"Symbolic noise analysis"

Symbolic noise analysis

Symbolic noise analysis results

Detector-referred noise spectrum

$$S_{out}=\frac{2 R_{a} T k \left(R_{b} - R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}} + \frac{4 R_{b} T k \left(R_{a} + R_{c} + R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}} + \frac{2 R_{c} T k \left(R_{b} - R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}} + \frac{4 R_{s} T k \left(R_{a} + R_{b} + R_{c}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}} + \frac{2 S_{i} \left(0.5 R_{a} R_{b} + 0.5 R_{a} R_{s} + 0.5 R_{b} R_{c} + R_{b} R_{s} + 0.5 R_{c} R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}} + \frac{2 S_{v} \left(R_{a} + 0.5 R_{b} + R_{c} + 0.5 R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}\, \mathrm{\left[\frac{A^2}{Hz}\right]}$$

Source-referred noise spectrum

$$S_{in}=\frac{2 R_{a} T k \left(R_{b} - R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}} + \frac{4 R_{b} T k \left(R_{a} + R_{c} + R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}} + \frac{2 R_{c} T k \left(R_{b} - R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}} + 4 R_{s} T k + \frac{2 S_{i} \left(0.5 R_{a} R_{b} + 0.5 R_{a} R_{s} + 0.5 R_{b} R_{c} + R_{b} R_{s} + 0.5 R_{c} R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}} + \frac{2 S_{v} \left(R_{a} + 0.5 R_{b} + R_{c} + 0.5 R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}}\, \mathrm{\left[\frac{V^2}{Hz}\right]}$$

Contributions of individual noise sources

Noise source: I1_XN
Spectral density:$S_{i}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$\frac{S_{i} \left(0.5 R_{a} R_{b} + 0.5 R_{a} R_{s} + 0.5 R_{b} R_{c} + R_{b} R_{s} + 0.5 R_{c} R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$\frac{S_{i} \left(0.5 R_{a} R_{b} + 0.5 R_{a} R_{s} + 0.5 R_{b} R_{c} + R_{b} R_{s} + 0.5 R_{c} R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: I1_XP
Spectral density:$S_{i}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$\frac{S_{i} \left(0.5 R_{a} R_{b} + 0.5 R_{a} R_{s} + 0.5 R_{b} R_{c} + R_{b} R_{s} + 0.5 R_{c} R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$\frac{S_{i} \left(0.5 R_{a} R_{b} + 0.5 R_{a} R_{s} + 0.5 R_{b} R_{c} + R_{b} R_{s} + 0.5 R_{c} R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: I_noise_RaN
Spectral density:$\frac{4 T k}{R_{a}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$\frac{R_{a} T k \left(R_{b} - R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$\frac{R_{a} T k \left(R_{b} - R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: I_noise_RaP
Spectral density:$\frac{4 T k}{R_{a}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$\frac{R_{a} T k \left(R_{b} - R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$\frac{R_{a} T k \left(R_{b} - R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: I_noise_Rb
Spectral density:$\frac{4 T k}{R_{b}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$\frac{4 R_{b} T k \left(R_{a} + R_{c} + R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$\frac{4 R_{b} T k \left(R_{a} + R_{c} + R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: I_noise_RcN
Spectral density:$\frac{4 T k}{R_{c}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$\frac{R_{c} T k \left(R_{b} - R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$\frac{R_{c} T k \left(R_{b} - R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: I_noise_RcP
Spectral density:$\frac{4 T k}{R_{c}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$\frac{R_{c} T k \left(R_{b} - R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$\frac{R_{c} T k \left(R_{b} - R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: V1_XN
Spectral density:$S_{v}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Detector-referred:$\frac{S_{v} \left(R_{a} + 0.5 R_{b} + R_{c} + 0.5 R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$\frac{S_{v} \left(R_{a} + 0.5 R_{b} + R_{c} + 0.5 R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: V1_XP
Spectral density:$S_{v}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Detector-referred:$\frac{S_{v} \left(R_{a} + 0.5 R_{b} + R_{c} + 0.5 R_{s}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$\frac{S_{v} \left(R_{a} + 0.5 R_{b} + R_{c} + 0.5 R_{s}\right)^{2}}{\left(R_{a} + R_{b} + R_{c}\right)^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: VsN
Spectral density:$2 R_{s} T k$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Detector-referred:$\frac{2 R_{s} T k \left(R_{a} + R_{b} + R_{c}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$2 R_{s} T k$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: VsP
Spectral density:$2 R_{s} T k$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Detector-referred:$\frac{2 R_{s} T k \left(R_{a} + R_{b} + R_{c}\right)^{2}}{\left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$2 R_{s} T k$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$

Go to Balanced-Cross-Coupled-Noisy-Nullor-Analysis_index

SLiCAP: Symbolic Linear Circuit Analysis Program, Version 2.0.1 © 2009-2023 SLiCAP development team

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

Last project update: 2023-11-25 20:52:48