Difference between revisions of "Example:Radio-frequency single electron transistor"
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== Theory and background == | == Theory and background == | ||
− | + | Radio-frequency single-electron transistor (RF-SET) is a sensitive charge detector. It's charge sensitivity <math>\delta q [e/\sqrt{Hz}]\,</math> in normal (not superconducting) operation is | |
+ | typically set by pre-amplifier noise temperature <math>T_0 [K]\,</math>, charging energy <math>E_C [J]\,</math>, transistor island | ||
+ | electron temperature <math>T [K]\,</math>, SET high bias DC resistance <math>R_\Sigma [\Omega]\,</math> and LC-transformer impedance | ||
+ | <math>Z_{TR} [\Omega]\,</math> according to relation | ||
+ | <ref>L. Roschier, M. Sillanpää, W. Taihong, M. Ahlskog, S. Iijima and P. Hakonen, “Carbon nanotube radio-frequency single-electron transistor”, Journal of Low Temperature Physics, 136, 465 (2004).</ref> | ||
− | <math> | + | <math>\delta q \approx \frac{2(3\frac{R_\Sigma}{Z_{TR}}+\frac{Z_{TR}}{Z_T}) \sqrt{k_B T_0 Z_T}}{2\times 0.41 t^{-1.74} 0.9 E_C/e^2}. \,</math> |
− | + | ==== References ==== | |
+ | <references /> | ||
== Construction of the nomograph == | == Construction of the nomograph == |
Revision as of 20:57, 13 September 2008
Second order equation | |
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author | Leif Roschier |
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Contents
Theory and background
Radio-frequency single-electron transistor (RF-SET) is a sensitive charge detector. It's charge sensitivity [math]\delta q [e/\sqrt{Hz}]\,[/math] in normal (not superconducting) operation is typically set by pre-amplifier noise temperature [math]T_0 [K]\,[/math], charging energy [math]E_C [J]\,[/math], transistor island electron temperature [math]T [K]\,[/math], SET high bias DC resistance [math]R_\Sigma [\Omega]\,[/math] and LC-transformer impedance [math]Z_{TR} [\Omega]\,[/math] according to relation [1]
[math]\delta q \approx \frac{2(3\frac{R_\Sigma}{Z_{TR}}+\frac{Z_{TR}}{Z_T}) \sqrt{k_B T_0 Z_T}}{2\times 0.41 t^{-1.74} 0.9 E_C/e^2}. \,[/math]
References
- ↑ L. Roschier, M. Sillanpää, W. Taihong, M. Ahlskog, S. Iijima and P. Hakonen, “Carbon nanotube radio-frequency single-electron transistor”, Journal of Low Temperature Physics, 136, 465 (2004).
Construction of the nomograph
A type 10 is the block for the construction.
Generated nomograph
Second order equation | |
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Generated portable document file (pdf): | File:Ex second order eq.pdf |
Source code
""" ex_second_order_eq.py Second order equation: z**2+p*z+q=0 Copyright (C) 2007-2008 Leif Roschier This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>. """ from nomographer import * N_params_1={ 'u_min':-10.0, 'u_max':10.0, 'function':lambda u:u, 'title':r'$p$', 'tick_levels':3, 'tick_text_levels':2, 'tick_side':'left' } N_params_2={ 'u_min':-10.0, 'u_max':10.0, 'function':lambda u:u, 'title':r'$q$', 'tick_levels':3, 'tick_text_levels':2, 'tick_side':'right', } N_params_3={ 'u_min':0.0, 'u_max':5.0, 'function_3':lambda u:u, 'function_4':lambda u:u**2, 'title':r'$z$', 'tick_levels':0, 'tick_text_levels':0, 'title_draw_center':True, 'title_opposite_tick':False, 'extra_params':[{'tick_side':'left', 'u_min':0.1, 'u_max':12.0, 'tick_text_levels':2, 'tick_levels':3 }] } block_1_params={ 'block_type':'type_10', 'width':10.0, 'height':10.0, 'f1_params':N_params_1, 'f2_params':N_params_2, 'f3_params':N_params_3, } main_params={ 'filename':'ex_second_order_eq.pdf', 'paper_height':10.0, 'paper_width':10.0, 'block_params':[block_1_params], 'transformations':[('rotate',0.01),('scale paper',)], 'title_str':r'$z^2+pz+q=0$' } Nomographer(main_params)