"Determination of NMOS $W$, $L$ and $ID$"

Determination of NMOS $W$, $L$ and $ID$

Noise model for determination of $W$ and $L$ and $ID$.

Initial estimate of the inversion coefficient and the channel length.

We assume that this transistor with very large input capacitance and low transconductance operates in weak inversion.

The initial value of the inversion coefficient is estamated as $0.00878$. This value can later be adjusted

The channel length of the input transistor is selected as: $1.0 \cdot 10^{-5}$.

Determination of the channel width $W$

SLiCAP's EKV noise model 'N18_noise' evaluates the noise performance of an NMOS with $W$ and $L$ and $ID$ as input parameters.

By doing so, it calculates the inversion coefficient from these input parameters.

If we delete the model definition of the inversion coefficient, we can use it as input parameter, rather than the drain current.

We can then express $c_{iss}$ in terms of the inversion coefficient:

\begin{equation} c_{iss}=\frac{0.02583 L W \left(0.6667 - \frac{0.3333 \left(\left(IC_{XU1} + 0.25\right)^{0.5} + 1.5\right)}{\left(\left(IC_{XU1} + 0.25\right)^{0.5} + 0.5\right)^{2}}\right)}{\pi} + \frac{0.001987 L W \left(1 + \frac{\left(IC_{XU1} + 0.25\right)^{0.5} + 1.5}{\left(\left(IC_{XU1} + 0.25\right)^{0.5} + 0.5\right)^{2}}\right)}{\pi} + 2.0 \cdot 10^{-12} L + 7.8 \cdot 10^{-10} W \end{equation}

With our first esimate of the inversion coefficient and the selected channel length, we can find the width using the result from the previous design step:

\begin{equation} c_{iss}=2.839 \cdot 10^{-11} \end{equation}

We obtain:

\begin{equation} W=0.001399 \end{equation}

We will round this to a number of $27$ fingers, each with a width of $49.99999999999999\, \mu$m.

Determination of the drain current $ID$

After substitution of all the know variable, the EKV noise model provides the transconductance $g_m$ as a function of the drain current $ID$:

\begin{equation} g_{m}=\frac{29.76 ID}{\left(0.002794 \pi \left(9.777 \cdot 10^{-6} \pi + 1\right)^{0.5} \cdot \left(9.777 \cdot 10^{-6} \pi \left(9.777 \cdot 10^{-6} \pi + 1\right)^{0.5} + 1\right) + 0.02643 \pi^{0.5} \left(9.777 \cdot 10^{-6} \pi + 1\right)^{0.25} \left(9.777 \cdot 10^{-6} \pi \left(9.777 \cdot 10^{-6} \pi + 1\right)^{0.5} + 1\right)^{0.5} + 1\right)^{0.5}} \end{equation}

From this equation and the desired value of $g_m$ obtained from our previous design step, we obtain $ID$:

\begin{equation} ID=1.066 \cdot 10^{-6} \end{equation}

Design verification

The noise spectrum at the output of the receive coil amplifier is shown below.

The DIN A weighted RMS output noise over the frequency range of interest amounts $11.1\,\mu$V.

Go to noiseWLI_n_index

SLiCAP: Symbolic Linear Circuit Analysis Program, Version 2.0.1 © 2009-2023 SLiCAP development team

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Last project update: 2023-12-28 22:44:08