Electronic – Time constant vs Length of Pulse in RC circuit

capacitorresistorstime constant

Reading through "The Art of Electronics", I came to a statement where the writer states that the time constant (t) of RC circuit must be many times bigger than the Length of pulse you want to couple through the capacitor.

These are the words from the book:

you might use a
blocking capacitor to couple pulses, or square waves. In
such situations you encounter waveform distortion, in the
form of “droop” and overshoot (rather than the simple amplitude
attenuation and phase shift you get with sinusoidal
waves). Thinking in the time domain, the criterion you use
to avoid waveform distortion in a pulse of duration T is
that the time constant τ=RC>>T.

Imagine a situation where I need to couple 1us rectangular pulse. Following the book, let's take time constant t=100us.

According to my understanding, time constant is the time required for the circuit to respond to the change. So, whenever the rising edge of the pulse comes in, the circuit is going to take 100us to respond. But the pulse would have already died by the time this circuit settles.

I thought this condition is valid since it wont let any fluctuations happen whenever the pulse is in either high or low state. But in the case of switching from one state to another, I think this condition is invalid.

What is the actual thing going behind the scenes?

Best Answer

That's right.

If the RC circuit has time constant of 100us, it has no chance to react to the 1us pulse, so it will pass on right through.

If on the other hand you needed to pass a 100us pulse with a RC circuit having also 100us time constant, the 100us pulse would have enough time charge up the RC circuit, so the waveform would have droop.

Same thing can be explained in frequency domain as well. If you have an RC high pass filter with 1 kHz cutoff frequency, it can pass 10kHz sine wave almost at the same amplitude as it comes in, but a 1 kHz sine wave would have attenuated by 3dB, because the signal is slow enough to charge the RC.

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