# Theorem on typical L-network for impedance matching in NMR tanks

Posted 9 years ago
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 Source tree on Githubhttps://github.com/Altoidnerd/NMR-Tank-CircuitsRaw copy pasta for mathematica https://raw.githubusercontent.com/Altoidnerd/NMR-Tank-Circuits/master/L_network_parallel_resonance_main.nbI think I have a result that is useful in the practice of NMR and applies to a particular probe design. This circuit is common in practicehttp://i.imgur.com/6ZCDvyY.jpg?1Please note however unlike this drawing, for this result we should model the resistor in series with the inductance. Excuse the confusion. The inductive load is tuned and matched to the characteristic impedance of a transmission line Z0 (usually 50 ohms) by the two variable capacitors. Postulate: If the series losses in the coil are set tor = Z0 / 4, then C_tune =~ C_matchfor any reasonable L and f where f is frequency of operation and f > 500 KHz. For f < 500 KHz the approximation begins to break down.Typical Values for L are200 nH < L < 30 uHTypical values for f are1 MHz < f < 200 MHzI do not know why this works, but I discovered it while investigating the space in mathematica.  See source code herehttps://raw.githubusercontent.com/Altoidnerd/NMR-Tank-Circuits/master/L_network_parallel_resonance_main.nbIs this correct?Discussion on Reddit: http://www.reddit.com/r/ECE/comments/232wuh/i_think_i_have_a_little_theorem_about_a_matching/
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Posted 9 years ago