DC variance analysis

Dcvar analysis results

DC solution of the network

$$\left[\begin{matrix}I_{V1}\\V_{1}\\V_{out}\end{matrix}\right]=\left[\begin{matrix}- \frac{V_{s}}{R_{a} + R_{b}}\\V_{s}\\\frac{R_{b} V_{s}}{R_{a} + R_{b}}\end{matrix}\right]$$

Detector-referred variance

$$\sigma_{out}^2=\frac{R_{a}^{2} R_{b}^{2} V_{s}^{2} \sigma_{2}^{2}}{\left(R_{a} + R_{b}\right)^{4}} + \frac{R_{a}^{2} R_{b}^{2} V_{s}^{2} \sigma_{3}^{2}}{\left(R_{a} + R_{b}\right)^{4}} + \frac{R_{b}^{2} V_{s}^{2} \sigma_{1}^{2}}{\left(R_{a} + R_{b}\right)^{2}}\, \mathrm{\left[ V^2 \right]}$$

Contributions of individual component variances

Variance of source: I_dcvar_R1
Source variance:$\frac{V_{s}^{2} \sigma_{2}^{2}}{\left(R_{a} + R_{b}\right)^{2}}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{R_{a}^{2} R_{b}^{2} V_{s}^{2} \sigma_{2}^{2}}{\left(R_{a} + R_{b}\right)^{4}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: I_dcvar_R2
Source variance:$\frac{V_{s}^{2} \sigma_{3}^{2}}{\left(R_{a} + R_{b}\right)^{2}}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{R_{a}^{2} R_{b}^{2} V_{s}^{2} \sigma_{3}^{2}}{\left(R_{a} + R_{b}\right)^{4}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: V1
Source variance:$V_{s}^{2} \sigma_{1}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Detector-referred:$\frac{R_{b}^{2} V_{s}^{2} \sigma_{1}^{2}}{\left(R_{a} + R_{b}\right)^{2}}$$\,\mathrm{\left[ V^2 \right]}$

Go to vDivider_index

SLiCAP: Symbolic Linear Circuit Analysis Program, Version 2.0.1 © 2009-2024 SLiCAP development team

For documentation, examples, support, updates and courses please visit: analog-electronics.tudelft.nl

Last project update: 2024-10-20 16:54:18