# Phase Shift Oscillator | Theoretical Frequency Mismatch

I am working with a few colleagues to build a transceiver system 100% from scratch. A necessary component here is the local oscillator system - we have opted to use a phase shift oscillator to generate our target frequencies. Below is the oscillator circuit we built, modeled through LTSpice:

As I understand, the frequency output should be determined according to the relation: $$f = \frac{1}{2\pi RC\sqrt{2N}}$$ Where N is the number of phase-shift networks and R,C are the values of resistance and capacitance in these networks, respectively.

Based on these assumptions, the above circuit should have N=3, R=10,000, & C=270E-12 - the sinusoidal output is expected to be very near 24KHz. However, both the simulation and actualized circuits are producing a frequency double this, in the vicinity of 47-50KHz. Have I made a poor assumption? Have I overlooked something simple? Why is the actual frequency output double my expected value?

• Your oscillator may be more reliable if you use a low-pass network instead of a high-pass one. That's probably not what's causing your current difficulty, though. Oct 23, 2019 at 0:48
• you will have high phase noise. Will that effect the usefulness of your transceiver? Oct 23, 2019 at 4:14
• @TimWescott An interesting suggestion; under what circumstances would you expect a lowpass network-based oscillator to be more stable?
– OPET
Oct 23, 2019 at 8:22
• @analogsystemsrf Almost certainly! I expect noise figure calculations to be the main concern in the next iteration. For now, my computer engineers are eager to begin flushing out their communications protocols, so I've opted to throw together a "quick and dirty" 4QAM channel across a handful of subcarriers - an insufficient bitrate for later data transfers, but enough to work through basic handshakes and such. I (optimistically) expect our receiver to distinguish between 2 distinct phase states in the presence of this noise for now
– OPET
Oct 23, 2019 at 8:28
• It's just that circuits are less predictable at high frequencies, with more parasitic components having an effect. A low-pass network just naturally cuts off the possibility of oscillation or noise amplification at high frequencies. Oct 23, 2019 at 13:57