"Symbolic noise analysis"

Symbolic noise analysis

Symbolic noise analysis results

Detector-referred noise spectrum

$$S_{out}=\frac{8 \Gamma_{XN} N_{s N18} T g_{m XN} k \left(\left(\frac{f_{\ell XN}}{f}\right)^{AF_{N18}} + 1\right) \left(0.125 R_{a}^{2} R_{b}^{2} f^{2} g_{m X}^{2} + 0.25 R_{a}^{2} R_{b} R_{s} f^{2} g_{m X}^{2} + 0.125 R_{a}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a}^{2} f_{T X}^{2} + 0.25 R_{a} R_{b}^{2} R_{c} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} f_{T X}^{2} + 0.25 R_{a} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + R_{a} R_{c} f_{T X}^{2} + 0.5 R_{a} R_{s} f_{T X}^{2} + 0.125 R_{b}^{2} R_{c}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.125 R_{b}^{2} f_{T X}^{2} + 0.25 R_{b} R_{c}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} f_{T X}^{2} + 0.25 R_{b} R_{s} f_{T X}^{2} + 0.125 R_{c}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{c}^{2} f_{T X}^{2} + 0.5 R_{c} R_{s} f_{T X}^{2} + 0.125 R_{s}^{2} f_{T X}^{2}\right)}{f_{T X}^{2} g_{m X}^{2} \cdot \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{8 \Gamma_{XP} N_{s N18} T g_{m XP} k \left(\left(\frac{f_{\ell XP}}{f}\right)^{AF_{N18}} + 1\right) \left(0.125 R_{a}^{2} R_{b}^{2} f^{2} g_{m X}^{2} + 0.25 R_{a}^{2} R_{b} R_{s} f^{2} g_{m X}^{2} + 0.125 R_{a}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a}^{2} f_{T X}^{2} + 0.25 R_{a} R_{b}^{2} R_{c} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} f_{T X}^{2} + 0.25 R_{a} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + R_{a} R_{c} f_{T X}^{2} + 0.5 R_{a} R_{s} f_{T X}^{2} + 0.125 R_{b}^{2} R_{c}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.125 R_{b}^{2} f_{T X}^{2} + 0.25 R_{b} R_{c}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} f_{T X}^{2} + 0.25 R_{b} R_{s} f_{T X}^{2} + 0.125 R_{c}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{c}^{2} f_{T X}^{2} + 0.5 R_{c} R_{s} f_{T X}^{2} + 0.125 R_{s}^{2} f_{T X}^{2}\right)}{f_{T X}^{2} g_{m X}^{2} \cdot \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}}\, \mathrm{\left[\frac{A^2}{Hz}\right]}$$

Source-referred noise spectrum

$$S_{in}=\frac{8 \Gamma_{XN} N_{s N18} T g_{m XN} k \left(\left(\frac{f_{\ell XN}}{f}\right)^{AF_{N18}} + 1\right) \left(0.125 R_{a}^{2} R_{b}^{2} f^{2} g_{m X}^{2} + 0.25 R_{a}^{2} R_{b} R_{s} f^{2} g_{m X}^{2} + 0.125 R_{a}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a}^{2} f_{T X}^{2} + 0.25 R_{a} R_{b}^{2} R_{c} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} f_{T X}^{2} + 0.25 R_{a} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + R_{a} R_{c} f_{T X}^{2} + 0.5 R_{a} R_{s} f_{T X}^{2} + 0.125 R_{b}^{2} R_{c}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.125 R_{b}^{2} f_{T X}^{2} + 0.25 R_{b} R_{c}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} f_{T X}^{2} + 0.25 R_{b} R_{s} f_{T X}^{2} + 0.125 R_{c}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{c}^{2} f_{T X}^{2} + 0.5 R_{c} R_{s} f_{T X}^{2} + 0.125 R_{s}^{2} f_{T X}^{2}\right)}{f_{T X}^{2} g_{m X}^{2} \left(R_{a} + R_{b} + R_{c}\right)^{2}} + \frac{8 \Gamma_{XP} N_{s N18} T g_{m XP} k \left(\left(\frac{f_{\ell XP}}{f}\right)^{AF_{N18}} + 1\right) \left(0.125 R_{a}^{2} R_{b}^{2} f^{2} g_{m X}^{2} + 0.25 R_{a}^{2} R_{b} R_{s} f^{2} g_{m X}^{2} + 0.125 R_{a}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a}^{2} f_{T X}^{2} + 0.25 R_{a} R_{b}^{2} R_{c} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} f_{T X}^{2} + 0.25 R_{a} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + R_{a} R_{c} f_{T X}^{2} + 0.5 R_{a} R_{s} f_{T X}^{2} + 0.125 R_{b}^{2} R_{c}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.125 R_{b}^{2} f_{T X}^{2} + 0.25 R_{b} R_{c}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} f_{T X}^{2} + 0.25 R_{b} R_{s} f_{T X}^{2} + 0.125 R_{c}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{c}^{2} f_{T X}^{2} + 0.5 R_{c} R_{s} f_{T X}^{2} + 0.125 R_{s}^{2} f_{T X}^{2}\right)}{f_{T X}^{2} g_{m X}^{2} \left(R_{a} + R_{b} + R_{c}\right)^{2}} + 4 R_{s} T k\, \mathrm{\left[\frac{V^2}{Hz}\right]}$$

Contributions of individual noise sources

Noise source: I2_XN
Spectral density:$0$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$0$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$0$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: I2_XP
Spectral density:$0$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$0$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$0$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: In_XN
Spectral density:$4 \Gamma_{XN} N_{s N18} T g_{m XN} k \left(\left(\frac{f_{\ell XN}}{f}\right)^{AF_{N18}} + 1\right)$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$\frac{8 \Gamma_{XN} N_{s N18} T g_{m XN} k \left(\left(\frac{f_{\ell XN}}{f}\right)^{AF_{N18}} + 1\right) \left(0.125 R_{a}^{2} R_{b}^{2} f^{2} g_{m X}^{2} + 0.25 R_{a}^{2} R_{b} R_{s} f^{2} g_{m X}^{2} + 0.125 R_{a}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a}^{2} f_{T X}^{2} + 0.25 R_{a} R_{b}^{2} R_{c} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} f_{T X}^{2} + 0.25 R_{a} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + R_{a} R_{c} f_{T X}^{2} + 0.5 R_{a} R_{s} f_{T X}^{2} + 0.125 R_{b}^{2} R_{c}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.125 R_{b}^{2} f_{T X}^{2} + 0.25 R_{b} R_{c}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} f_{T X}^{2} + 0.25 R_{b} R_{s} f_{T X}^{2} + 0.125 R_{c}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{c}^{2} f_{T X}^{2} + 0.5 R_{c} R_{s} f_{T X}^{2} + 0.125 R_{s}^{2} f_{T X}^{2}\right)}{f_{T X}^{2} g_{m X}^{2} \cdot \left(0.25 \pi^{2} C_{ocm}^{2} R_{\ell}^{2} f^{2} + 1\right) \left(R_{a} R_{b} + R_{b} R_{s} + R_{c} R_{s}\right)^{2}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$\frac{8 \Gamma_{XN} N_{s N18} T g_{m XN} k \left(\left(\frac{f_{\ell XN}}{f}\right)^{AF_{N18}} + 1\right) \left(0.125 R_{a}^{2} R_{b}^{2} f^{2} g_{m X}^{2} + 0.25 R_{a}^{2} R_{b} R_{s} f^{2} g_{m X}^{2} + 0.125 R_{a}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a}^{2} f_{T X}^{2} + 0.25 R_{a} R_{b}^{2} R_{c} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} f_{T X}^{2} + 0.25 R_{a} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + R_{a} R_{c} f_{T X}^{2} + 0.5 R_{a} R_{s} f_{T X}^{2} + 0.125 R_{b}^{2} R_{c}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.125 R_{b}^{2} f_{T X}^{2} + 0.25 R_{b} R_{c}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} f_{T X}^{2} + 0.25 R_{b} R_{s} f_{T X}^{2} + 0.125 R_{c}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{c}^{2} f_{T X}^{2} + 0.5 R_{c} R_{s} f_{T X}^{2} + 0.125 R_{s}^{2} f_{T X}^{2}\right)}{f_{T X}^{2} g_{m X}^{2} \left(R_{a} + R_{b} + R_{c}\right)^{2}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: In_XP
Spectral density:$4 \Gamma_{XP} N_{s N18} T g_{m XP} k \left(\left(\frac{f_{\ell XP}}{f}\right)^{AF_{N18}} + 1\right)$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$\frac{8 \Gamma_{XP} N_{s N18} T g_{m XP} k \left(\left(\frac{f_{\ell XP}}{f}\right)^{AF_{N18}} + 1\right) \left(0.125 R_{a}^{2} R_{b}^{2} f^{2} g_{m X}^{2} + 0.25 R_{a}^{2} R_{b} R_{s} f^{2} g_{m X}^{2} + 0.125 R_{a}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a}^{2} f_{T X}^{2} + 0.25 R_{a} R_{b}^{2} R_{c} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} f_{T X}^{2} + 0.25 R_{a} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + R_{a} R_{c} f_{T X}^{2} + 0.5 R_{a} R_{s} f_{T X}^{2} + 0.125 R_{b}^{2} R_{c}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.125 R_{b}^{2} f_{T X}^{2} + 0.25 R_{b} R_{c}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} f_{T X}^{2} + 0.25 R_{b} R_{s} f_{T X}^{2} + 0.125 R_{c}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{c}^{2} f_{T X}^{2} + 0.5 R_{c} R_{s} f_{T X}^{2} + 0.125 R_{s}^{2} f_{T X}^{2}\right)}{f_{T X}^{2} g_{m X}^{2} \cdot \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}}$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$\frac{8 \Gamma_{XP} N_{s N18} T g_{m XP} k \left(\left(\frac{f_{\ell XP}}{f}\right)^{AF_{N18}} + 1\right) \left(0.125 R_{a}^{2} R_{b}^{2} f^{2} g_{m X}^{2} + 0.25 R_{a}^{2} R_{b} R_{s} f^{2} g_{m X}^{2} + 0.125 R_{a}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a}^{2} f_{T X}^{2} + 0.25 R_{a} R_{b}^{2} R_{c} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{a} R_{b} f_{T X}^{2} + 0.25 R_{a} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + R_{a} R_{c} f_{T X}^{2} + 0.5 R_{a} R_{s} f_{T X}^{2} + 0.125 R_{b}^{2} R_{c}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{c} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.125 R_{b}^{2} f_{T X}^{2} + 0.25 R_{b} R_{c}^{2} R_{s} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{b} R_{c} f_{T X}^{2} + 0.25 R_{b} R_{s} f_{T X}^{2} + 0.125 R_{c}^{2} R_{s}^{2} f^{2} g_{m X}^{2} + 0.5 R_{c}^{2} f_{T X}^{2} + 0.5 R_{c} R_{s} f_{T X}^{2} + 0.125 R_{s}^{2} f_{T X}^{2}\right)}{f_{T X}^{2} g_{m X}^{2} \left(R_{a} + R_{b} + R_{c}\right)^{2}}$$\,\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-MOSFET-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