"Symbolic noise analysis"

Symbolic noise analysis

Symbolic noise analysis results

Detector-referred noise spectrum

$$S_{out}=\frac{R_{B}^{2} R_{\ell}^{2} S_{i}}{R_{\ell}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right) + R_{\ell} R_{o} \left(2 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 2\right) + R_{o}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)} + \frac{4 R_{B} R_{\ell}^{2} T k}{R_{\ell}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right) + R_{\ell} R_{o} \left(2 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 2\right) + R_{o}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)} + \frac{4 R_{\ell}^{2} R_{o} T k \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}{R_{\ell}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right) + R_{\ell} R_{o} \left(2 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 2\right) + R_{o}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)} + \frac{R_{\ell}^{2} S_{v} \left(9 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}{R_{\ell}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right) + R_{\ell} R_{o} \left(2 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 2\right) + R_{o}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}\, \mathrm{\left[\frac{V^2}{Hz}\right]}$$

Source-referred noise spectrum

$$S_{in}=\frac{S_{i}}{4 \pi^{2} C_{A}^{2} f^{2}} + \frac{T k}{\pi^{2} C_{A}^{2} R_{B} f^{2}} + \frac{R_{o} T k \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}{\pi^{2} C_{A}^{2} R_{B}^{2} f^{2}} + \frac{S_{v} \left(9 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}{4 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2}}\, \mathrm{\left[\frac{V^2}{Hz}\right]}$$

Contributions of individual noise sources

Noise source: I1
Spectral density:$\frac{4 T k}{R_{B}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$\frac{4 R_{B} R_{\ell}^{2} T k}{R_{\ell}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right) + R_{\ell} R_{o} \left(2 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 2\right) + R_{o}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Source-referred:$\frac{T k}{\pi^{2} C_{A}^{2} R_{B} f^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: I1_XU1
Spectral density:$S_{i}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$\frac{R_{B}^{2} R_{\ell}^{2} S_{i}}{R_{\ell}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right) + R_{\ell} R_{o} \left(2 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 2\right) + R_{o}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Source-referred:$\frac{S_{i}}{4 \pi^{2} C_{A}^{2} f^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: I2
Spectral density:$\frac{4 T k}{R_{o}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$\frac{4 R_{\ell}^{2} R_{o} T k \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}{R_{\ell}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right) + R_{\ell} R_{o} \left(2 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 2\right) + R_{o}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Source-referred:$\frac{R_{o} T k \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}{\pi^{2} C_{A}^{2} R_{B}^{2} f^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: V1
Spectral density:$0$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Detector-referred:$0$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Source-referred:$0$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: V1_XU1
Spectral density:$S_{v}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Detector-referred:$\frac{R_{\ell}^{2} S_{v} \left(9 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}{R_{\ell}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right) + R_{\ell} R_{o} \left(2 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 2\right) + R_{o}^{2} \left(\pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Source-referred:$\frac{S_{v} \left(9 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2} + 1\right)}{4 \pi^{2} C_{A}^{2} R_{B}^{2} f^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$

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Last project update: 2022-04-01 16:59:05