Calculation of noise multiplication factor (γ) for Ring VCO

Dear  Upendra Ch,

Upendra Ch said:

In noise calculation in Ring VCO, there is a noise multiplication factor (γ). How to calculate γ in different technology.

I am not sure if I fully understand your question. Let me try to answer what I think you might be asking.

If you are asking about the noise multiplication factor associated with MOS devices used in a CMOS buffer or ring based oscillator (series of CMOS buffers), this has nothing to do with a Cadence noise analysis, but is a function of the MOS process node and specific device attributes. The information is not visible as it is included in a device model of your PDK. The entire reason for have a noise multiplication factor is that the exact noise of given device is not a deterministic quantity related to its parameters and process - but is often some factor difference from the "theoretical value". 

Shawn

Thank you for your response,

I am talking about the thermal noise of the MOS i.e 4KTγgm. This γ value, how do we calculate this?   Is it the same what you have mentioned in your comments? 

Thanks

Dear Upendra Ch,

Upendra Ch said:

I am talking about the thermal noise of the MOS i.e 4KTγgm.

Aha! Now, I understand your question. Thank you for clarifying this!

Upendra Ch said:

This γ value, how do we calculate this? 

To my knowledge, the value of gamma can only be calculated based on a model for a long channel device. Basically, the assumption is that the channel is composed of many small resistor segments dR and hence each contributes a noise term of  noise term of v^2 = 4kTdR. The current noise is related to the voltage noise by the channel impedance - which will vary across the channel. When integrated (summed) over the depletion width of the channel length in strong inversion, the total is i^2 = 4kTgm*2/3 where gm is the small-signal transconductance. The factor of 2/3 is what you are referring to as the "gamma" I believe. This simplified model is only valid for MOS devices with relatively long channel lengths as at short channel lengths the current flow is limited by other effects other than solely channel resistance.

Hence, as you might imagine, computing or measuring the value of gamma for a specific device in a technology requires knowledge of the mechanisms impeding current flow. Therefore, in general for short channel devices, the gamma value is not easily computed nor predicted.

From reference [1], Figure 1 shows the variation in gamma for a number of technologies and compares the values to the long-channel value of 2/3. If you have an interest, you might consider the article I include as reference [2].

I hope this helps Upendra Ch!

Shawn

Figure 1 (from reference [1])

References:

[1] Y. P. Tsividis, Operation and Modeling of the MOS Transistor, New York: Wiley, 1987.

[2] R. Navid, R. Navid, T. H. Lee and R. W. Dutton, "A Circuit-Based Noise Parameter Extraction Technique for MOSFETs," 2007 IEEE International Symposium on Circuits and Systems, New Orleans, LA, USA, 2007, pp. 3347-3350,

If you want to find it with simulation, grab a long-channel FET, run noise simulation, take a look at drain noise voltage PSD (assuming all drain noise current passes through 1-ohm load resistor), then roughly by knowing V^2(noise)=4kTgamma(gm), and also using calc to find gm, you can estimate gamma!

Thank You for your response.