"DC variance analysis"

DC variance analysis

Symbolic dcvar analysis results

DC solution of the network

$$\left[\begin{matrix}I_{L1}\\I_{V1}\\I_{V2}\\Ii_{F1 XU1}\\I_{Vo XU1}\\Io_{N1 XU1}\\V_{3 XU1}\\V_{5 XU1}\\V_{N001}\\V_{N002}\\V_{N003}\\V_{N004}\\V_{N005}\\V_{P001}\\V_{P002}\\V_{P003}\\V_{out}\end{matrix}\right]=\left[\begin{matrix}\frac{I_{bT} R_{ds}}{R_{ds} + R_{s}}\\0\\\frac{- I_{bT} R_{BT2} - V_{supply}}{R_{BT1} + R_{BT2}}\\I_{bT}\\0\\- I_{bT}\\\frac{- I_{bT} R_{BT} R_{BT1} - I_{bT} R_{BT} R_{BT2} - I_{bT} R_{BT1} R_{BT2} + R_{BT2} V_{supply}}{R_{BT1} + R_{BT2}}\\0\\V_{supply}\\\frac{R_{BT2} \left(- I_{bT} R_{BT1} + V_{supply}\right)}{R_{BT1} + R_{BT2}}\\\frac{- I_{bT} R_{BT} R_{BT1} - I_{bT} R_{BT} R_{BT2} - I_{bT} R_{BT1} R_{BT2} + R_{BT2} V_{supply}}{R_{BT1} + R_{BT2}}\\\frac{- I_{bT} R_{BT} R_{BT1} - I_{bT} R_{BT} R_{BT2} - I_{bT} R_{BT1} R_{BT2} + R_{BT2} V_{supply}}{R_{BT1} + R_{BT2}}\\0\\\frac{- I_{bT} R_{BT} R_{BT1} - I_{bT} R_{BT} R_{BT2} - I_{bT} R_{BT1} R_{BT2} + R_{BT2} V_{supply}}{R_{BT1} + R_{BT2}}\\\frac{- I_{bT} R_{BT} R_{BT1} - I_{bT} R_{BT} R_{BT2} - I_{bT} R_{BT1} R_{BT2} + R_{BT2} V_{supply}}{R_{BT1} + R_{BT2}}\\0\\\frac{- I_{bT} R_{BT} R_{BT1} R_{ds} - I_{bT} R_{BT} R_{BT1} R_{s} - I_{bT} R_{BT} R_{BT2} R_{ds} - I_{bT} R_{BT} R_{BT2} R_{s} - I_{bT} R_{BT1} R_{BT2} R_{ds} - I_{bT} R_{BT1} R_{BT2} R_{s} + I_{bT} R_{BT1} R_{ds} R_{s} + I_{bT} R_{BT2} R_{ds} R_{s} + R_{BT2} R_{ds} V_{supply} + R_{BT2} R_{s} V_{supply}}{\left(R_{BT1} + R_{BT2}\right) \left(R_{ds} + R_{s}\right)}\end{matrix}\right]$$

Detector-referred variance

$$\sigma_{out}^2=I_{bT}^{2} R_{BT}^{2} \sigma_{R}^{2} + \frac{I_{bT}^{2} R_{ds}^{2} R_{s}^{4} \sigma_{R}^{2}}{\left(R_{ds} + R_{s}\right)^{4}} + \frac{R_{BT1}^{2} R_{BT2}^{2} \sigma_{R}^{2} \left(I_{bT} R_{BT1} - V_{supply}\right)^{2}}{\left(R_{BT1} + R_{BT2}\right)^{4}} + \frac{R_{BT1}^{2} R_{BT2}^{2} \sigma_{R}^{2} \left(I_{bT} R_{BT2} + V_{supply}\right)^{2}}{\left(R_{BT1} + R_{BT2}\right)^{4}} + \frac{R_{BT2}^{2} \sigma_{V}^{2}}{\left(R_{BT1} + R_{BT2}\right)^{2}} + \frac{\sigma_{ibT}^{2} \left(R_{BT} R_{BT1} R_{ds} + R_{BT} R_{BT1} R_{s} + R_{BT} R_{BT2} R_{ds} + R_{BT} R_{BT2} R_{s} + R_{BT1} R_{BT2} R_{ds} + R_{BT1} R_{BT2} R_{s} - R_{BT1} R_{ds} R_{s} - R_{BT2} R_{ds} R_{s}\right)^{2}}{\left(R_{BT1} + R_{BT2}\right)^{2} \left(R_{ds} + R_{s}\right)^{2}} + \frac{\sigma_{ioT}^{2} \left(R_{BT} R_{BT1} R_{ds} + R_{BT} R_{BT1} R_{s} + R_{BT} R_{BT2} R_{ds} + R_{BT} R_{BT2} R_{s} + R_{BT1} R_{BT2} R_{ds} + R_{BT1} R_{BT2} R_{s} + R_{BT1} R_{ds} R_{s} + R_{BT2} R_{ds} R_{s}\right)^{2}}{\left(R_{BT1} + R_{BT2}\right)^{2} \left(R_{ds} + R_{s}\right)^{2}} + \sigma_{voT}^{2}\, \mathrm{\left[ V^2 \right]}$$

Contributions of individual component variances

Variance of source: I_dcvar_R1
Source variance:$0$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$0$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: I_dcvar_R2
Source variance:$\frac{\sigma_{R}^{2} \left(I_{bT} R_{BT2} + V_{supply}\right)^{2}}{\left(R_{BT1} + R_{BT2}\right)^{2}}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{R_{BT1}^{2} R_{BT2}^{2} \sigma_{R}^{2} \left(I_{bT} R_{BT2} + V_{supply}\right)^{2}}{\left(R_{BT1} + R_{BT2}\right)^{4}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: I_dcvar_R4
Source variance:$\frac{\sigma_{R}^{2} \left(- I_{bT} R_{BT1} + V_{supply}\right)^{2}}{\left(R_{BT1} + R_{BT2}\right)^{2}}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{R_{BT1}^{2} R_{BT2}^{2} \sigma_{R}^{2} \left(I_{bT} R_{BT1} - V_{supply}\right)^{2}}{\left(R_{BT1} + R_{BT2}\right)^{4}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: I_dcvar_R5
Source variance:$\frac{I_{bT}^{2} R_{s}^{2} \sigma_{R}^{2}}{\left(R_{ds} + R_{s}\right)^{2}}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{I_{bT}^{2} R_{ds}^{2} R_{s}^{4} \sigma_{R}^{2}}{\left(R_{ds} + R_{s}\right)^{4}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: I_dcvar_R6
Source variance:$I_{bT}^{2} \sigma_{R}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$I_{bT}^{2} R_{BT}^{2} \sigma_{R}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: Ib_XU1
Source variance:$\sigma_{ibT}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{\sigma_{ibT}^{2} \left(R_{BT} R_{BT1} R_{ds} + R_{BT} R_{BT1} R_{s} + R_{BT} R_{BT2} R_{ds} + R_{BT} R_{BT2} R_{s} + R_{BT1} R_{BT2} R_{ds} + R_{BT1} R_{BT2} R_{s} - R_{BT1} R_{ds} R_{s} - R_{BT2} R_{ds} R_{s}\right)^{2}}{\left(R_{BT1} + R_{BT2}\right)^{2} \left(R_{ds} + R_{s}\right)^{2}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: Io_XU1
Source variance:$\sigma_{ioT}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$\frac{\sigma_{ioT}^{2} \left(R_{BT} R_{BT1} R_{ds} + R_{BT} R_{BT1} R_{s} + R_{BT} R_{BT2} R_{ds} + R_{BT} R_{BT2} R_{s} + R_{BT1} R_{BT2} R_{ds} + R_{BT1} R_{BT2} R_{s} + R_{BT1} R_{ds} R_{s} + R_{BT2} R_{ds} R_{s}\right)^{2}}{\left(R_{BT1} + R_{BT2}\right)^{2} \left(R_{ds} + R_{s}\right)^{2}}$$\,\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: V2
Source variance:$\sigma_{V}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Detector-referred:$\frac{R_{BT2}^{2} \sigma_{V}^{2}}{\left(R_{BT1} + R_{BT2}\right)^{2}}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: Vo_XU1
Source variance:$\sigma_{voT}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Detector-referred:$\sigma_{voT}^{2}$$\,\mathrm{\left[ V^2 \right]}$

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