Time average of the input voltage

Thread Starter

asdasd12e12

Joined Nov 24, 2021
48
Based in the accepted answer, with a RC circuit i would obtain a time average of the input voltage, normalized by the reciprocal time constant 1/RC. If i were to implement this circuit what should i expect from this equation:

1.PNG

So lets say i have the circuit below and its input and output waves.

1.PNG

Solving the equation for time equal to 50ms

1.PNG
I get 10... I should have something around 1V. What am i doing wrong
 
Last edited:

WBahn

Joined Mar 31, 2012
29,978
Based in the accepted answer, with a RC circuit i would obtain a time average of the input voltage, normalized by the reciprocal time constant 1/RC. If i were to implement this circuit what should i expect from this equation:

View attachment 280222

So lets say i have the circuit below and its input and output waves.



Solving the equation for time equal to 50ms

View attachment 280237
I get 10... I should have something around 1V. What am i doing wrong
Let's give your basic premise some consideration.

You are claiming that this circuit is going to give the average. But does that make sense?

Let's say that the input voltage is 2 V for 1 s and then 0 V for 1 s. The average would be 1 V. The RC might scale that to some other value, but we can take that into account by considering another example in which the input voltage is 2 V for 9 s and 0 V for 1 s, making the average 1.8 V. Whatever factor the RC imposes get applied to both, so the actual voltage from the second case should be 1.8x whatever the actual voltage from the first us.

Yet, in both cases, that final 1 s with a 0 V input is more than enough to sufficiently discharge the capacitor from whatever value it had obtained. In fact, with a time constant of barely 5 ms, everything that happened more than about 25 ms ago is completely lost. So the circuit does NOT give the average of the input voltage, it favors the recent values of the input voltage with the influence of older voltages decreasing exponentially as since they appeared increases.

How much math have you had? In particular, what techniques do you know to solve differential equations? Do you know Laplace transforms?
 

Thread Starter

asdasd12e12

Joined Nov 24, 2021
48
Let's give your basic premise some consideration.

You are claiming that this circuit is going to give the average. But does that make sense?

Let's say that the input voltage is 2 V for 1 s and then 0 V for 1 s. The average would be 1 V. The RC might scale that to some other value, but we can take that into account by considering another example in which the input voltage is 2 V for 9 s and 0 V for 1 s, making the average 1.8 V. Whatever factor the RC imposes get applied to both, so the actual voltage from the second case should be 1.8x whatever the actual voltage from the first us.

Yet, in both cases, that final 1 s with a 0 V input is more than enough to sufficiently discharge the capacitor from whatever value it had obtained. In fact, with a time constant of barely 5 ms, everything that happened more than about 25 ms ago is completely lost. So the circuit does NOT give the average of the input voltage, it favors the recent values of the input voltage with the influence of older voltages decreasing exponentially as since they appeared increases.

How much math have you had? In particular, what techniques do you know to solve differential equations? Do you know Laplace transforms?
Yes, i know laplace transform
 
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