DC variance analysis

Dcvar analysis results

DC solution of the network

$$\left[\begin{matrix}I_{V1}\\Ii_{F1 X1}\\I_{Vo X1}\\Io_{N1 X1}\\V_{1}\\V_{2}\\V_{3}\\V_{3 X1}\\V_{4}\\V_{5 X1}\\V_{out}\end{matrix}\right]=\left[\begin{matrix}\frac{- I_{b} R_{b} - V_{P}}{R_{a} + R_{b}}\\I_{b}\\0\\- I_{b}\\V_{P}\\\frac{R_{b} \left(- I_{b} R_{a} + V_{P}\right)}{R_{a} + R_{b}}\\\frac{- I_{b} R_{a} R_{b} - I_{b} R_{a} R_{c} - I_{b} R_{b} R_{c} + R_{b} V_{P}}{R_{a} + R_{b}}\\\frac{- I_{b} R_{a} R_{b} - I_{b} R_{a} R_{c} - I_{b} R_{b} R_{c} + R_{b} V_{P}}{R_{a} + R_{b}}\\\frac{- I_{b} R_{a} R_{b} - I_{b} R_{a} R_{c} - I_{b} R_{b} R_{c} + R_{b} V_{P}}{R_{a} + R_{b}}\\0\\\frac{I_{b} R \left(A_{v} - 1\right) \left(R_{a} + R_{b}\right) - I_{b} \left(R_{a} R_{b} + R_{a} R_{c} + R_{b} R_{c}\right) + R_{b} V_{P}}{R_{a} + R_{b}}\end{matrix}\right]$$

Detector-referred variance

$$\sigma_{out}^2=I_{b}^{2} R^{2} \sigma_{R}^{2} \left(A_{v} - 1\right)^{2} + I_{b}^{2} R_{c}^{2} \sigma_{R}^{2} + \frac{I_{b}^{2} \sigma_{ib}^{2} \left(A_{v} R R_{a} + A_{v} R R_{b} - R R_{a} - R R_{b} - R_{a} R_{b} - R_{a} R_{c} - R_{b} R_{c}\right)^{2}}{\left(R_{a} + R_{b}\right)^{2}} + \frac{R_{a}^{2} R_{b}^{2} \sigma_{R}^{2} \left(I_{b} R_{a} - V_{P}\right)^{2}}{\left(R_{a} + R_{b}\right)^{4}} + \frac{R_{a}^{2} R_{b}^{2} \sigma_{R}^{2} \left(I_{b} R_{b} + V_{P}\right)^{2}}{\left(R_{a} + R_{b}\right)^{4}} + \frac{i_{off}^{2} \left(A_{v} R R_{a} + A_{v} R R_{b} - R R_{a} - R R_{b} + R_{a} R_{b} + R_{a} R_{c} + R_{b} R_{c}\right)^{2}}{\left(R_{a} + R_{b}\right)^{2}} + v_{off}^{2}\, \mathrm{\left[ V^2 \right]}$$

Contributions of individual component variances

Variance of source: I_dcvar_R1
Source variance:$\frac{\sigma_{R}^{2} \left(I_{b} R_{b} + V_{P}\right)^{2}}{\left(R_{a} + R_{b}\right)^{2}}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{R_{a}^{2} R_{b}^{2} \sigma_{R}^{2} \left(I_{b} R_{b} + V_{P}\right)^{2}}{\left(R_{a} + R_{b}\right)^{4}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: I_dcvar_R2
Source variance:$\frac{\sigma_{R}^{2} \left(- I_{b} R_{a} + V_{P}\right)^{2}}{\left(R_{a} + R_{b}\right)^{2}}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{R_{a}^{2} R_{b}^{2} \sigma_{R}^{2} \left(I_{b} R_{a} - V_{P}\right)^{2}}{\left(R_{a} + R_{b}\right)^{4}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: I_dcvar_R3
Source variance:$I_{b}^{2} \sigma_{R}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$I_{b}^{2} R_{c}^{2} \sigma_{R}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: I_dcvar_R4
Source variance:$I_{b}^{2} \sigma_{R}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$I_{b}^{2} R^{2} \sigma_{R}^{2} \left(A_{v} - 1\right)^{2}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: Ib_X1
Source variance:$I_{b}^{2} \sigma_{ib}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{I_{b}^{2} \sigma_{ib}^{2} \left(A_{v} R R_{a} + A_{v} R R_{b} - R R_{a} - R R_{b} - R_{a} R_{b} - R_{a} R_{c} - R_{b} R_{c}\right)^{2}}{\left(R_{a} + R_{b}\right)^{2}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: Io_X1
Source variance:$i_{off}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{i_{off}^{2} \left(A_{v} R R_{a} + A_{v} R R_{b} - R R_{a} - R R_{b} + R_{a} R_{b} + R_{a} R_{c} + R_{b} R_{c}\right)^{2}}{\left(R_{a} + R_{b}\right)^{2}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: V1
Source variance:$0$$\,\mathrm{\left[ V^2 \right]}$
Detector-referred:$0$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: Vo_X1
Source variance:$v_{off}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Detector-referred:$v_{off}^{2}$$\,\mathrm{\left[ V^2 \right]}$

Go to VampBiasTotal_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