# How the envelope detector works?

Suppose we have an ideal diode cascaded with an RC filter , what is exactly the analytical expression of the voltage across the resistance R in terms of our initial (ac) voltage , that is : how to do a circuit analysis in the presence of the ideal diode ?

If the input voltage is less than the output voltage, the output is an exponentially decaying voltage governed by R and C i.e.

$V_{out}=V_xe^{\frac{-t}{RC}}$

$V_x$ is the voltage when the input voltage became less than the output voltage

At all other times the output voltage equals the input voltage. There is no linear equation (that I'm aware of) that satisfies this particular circuit.

• Thanks . i have one more question : and that's about the particular shape of the output voltage , i know that the diode passes current if the input voltage is positive , but can we also say that it only passes current if the variation of the input voltage is also positive and do not passes if the variation is negative , and that's why we obtain that particular shape ? – MicroGame Feb 9 '14 at 7:26
• the ideal diode in the question will not conduct current when the input voltage is less than the output voltage. – Andy aka Feb 9 '14 at 10:23