playground:playground
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playground:playground [2009/07/06 21:26] szymon.kulis |
playground:playground [2019/03/08 14:08] (current) |
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| ====== PlayGround ====== | ====== PlayGround ====== | ||
| - | ===== latex ===== | ||
| - | <latex> | ||
| - | \frac{3}{4 \pi} \sqrt{4 \cdot x^2 12}\\ | ||
| - | \lim_{n \to \infty} | ||
| - | \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}\\ | ||
| - | \it{f}(x) = \frac{1}{\sqrt{x} x^2}\\ | ||
| - | e^{i \pi} + 1 = 0}\; | ||
| - | </latex> | ||
| - | |||
| - | ===== image ref ===== | ||
| - | |||
| - | <imgcaption image1 | This is my little caption> | ||
| - | {{:hw:fpga:virtex5fxt:xlx-drc-virtex5fxt-evl.jpg}} | ||
| - | </imgcaption> | ||
| - | |||
| - | Rysunek : <imgref image1> | ||
| - | |||
| - | <imgcaption image2 | This is my little caption> | ||
| - | {{:hw:fpga:virtex5fxt:xlx-drc-virtex5fxt-evl.jpg}} | ||
| - | </imgcaption> | ||
| - | |||
| - | Rysunek : <imgref image1> | ||
| - | |||
| - | ~~NOCACHE~~ | ||
| - | |||
| - | In such case the minimum ENC equals: | ||
| - | |||
| - | <latex> | ||
| - | ENC_{min} = \frac{e^n n!}{q n^n} \\ | ||
| - | \sqrt{\frac{\Gamma(n - \frac{1}{2}) (C_{in}+C_f)}{8 \sqrt{\pi} \sqrt{n!}} | ||
| - | \sqrt{ (2n-1) \cdot v_{eqw}^2 \cdot (i_{eqw}^2 + 2qI_{leak} + \frac{4kT}{R_{f}}) }} | ||
| - | \label{eq:enc_min} | ||
| - | </latex> | ||
| - | |||
| - | For practical applications it is often more convinient to study the noise performance | ||
| - | as the function of <latex>T_{peak}</latex> instead of <latex>\tau</latex>. In this case the formula <latex>\ref{eq:enc1}</latex> | ||
| - | will be espressed as: | ||
| - | |||
| - | <latex> | ||
| - | ENC = \frac{e^n n!}{q n^n} \\ | ||
| - | \sqrt{\frac{\Gamma(n - \frac{1}{2})}{8 \sqrt{\pi} \sqrt{n!} } \\ | ||
| - | \left( \frac{n v_{eqw}^2}{T_{peak}} (C_{in} + C_{f})^2 + T_{peak} \frac{2n - 1}{n} \\ | ||
| - | (i_{eqw}^2 + 2qI_{leak} + \frac{4kT}{R_{f}}) \right)\\ | ||
| - | + (C_{in} + C_{f})^2 \frac{v_{1/f}^2}{2n} } | ||
| - | |||
| - | + (C_{in} + C_{f})^2} | ||
| - | } | ||
| - | \label{eq:enc2} | ||
| - | </latex> | ||
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