"Symbolic DC variance analysis"

Symbolic DC variance analysis

Symbolic dcvar analysis results

DC solution of the network

$$\left[\begin{matrix}I_{V1}\\Io_{N1 XU1}\\Ii_{F1 XU1}\\I_{Vo XU1}\\V_{3 XU1}\\V_{5 XU1}\\V_{N001}\\V_{N002}\\V_{N003}\\V_{out}\end{matrix}\right]=\left[\begin{matrix}0\\- \frac{I_{b} \left(R_{B} + R_{\ell} + R_{o}\right)}{R_{\ell} + R_{o}}\\I_{b}\\0\\0\\0\\0\\0\\\frac{I_{b} R_{B} R_{\ell}}{R_{\ell} + R_{o}}\\I_{b} R_{B}\end{matrix}\right]$$

Detector-referred variance

$$\sigma_{out}^2=R_{B}^{2} \sigma_{ib}^{2} + R_{B}^{2} \sigma_{io}^{2} + \sigma_{vo}^{2}\, \mathrm{\left[ V^2 \right]}$$

Source-referred variance

$$\sigma_{in}^2=\tilde{\infty} R_{B}^{2} \sigma_{ib}^{2} + \tilde{\infty} R_{B}^{2} \sigma_{io}^{2} + \tilde{\infty} \sigma_{vo}^{2}\, \mathrm{\left[ V^2 \right]}$$

Contributions of individual component variances

Variance of source: Ib_XU1
Source variance:$\sigma_{ib}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$R_{B}^{2} \sigma_{ib}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Source-referred:$\tilde{\infty} R_{B}^{2} \sigma_{ib}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: Io_XU1
Source variance:$\sigma_{io}^{2}$$\,\mathrm{\left[ A^2 \right]}$
Detector-referred:$R_{B}^{2} \sigma_{io}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Source-referred:$\tilde{\infty} R_{B}^{2} \sigma_{io}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Variance of source: Vo_XU1
Source variance:$\sigma_{vo}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Detector-referred:$\sigma_{vo}^{2}$$\,\mathrm{\left[ V^2 \right]}$
Source-referred:$\tilde{\infty} \sigma_{vo}^{2}$$\,\mathrm{\left[ V^2 \right]}$

$R_B$ converts the input bias current of the controller into an output offset voltage. The total output offset voltage is the sum of the offset voltage of the controller and the procuct of $R_B$ and the sum of the input bias current and the input offset current of the controller.

A show-stopper value of $R_B$ is found if the voltage drop across it reduces the output voltage drive capability below the required value. An upper limit for the total DC current that flows in the OpAmp (controller) terminals can be found by considering the noise associated with this current. This current noise can be converted into a source-referred voltage noise, similar as that of $R_B$. A show-stopper value of the bias current can thus be found from:

\begin{equation} 2 I_{b} q=\frac{4 T k}{R_{B}} \end{equation}

From which we obtain:

\begin{equation} I_{b max}=4.894 \cdot 10^{-9} \end{equation}

Hence the maximum voltage drop across $R_B$ with $R_B=R_{B_{min_{noise}}}$ amounts:

\begin{equation} V_{dc RB}=0.05175\,\left[ \mathrm{V}\right] \end{equation}

Hence, with a low-bias OpAmp, the DC voltage drop across the bias resistor will not significantly reduce the load voltage drive capability.

Go to RB_DCvar_index

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Last project update: 2021-04-05 16:24:22