# Semiconductor devices - Integrator

Semiconductor device tutorial
2020-11-20 02:50:34
# Semiconductor devices - Integrator

The following figure shows that the feedback component used is a capacitor and the connection result is called as integrator.

The equivalent of virtual earth shows that an expression of the voltage between the input and the output can be derived in terms of current (I), from the input to the output. Recall that virtual earth means that we can consider the voltage at the junction of R and X _{ C } as being ground (since V _{ i } ≈ 0 V) however no current enters the earth at this time. The capacitive impedance can be expressed by

$$ X_C = frac {1} {jwC} = frac {1} {sC} $$

Where ** s ** = jw as in Laplace notation. Solving the equation for $ V_o / V_i $ gives the following equation

$$ I= frac {V_1} {R_1} = frac {-V_0} {X_c} = frac {- frac {V_0} {I}} {sC} = frac {V_0} {V_1} $$

$ $ frac {V_0} {V_1} = frac {-1} {sCR_1} $$

It can be written in the time domain as

$$ V_o (t) = - frac {1} {RC} int V_1 (t) dt $$