Simulating the LC tank to determine the oscillation frequency

Dear wgtkan,

wgtkan said:

I am trying to determine the center frequency of an LC tank for an NMOS LC VCO. I followed this note from a previous question. https://community.cadence.com/cadence_technology_forums/f/rf-design/32224/lc-parallel-circuit-at-resonant-frequency

I did run an s-parameter simulation of the impedance against the frequency on the ideal LC tank and s11 produces the expected response. I am attaching the circuit and the response. On the other hand, when I use real devices, it is producing something different. I consulted the model file for the 130nm hp process but I am not getting it to produce the desired response. I am attaching the schematic and the waveform I am getting.

What am I doing wrong?

I have explained the reason for this and provided a means to better estimate the frequency of oscillation of an oscillator in the past in these forums, If you don't mind, I would like to refer you to one of the more recent responses in lieu of re-typing the same basic information. If you examine the responses at:

community.cadence.com/.../1366802

I'm not sure, but you may find other portions of the discussion insightful too wgtkan. Let me know if anything is not clear or if you feel this is not addressing your basic concern. I've included a portion of that response below that might save you some time. There are other posts that I've not included where I explaing the concept of "negative resistance" and a means to estimate it for a sustaining amplifier.

Shawn

From post URL provided above:

A VCO  with a "real" sustaining amplifier (such as you are using) will not operate at a frequency exactly as the resonance of discrete L and C you included in your schematic. Basically, you are neglecting the MOS capacitances and resistances of your sustaining amplifier and its trace parasitics. A way to estimate (and only estimate) the frequency your VCO will operate is to perform a set of small-signal (large signal is more accurate) negative resistance simulations where you separate the LC tank from the sustaining amplifer and drivie the nodes that the resonator is connected to with an ideal current source. Examine the impedance (real and imaginary parts) of the sustaining amplifier (i.e., the impedance it presents to the LC resonator that was connected to those nodes). You may estimate (and I stress this is only an estimate) the final operating, steady-state frequency, by changing the frequency of your analysis results to find the frequency at the the imaginary part of the sustaining amplifer is equal and opposite to the imaginary part of the LC resonator. 

You will also note that the real impedance of the sustaining amplifier is not constant with frequency. Hence, as you change your ideal C, the amount of gain the sustaining amplifier will chance with frequency. This means that the steady-state amplitude of the VCO will vary over frequency and not be simply given by the expression "4*Id*Rp/pi.

I know there is a lot I've "packed" into this response and it will take some time to digest, but I wanted to as clear as I could to help you understand the issue.

I am also attaching a response I provided a number of years back to a similarly phrased question as yours. There is a bit more background and a link to a prior post with an example test bench to study the impedance of your resonator.

Shawn

--------------Post from 8/23/2019------------

Dear Tom,

Tom Brown said:
i want to simulate the frequency response of the tank impddance.
If you are interested in the tank impedance, I might suggest that in lieu of simulated the S parameters, you simulate the impedance (i.e., real and imaginary parts). This will also provide a much more intuitive view of the required negative resistance required from the sustaining amplifier to assure steady-state oscillation. Basically, separate the sustaining amplifier from the tank impedance (the latter can include any varactors if desired). You can then directly simulate the small-signal impedance of the tank impedance over frequency. If you are including the varactors in the tank impedance, you will need to simulate the impedance over the full range of the control voltage used to vary the varactor impedance.

If you can set the operating point of the sustaining amplifier to its large signal operating point at start-up, you may then also determine its small-signal impedance (at start-up). As you correctly noted, if the sustaining amplifier's negative real impedance exceeds in magnitude the real impedance of the tank at a given frequency, then as oscillation builds, the negative impedance of the sustaining amplifier will decrease towards 0 until it is equal and opposite in sign to the tank's real impedance.

If you are having trouble devising a test bench to determine the impedance of the tank/varactor network, I might suggest you examine an example at URL:

community.cadence.com/.../capacitance-vs-bias-voltage-curve-for-ferroelectric-varactor

I hope I understood your question correctly and this is somewhat useful Tom,