"DC variance analysis"

DC variance analysis

Symbolic dcvar analysis results

DC solution of the network

$$\left[\begin{matrix}I_{L2}\\I_{V1}\\I_{V2}\\Ii_{F1 XU1}\\I_{Vo XU1}\\Io_{N1 XU1}\\V_{3 XU1}\\V_{5 XU1}\\V_{N001}\\V_{N002}\\V_{N003}\\V_{N004}\\V_{N005}\\V_{P001}\\V_{P002}\\V_{P003}\\V_{out}\end{matrix}\right]=\left[\begin{matrix}0\\\frac{- I_{bR} R_{R2} - V_{supply}}{R_{BR1} + R_{R2}}\\0\\I_{bR}\\0\\- I_{bR}\\\frac{- I_{bR} R_{BR1} R_{R2} - I_{bR} R_{BR1} R_{dr} - I_{bR} R_{R2} R_{dr} + R_{R2} V_{supply}}{R_{BR1} + R_{R2}}\\0\\V_{supply}\\\frac{R_{R2} \left(- I_{bR} R_{BR1} + V_{supply}\right)}{R_{BR1} + R_{R2}}\\\frac{- I_{bR} R_{BR1} R_{R2} - I_{bR} R_{BR1} R_{dr} - I_{bR} R_{R2} R_{dr} + R_{R2} V_{supply}}{R_{BR1} + R_{R2}}\\\frac{- I_{bR} R_{BR1} R_{R2} - I_{bR} R_{BR1} R_{dr} - I_{bR} R_{R2} R_{dr} + R_{R2} V_{supply}}{R_{BR1} + R_{R2}}\\0\\0\\0\\\frac{- I_{bR} R_{BR1} R_{R2} - I_{bR} R_{BR1} R_{dr} - I_{bR} R_{R2} R_{dr} + R_{R2} V_{supply}}{R_{BR1} + R_{R2}}\\\frac{I_{bR} R_{BR} R_{BR1} + I_{bR} R_{BR} R_{R2} - I_{bR} R_{BR1} R_{R2} - I_{bR} R_{BR1} R_{dr} - I_{bR} R_{R2} R_{dr} + R_{R2} V_{supply}}{R_{BR1} + R_{R2}}\end{matrix}\right]$$

Detector-referred variance

$$\sigma_{out}^2=I_{bR}^{2} R_{BR}^{2} \sigma_{R}^{2} + I_{bR}^{2} R_{dr}^{2} \sigma_{R}^{2} + \frac{R_{BR1}^{2} R_{R2}^{2} \sigma_{R}^{2} \left(I_{bR} R_{BR1} - V_{supply}\right)^{2}}{\left(R_{BR1} + R_{R2}\right)^{4}} + \frac{R_{BR1}^{2} R_{R2}^{2} \sigma_{R}^{2} \left(I_{bR} R_{R2} + V_{supply}\right)^{2}}{\left(R_{BR1} + R_{R2}\right)^{4}} + \frac{R_{R2}^{2} \sigma_{V}^{2}}{\left(R_{BR1} + R_{R2}\right)^{2}} + \frac{\sigma_{ibR}^{2} \left(R_{BR} R_{BR1} + R_{BR} R_{R2} - R_{BR1} R_{R2} - R_{BR1} R_{dr} - R_{R2} R_{dr}\right)^{2}}{\left(R_{BR1} + R_{R2}\right)^{2}} + \frac{\sigma_{ioR}^{2} \left(R_{BR} R_{BR1} + R_{BR} R_{R2} + R_{BR1} R_{R2} + R_{BR1} R_{dr} + R_{R2} R_{dr}\right)^{2}}{\left(R_{BR1} + R_{R2}\right)^{2}} + \sigma_{voR}^{2}\, \mathrm{\left[ V^2 \right]}$$

Contributions of individual component variances

Variance of source: I_dcvar_R1
Source variance:$I_{bR}^{2} \sigma_{R}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$I_{bR}^{2} R_{BR}^{2} \sigma_{R}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: I_dcvar_R3
Source variance:$\frac{\sigma_{R}^{2} \left(I_{bR} R_{R2} + V_{supply}\right)^{2}}{\left(R_{BR1} + R_{R2}\right)^{2}}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{R_{BR1}^{2} R_{R2}^{2} \sigma_{R}^{2} \left(I_{bR} R_{R2} + V_{supply}\right)^{2}}{\left(R_{BR1} + R_{R2}\right)^{4}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: I_dcvar_R5
Source variance:$\frac{\sigma_{R}^{2} \left(- I_{bR} R_{BR1} + V_{supply}\right)^{2}}{\left(R_{BR1} + R_{R2}\right)^{2}}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{R_{BR1}^{2} R_{R2}^{2} \sigma_{R}^{2} \left(I_{bR} R_{BR1} - V_{supply}\right)^{2}}{\left(R_{BR1} + R_{R2}\right)^{4}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: I_dcvar_R6
Source variance:$I_{bR}^{2} \sigma_{R}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$I_{bR}^{2} R_{dr}^{2} \sigma_{R}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: Ib_XU1
Source variance:$\sigma_{ibR}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{\sigma_{ibR}^{2} \left(R_{BR} R_{BR1} + R_{BR} R_{R2} - R_{BR1} R_{R2} - R_{BR1} R_{dr} - R_{R2} R_{dr}\right)^{2}}{\left(R_{BR1} + R_{R2}\right)^{2}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: Io_XU1
Source variance:$\sigma_{ioR}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{\sigma_{ioR}^{2} \left(R_{BR} R_{BR1} + R_{BR} R_{R2} + R_{BR1} R_{R2} + R_{BR1} R_{dr} + R_{R2} R_{dr}\right)^{2}}{\left(R_{BR1} + R_{R2}\right)^{2}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: V1
Source variance:$\sigma_{V}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Detector-referred:$\frac{R_{R2}^{2} \sigma_{V}^{2}}{\left(R_{BR1} + R_{R2}\right)^{2}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: V2
Source variance:$0$$\,\mathrm{\left[ V^2 \right]}$
Detector-referred:$0$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: Vo_XU1
Source variance:$\sigma_{voR}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Detector-referred:$\sigma_{voR}^{2}$$\,\mathrm{\left[ V^2 \right]}$

Go to biasingConceptReceiver_index

SLiCAP: Symbolic Linear Circuit Analysis Program, Version 1.6.0 © 2009-2024 SLiCAP development team

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

Last project update: 2024-03-19 13:15:27