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Research Update 3/18/16

Today’s goal was to understand and model VCO nonlinearity, specifically in $k_{VCO}$. Rather than just have $k_{VCO}$ as a linear function, it’s actually more similar to hyperbolic tan ($tanh(x)$). While that’s an ugly function, the output is actually quite simple. Instead of just having a normal linear function, we just put limits on the positive and negative values we can get out of it. Nominally, these are nicely at $\pm1$.

HyperbolicTan (Courtesy WikiMedia)

Unfortunately my simulator doesn’t have trigonometric math functions available to it, so we have to use a polynomial fit. MATLAB’s is decent enough for me to use. A 5th order polynomial covers it pretty well, and gives the following output: