---+ Active Feedback

The following diagram shows the simplest possible reduction of the reading out of one bolometer.

By approximation, we can group all the impedances of the system, except the bolometer, into a single (frequency dependent) impedance z_s. We currently believe this approximation to be a good one, except for the SQUID amplifier. The current in the system then becomes:

%BEGINLATEX% \begin{equation} I = \frac{V_{in}-V_{bolo}}{z_s} \end{equation} %ENDLATEX%

Then if we wish to achieve a constant voltage across the bolometer we impose that:

%BEGINLATEX% \begin{equation} \frac{\partial V_{bolo}}{\partial t} = 0 \end{equation} %ENDLATEX%

Solving:

%BEGINLATEX% \begin{equation} \frac{\partial V_{in}}{\partial t} = z_s \frac{\partial I}{\partial t} \end{equation} %ENDLATEX%

Fortunately, can simplify the implementation of this equation through two facts:

• We only require V_bolo to remain constant over timescales much shorter than the time constant of the TES detector for strong electrothermal feedback.
• We only require | V_bolo | to remain constant, since the bolometer is insensitive to the phase of the (high frequency) voltage applied to it.

Discrete sampling

The first bullet point implies we can perform the derivative at a discrete sampling rate >> 60 Hz.

%BEGINLATEX% \begin{equation} \Delta V_{in} = z_s \Delta I \end{equation} %ENDLATEX%

Reducing the complex amplitudes

The second bullet point would imply we should change the magnitude of V_in according to product of the magnitude of I and the magnitude of z_s. However, a complication arises because the demodulator only measures one component of I (read: projection onto one axis in the complex plane) (or read: locks into one phase). I would therefore like to investigate whether approximating | I | by one component of I results in a constant V_bolo, and whether this condition is stable under perturbations.

Active Feedback Simulations

Before attempting the analytic solution, let's test the behaviour of this active feedback in my simulation of a TES.

-Tijmen

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This topic: ColdFeedback > WebHome > StrongElectrothermalFeedback2 Topic revision: r2 - 2011-09-28 - MattDobbs

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