacitive divider. The phase slope, ph|S21|, permits the loaded Q (QL) to be calculated from  ((pi).fo. delta phase) / (360 . delta freq) [3]. In this example, QL = 10.1. The QL value is required for phase noise calculation. 

Next up the complexity ladder is the 1-port technique described by Rohde KA2WEU [4]. After inserting a port (PORT1) between the inductor and ground (fig. 3), the real & imaginary parts and the magnitude of this port are evaluated; i.e. real(Z11), imag(Z11) and mag(Z11), respectively. Three different feedback capacitor values Cf were alternatively considered, 5 pF / 11.18 pF / 25 pF. Oscillation occurs when the imag(z11) trace crosses 0, e.g when Cf = 11.18 pF, this happens at 750 MHz (fig. 4). The real(Z11) associated with 11.18 pF shows a negative resistance of -0.4. At 25 pF, the real(Z11) is -0.1; i.e. the tiny negative resistance allows no margin for component tolerance & temperature effect. The 5 pF real(Z11) trace has the most negative resistance of -1.1, hence the most reliable starting. However, the bottom graph shows that 5 pF results in the lowest Q of all three values. So, 11.18 pF is the optimum trade-off between QL and reliable starting. 

The most complex technique, Harmonic Balance, can plot the Nyquist graph, amplitude spectrum of the fundamental and harmonics and phase noise (fig. 5). It is also useful for simulating load pulling and frequency pushing, etc.

References:

[1] R. Rhea, Oscillator design & computer simulation,  2nd ed., Georgia: Noble Publishing, 1995, ch. 8: L-C oscillators. 

[2] R. Rhea, “Microwave Oscillator Design using the Open-loop cascade Method”, Microwave J., Oct. 2010

[3] P. Vizmuller, RF design guide, Norwood, MA: Artech, 1995, pp 203. 

[4] U. L. Rohde, “Designing low-phase-noise oscillators", QEX, Oct. 1994.