"Loop Gain In terms of Transconductance and Gate Capacitance"

Loop Gain In terms of Transconductance and Gate Capacitance

Output Transconductance in terms of Maximum Loop Gain Error

The DC Loop gain and Servo Function are:

\begin{equation} L_{GDC}=- \frac{259.5 g_{mo}}{\frac{0.0004519 ID_{o}}{L_{o}} + 3.559} \end{equation}

Servo Function Gain Bandwidth in terms of Gate Capacitance:

\begin{equation} S_{func}=\frac{1.138 \cdot 10^{4} g_{mo} s \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right) + 259.5 g_{mo}}{C_{gso} \left(\frac{1.441 ID_{o} s^{2} \cdot \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right)}{L_{o}} + \frac{0.0206 ID_{o} s}{L_{o}} + 1.151 \cdot 10^{4} s^{2} \cdot \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right) + 164.6 s\right) + \frac{0.04493 ID_{o} s \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right)}{L_{o}} + \frac{0.0004519 ID_{o}}{L_{o}} + 1.138 \cdot 10^{4} g_{mo} s \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right) + 259.5 g_{mo} + 356.8 s \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right) + 3.559} \end{equation}

This is similar to determining the bandwidth for a system that has a loop gain and zeros in the feedback loop

That means the bandwidth is determined by the minimum between two functions.

So I can write the Servo function bandwidth as a function of $C_{gso}$ where:

\begin{equation} L_{Cgs}=\frac{\frac{0.04493 ID_{o} s \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right)}{L_{o}} + \frac{0.0004519 ID_{o}}{L_{o}} + 1.138 \cdot 10^{4} g_{mo} s \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right) + 259.5 g_{mo} + 356.8 s \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right) + 3.559}{C_{gso} \left(\frac{1.441 ID_{o} s^{2} \cdot \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right)}{L_{o}} + \frac{0.0206 ID_{o} s}{L_{o}} + 1.151 \cdot 10^{4} s^{2} \cdot \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right) + 164.6 s\right)} \end{equation} \begin{equation} S_{Cgs0}=\frac{1.138 \cdot 10^{4} g_{mo} s \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right) + 259.5 g_{mo}}{C_{gso} \left(\frac{0.04493 ID_{o} s \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right)}{L_{o}} + \frac{0.0004519 ID_{o}}{L_{o}} + 1.138 \cdot 10^{4} g_{mo} s \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right) + 259.5 g_{mo} + 356.8 s \left(1.87 \cdot 10^{-13} \pi + 1.979 \cdot 10^{-12}\right) + 3.559\right)} \end{equation}

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Last project update: 2023-11-25 20:52:48