RC network

An RC network is configured as a low-pass filter, and a voltage step input is provided to the indicated circuit. How could one quantify the duration it takes for the output voltage waveform to travel from a specified initial value to a final one? How do we know that the output waveform visits any voltage value in the indicated history only once?

by Kayraa
October 05, 2021

A low pass filter is generally analyzed assuming that the circuit which follows is of an infinite resistance and so, in parallel to the capacitor, that infinite resistance may be neglected. We are then left with a loop made of a voltage source, V, a resistance R and a capacitance C.

If V0 is the initial internal voltage related to the energy initially stored in the capacitor, and if the voltage of the source, V, is constant through time (for the time duration under consideration), then the voltage drops across the capacitor, through time, is

Vc = V0 + (V-V0) exp(-t/RC)

So, for Vc to reach a given value (between V0 and V) the required time is logarithmic.

A logarithmic function is not only monotonic but also continuous. (Discutable though, accordingly to mathematicians)

Note though that as in a river flowing in one direction, it is possible for a time that a small eddy creates a small local flow of water running in the reverse direction, the same is possible for an electrical circuit, as we zoom increasingly into the details. That is called "noise" and so, at the noise level, voltages values can be revisited. So, the proposed (exponential) equation is said to be exact far from the noise level in addition to consider ideal elements (even a simple resistor can create noise, capacitance, etc.), thermal currents and others possible considerations not taken into account.

by vanderghast
October 05, 2021
Add comment...

Please sign in or create an account to comment.

No Answers

No answers yet. Contribute your answer below!

Your Answer

You must log in or create an account (free!) to answer a question.

Log in Create an account

Go Ad-Free. Activate your CircuitLab membership. No more ads. Save unlimited circuits. Run unlimited simulations.

Search Questions & Answers

Ask a Question

Anyone can ask a question.

Did you already search (see above) to see if a similar question has already been answered? If you can't find the answer, you may ask a question.

About This Site

CircuitLab's Q&A site is a FREE questions and answers forum for electronics and electrical engineering students, hobbyists, and professionals.

We encourage you to use our built-in schematic & simulation software to add more detail to your questions and answers.

Acceptable Questions:

  • Concept or theory questions
  • Practical engineering questions
  • “Homework” questions
  • Software/hardware intersection
  • Best practices
  • Design choices & component selection
  • Troubleshooting

Unacceptable Questions:

  • Non-English language content
  • Non-question discussion
  • Non-electronics questions
  • Vendor-specific topics
  • Pure software questions
  • CircuitLab software support

Please respect that there are both seasoned experts and total newbies here: please be nice, be constructive, and be specific!

About CircuitLab

CircuitLab is an in-browser schematic capture and circuit simulation software tool to help you rapidly design and analyze analog and digital electronics systems.