"Symbolic noise analysis"

Symbolic noise analysis

Symbolic noise analysis results

Detector-referred noise spectrum

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

Source-referred noise spectrum

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

Contributions of individual noise sources

Noise source: I1_XN
Spectral density:$0$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Detector-referred:$0$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$0$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: I1_XP
Spectral density:$0$$\,\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: 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}}$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: V1_XN
Spectral density:$0$$\,\mathrm{\left[\frac{V^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: V1_XP
Spectral density:$0$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Detector-referred:$0$$\,\mathrm{\left[\frac{A^2}{Hz}\right]}$
Source-referred:$0$$\,\mathrm{\left[\frac{V^2}{Hz}\right]}$
Noise source: VsN
Spectral density:$2 R_{s} T k$$\,\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]}$

Noise figure

The noise figure is obtained as:

\begin{equation} F=4.343 \log{\left(\frac{0.5 R_{a} \left(R_{b} - R_{s}\right)^{2}}{R_{s} \left(R_{a} + R_{b} + R_{c}\right)^{2}} + \frac{R_{b} \left(R_{a} + R_{c} + R_{s}\right)^{2}}{R_{s} \left(R_{a} + R_{b} + R_{c}\right)^{2}} + \frac{0.5 R_{c} \left(R_{b} - R_{s}\right)^{2}}{R_{s} \left(R_{a} + R_{b} + R_{c}\right)^{2}} + 1 \right)}\,\left[ \mathrm{dB}\right] \end{equation}

Updated specifications

analysisequations specification

Table analysisequations specification
symboldescriptionvalueunits
$B_{fb eq}$The B T-1 Parameter for a Balanced Cross Coupled Feedback Circuit $\frac{R_{a} R_{b}}{R_{a} + R_{b} + R_{c}}$$\mathrm{\frac{V}{A}}$
$D_{fb eq}$The D T-1 Parameter for a Balanced Cross Coupled Feedback Circuit $\frac{R_{b} + R_{c}}{R_{a} + R_{b} + R_{c}}$$\mathrm{1}$
$NF_{fb eq}$The Noise Figure for a Balanced Cross Coupled Noisy Feedback Circuit $\frac{0.5 R_{a} \left(R_{b} - R_{s}\right)^{2}}{R_{s} \left(R_{a} + R_{b} + R_{c}\right)^{2}} + \frac{R_{b} \left(R_{a} + R_{c} + R_{s}\right)^{2}}{R_{s} \left(R_{a} + R_{b} + R_{c}\right)^{2}} + \frac{0.5 R_{c} \left(R_{b} - R_{s}\right)^{2}}{R_{s} \left(R_{a} + R_{b} + R_{c}\right)^{2}} + 1$$\mathrm{1}$

designequations specification

Table designequations specification
symboldescriptionvalueunits
$B_{eq}$Typical Voltage -> Current Gain$\frac{0.5}{A_{y}}$$\mathrm{\frac{V}{A}}$
$D_{eq}$Typical Current -> Current Gain$\frac{0.5}{A_{y} Z_{i}}$$\mathrm{1}$

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