Question

The circuit shown represents a low-pass filter. Assume R and C are known. The relation between the charge in the capacitor and $V_{in}$ is as follows: $(RC)\dot{q} + q = CV_{in}$ By treating $q$ as the output and using the above equation, a) Identify the time constant and sensitivity for this system. b) Derive the transfer function for this filter. Additional information from our earlier lectures: $\mathcal{L}\{f\} = F(s)$ $\mathcal{L}\{\dot{f}\} = sF(s) - f(0)$ $\mathcal{L}\{\ddot{f}\} = s^2F(s) - sf(0) - \dot{f}(0)$

          The circuit shown represents a low-pass filter. Assume R and C are known. The relation between
the charge in the capacitor and $V_{in}$ is as follows:
$(RC)\dot{q} + q = CV_{in}$
By treating $q$ as the output and using the above equation,
a) Identify the time constant and sensitivity for this system.
b) Derive the transfer function for this filter.
Additional information from our earlier lectures:
$\mathcal{L}\{f\} = F(s)$  $\mathcal{L}\{\dot{f}\} = sF(s) - f(0)$  $\mathcal{L}\{\ddot{f}\} = s^2F(s) - sf(0) - \dot{f}(0)$

$The circuit shown represents a low-pass filter. Assume R and C are known. The relation between the charge in the capacitor and Vin is as follows: (RC)q̇ + q = CVin By treating q as the output and using the above equation, a) Identify the time constant and sensitivity for this system. b) Derive the transfer function for this filter. Additional information from our earlier lectures: ℒ{f} = F(s) ℒ{ḟ} = sF(s) - f(0) ℒ{f̈} = s^2F(s) - sf(0) - ḟ(0)$

Added by Joseph T.

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