---+++ Gain Contraints For gain/impedance alone can consider the equivalent circuit for the tranformer of a capacitor, inductor and resistor in parallel. The resistance of the transformer Rt is given by

Rt = Rf/NG

where Rf is the feedback resistor, N is the number of turns of the transformer and G is the gain of the op amp that follows it.

Taking our band from 100kHz to 1MHz, and allowing the impedance to fall from the 50mOhms (equivalent to the SQUID) at resonance to 30mOhms at the edge of the band we can come up with constraints on the inductance the capacitance.

Summary

L > 60nH
C < 4.4uF

Note that these constraints are weaker than those produced by the noise of the amplifier referred to the bolometer, see AmplifierNoiseAmplification.

Derivation

At the lower limit only Rt and L matter, and the following impedance equation can be derived: %BEGINLATEX% \begin{equation} |Z_{in}| = \sqrt{\left(\frac{\omega^2 L^2 R_T}{\omega^2 L^2 + R_T^2}\right)^2 + \left(\frac{\omega L R_T^2}{\omega^2 L^2 + R_T^2}\right)^2} \end{equation} %ENDLATEX% plotting this in the region of interest provides the following:

At the upper frequency limit only Rt and C matter, so the following equation can be derived %BEGINLATEX% \begin{equation} |Z_{in}| = \sqrt{\left(\frac{R_T}{1+\omega^2 C^2 R_T^2}\right)^2 + \left(\frac{\omega C R_T^2}{1+\omega^2 C^2 R_T^2} \right)^2} \end{equation} %ENDLATEX% and the following plot produced:

-- KevinMacDermid - 04 Mar 2010

---

This topic: ColdFeedback > WebHome > ColdTransformerOpampSpecifications > GainContraints Topic revision: r2 - 2011-11-17 - TijmenDeHaan

---