"Determination of show-stopper values of noise sources"

Determination of show-stopper values of noise sources

Circuit diagram

Symbolic determination of show-stopper values

I1

Spectral contribution of I1:.

\begin{equation} I_{1}=\frac{L_{r} L_{s} R_{g}^{2} S_{iT} k_{c}^{2}}{A_{R}^{2} B_{T}^{2}}\,\left[ \mathrm{\frac{A^{2}}{Hz}}\right] \end{equation}

Show stopper value for noise contribution of I1:.

\begin{equation} S_{iT}=\frac{A_{R}^{2} B_{T}^{2} v_{on}^{2}}{L_{r} L_{s} R_{g}^{2} k_{c}^{2} \left(f_{max} - f_{min}\right)}\,\left[ \mathrm{\frac{A^{2}}{Hz}}\right] \end{equation}

V2

Spectral contribution of V2:.

\begin{equation} V_{2}=\frac{L_{r} L_{s} S_{vT} k_{c}^{2}}{A_{R}^{2} B_{T}^{2}}\,\left[ \mathrm{\frac{V^{2}}{Hz}}\right] \end{equation}

Show stopper value for noise contribution of V2:.

\begin{equation} S_{vT}=\frac{A_{R}^{2} B_{T}^{2} v_{on}^{2}}{L_{r} L_{s} k_{c}^{2} \left(f_{max} - f_{min}\right)}\,\left[ \mathrm{\frac{V^{2}}{Hz}}\right] \end{equation}

I2

Spectral contribution of I2:.

\begin{equation} I_{2}=\frac{0.25 S_{iR} \left(4 \pi^{2} L_{r}^{2} f^{2} + R_{r}^{2}\right)}{\pi^{2} A_{R}^{2} f^{2}}\,\left[ \mathrm{\frac{A^{2}}{Hz}}\right] \end{equation}

Show stopper value for noise contribution of I2:.

\begin{equation} S_{iR}=\frac{4 \pi^{2} A_{R}^{2} f_{max} f_{min} v_{on}^{2}}{\left(f_{max} - f_{min}\right) \left(4 \pi^{2} L_{r}^{2} f_{max} f_{min} + R_{r}^{2}\right)}\,\left[ \mathrm{\frac{A^{2}}{Hz}}\right] \end{equation}

V3

Spectral contribution of V3:.

\begin{equation} V_{3}=\frac{0.25 S_{vR}}{\pi^{2} A_{R}^{2} f^{2}}\,\left[ \mathrm{\frac{V^{2}}{Hz}}\right] \end{equation}

Show stopper value for noise contribution of V3:.

\begin{equation} S_{vR}=\frac{4 \pi^{2} A_{R}^{2} f_{max} f_{min} v_{on}^{2}}{f_{max} - f_{min}}\,\left[ \mathrm{\frac{V^{2}}{Hz}}\right] \end{equation}

V1

RMS output noise voltage caused by V1:.

\begin{equation} RMS_{V1}=0\,\left[ \mathrm{V}\right] \end{equation}

I_noise_R1

RMS output noise voltage caused by I_noise_R1:.

\begin{equation} RMS_{I noise R1}=0\,\left[ \mathrm{V}\right] \end{equation}

I_noise_R2

Spectral contribution of I_noise_R2:.

\begin{equation} I_{noise R2}=\frac{4 L_{r} L_{s} R_{g} T k k_{c}^{2}}{A_{R}^{2} B_{T}^{2}}\,\left[ \mathrm{\frac{A^{2}}{Hz}}\right] \end{equation}

Show stopper value for noise contribution of I_noise_R2:.

\begin{equation} R_{g}=\frac{0.25 A_{R}^{2} B_{T}^{2} v_{on}^{2}}{L_{r} L_{s} T k k_{c}^{2} \left(f_{max} - f_{min}\right)}\,\left[ \mathrm{\Omega}\right] \end{equation}

I_noise_R4

RMS output noise voltage caused by I_noise_R4:.

\begin{equation} RMS_{I noise R4}=\left(\frac{R_{r} T k}{\pi^{2} A_{R}^{2} f_{min}} - \frac{R_{r} T k}{\pi^{2} A_{R}^{2} f_{max}}\right)^{0.5}\,\left[ \mathrm{V}\right] \end{equation}

Numeric determination of show-stopper values

I1

Spectral contribution of I1:.

\begin{equation} I_{1}=\frac{0.6169 R_{g}^{2} S_{iT}}{\pi^{2}}\,\left[ \mathrm{\frac{A^{2}}{Hz}}\right] \end{equation}

Show stopper value for noise contribution of I1:.

\begin{equation} S_{iT}=\frac{1.071 \cdot 10^{-11}}{R_{g}^{2}}\,\left[ \mathrm{\frac{A^{2}}{Hz}}\right] \end{equation}

V2

Spectral contribution of V2:.

\begin{equation} V_{2}=\frac{0.6169 S_{vT}}{\pi^{2}}\,\left[ \mathrm{\frac{V^{2}}{Hz}}\right] \end{equation}

Show stopper value for noise contribution of V2:.

\begin{equation} S_{vT}=1.071 \cdot 10^{-11}\,\left[ \mathrm{\frac{V^{2}}{Hz}}\right] \end{equation}

I2

Spectral contribution of I2:.

\begin{equation} I_{2}=\frac{8.433 \cdot 10^{16} S_{iR} \left(7.149 \cdot 10^{-6} f^{2} + 1\right)}{\pi^{2} f^{2}}\,\left[ \mathrm{\frac{A^{2}}{Hz}}\right] \end{equation}

Show stopper value for noise contribution of I2:.

\begin{equation} S_{iR}=9.484 \cdot 10^{-24}\,\left[ \mathrm{\frac{A^{2}}{Hz}}\right] \end{equation}

V3

Spectral contribution of V3:.

\begin{equation} V_{3}=\frac{1.527 \cdot 10^{12} S_{vR}}{\pi^{2} f^{2}}\,\left[ \mathrm{\frac{V^{2}}{Hz}}\right] \end{equation}

Show stopper value for noise contribution of V3:.

\begin{equation} S_{vR}=3.893 \cdot 10^{-18}\,\left[ \mathrm{\frac{V^{2}}{Hz}}\right] \end{equation}

V1

RMS output noise voltage caused by V1:.

\begin{equation} RMS_{V1}=0\,\left[ \mathrm{V}\right] \end{equation}

I_noise_R1

RMS output noise voltage caused by I_noise_R1:.

\begin{equation} RMS_{I noise R1}=0\,\left[ \mathrm{V}\right] \end{equation}

I_noise_R2

Spectral contribution of I_noise_R2:.

\begin{equation} I_{noise R2}=\frac{1.022 \cdot 10^{-20} R_{g}}{\pi^{2}}\,\left[ \mathrm{\frac{A^{2}}{Hz}}\right] \end{equation}

Show stopper value for noise contribution of I_noise_R2:.

\begin{equation} R_{g}=6.464 \cdot 10^{8}\,\left[ \mathrm{\Omega}\right] \end{equation}

I_noise_R4

RMS output noise voltage caused by I_noise_R4:.

\begin{equation} RMS_{I noise R4}=0.0001\,\left[ \mathrm{V}\right] \end{equation}

FOUND SHOW-STOPPER: increase transmitter drive level!

Go to noiseBudgeting_index

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

Last project update: 2024-03-04 22:12:16