Injection Locking using CMOS Ring Oscillator and LC Tank

[Midisaurus]

Hello, I am currently doing some undergraduate research, using SPICE3 to simulate a 9-stage Ring Oscillator in series with an LC tank.

Using a combination of SPICE3's transient analysis and MATLAB, I am attempting to plot the change in oscillation frequency as a function of slight changes in VDD. I have successfully plotted this relation for two circuits: one with and one without the LC Tank.

I was hoping to see some locking range centered around the resonant frequency of the LC tank. However, the LC tank circuit simulation produced a plot nearly identical to the circuit without the tank. (See attached PNGs)

I am using a circuit topology based on a diagram in a paper which claims to have proven a locking range when VDD is adjusted by +/-0.5%. I can attach a rough sketch of my design if needed.

Can anyone suggest what I might change to allow the circuit to lock to the LC resonant frequency at a certain range of VDD?

A few of my suspicions are:
Frequency magnitude (~8GHz)?
The LC Tank should also include a resistance in parallel?
SPICE's numerical analysis/convergence issues. (I have my options set fairly strictly, so I don't want to assume this to be the issue yet.)

Thank you in advance.

- - - Updated - - -

The difference between the two figures is only the VDD range.
With FREQvVDD3, I tried to "zoom in" on a small area of FREQvVDD1 in hopes of seeing some locking at smaller steps of VDD, but no luck.

 

[jiripolivka]

I do not do ay modeling. Generally any oscillator can be injection-locked by injecting an external control signal with a frequency close to the free-running frequency of the oscillator.
I did many experiments and all worked well with real oscillators. If you need models, try to MAKE an oscillator and try it.

 

[Midisaurus]

Yes, I agree that ideally the experiment should be physically constructed and proven to operate. In fact, that is the plan eventually.
However we are trying to prove that a circuit using mulit-gate MOSFETs can exhibit the same locking proven to occur in single-gate
designs. The university may be able to get some pre-production models of these transistors, but either way I would like have both simulated and lab data to compare.

The simulation itself is less of an issue. I suppose I should be asking, can I expect to see the oscillator center frequency locking near the
resonant frequency of an LC tank if I simply place the LC tank in parallel with the oscillator? (I will attach a PDF of a rough topology of the circuit)

I understand that many injection locking examples include an explicit current source injected at a known frequency to influence the oscillator
at a particular range of frequencies. The paper I have read claims to be doing this simply with an LC tank. Though it may be more suitable to
call it locking through "resonance" or something of that nature, the paper uses the term "injection locking".

 

[jiripolivka]

Yes, I agree that ideally the experiment should be physically constructed and proven to operate. In fact, that is the plan eventually.
However we are trying to prove that a circuit using mulit-gate MOSFETs can exhibit the same locking proven to occur in single-gate
designs. The university may be able to get some pre-production models of these transistors, but either way I would like have both simulated and lab data to compare.

The simulation itself is less of an issue. I suppose I should be asking, can I expect to see the oscillator center frequency locking near the
resonant frequency of an LC tank if I simply place the LC tank in parallel with the oscillator? (I will attach a PDF of a rough topology of the circuit)

I understand that many injection locking examples include an explicit current source injected at a known frequency to influence the oscillator
at a particular range of frequencies. The paper I have read claims to be doing this simply with an LC tank. Though it may be more suitable to
call it locking through "resonance" or something of that nature, the paper uses the term "injection locking".

Yes, I think you can couple an external LC circuit to oscillator LC circuit. Best "injection locking" is achieved if the external LC circuit has a higher Q, so it will then determine the frequency.
Oscillators to be locked usually are designed to have the free-running frequency wandering around (due to a lower Q of their LC cicuit), so the external injection signal can take control of the frequency. Higher coupling (or injected power) usually means that the resulting frequency is controllable over a wider range.