.. 4.5

RC Integration & Differentiation
================================

**Objective**

RC circuits can integrate or differentiate a voltage waveform with
respect to time. A square wave is integrated to get a triangular wave
and differentiated to get spikes at the transitions.\begin_inset
Separator latexpar\end_inset

.. image:: schematics/RCintegration.svg
	   :width: 300px
.. image:: schematics/RCsteadystate.svg
	   :width: 300px

**Procedure**

-  Select WG triangular wave option
-  Set WG to 500Hz (:math:`T = 2~ms`), :math:`R = 1~k\Omega` and :math:`C = 1~\mu F`
-  Adjust the horizontal scale to view more than 4 cycles.
-  Repeat the same for RC differentiator, at :math:`50~Hz`.

**Discussion**

Integration of a triangular waveform gives parabolic shape and
differentiation gives a square shape. The differentiation can only be
shown at lower frequency. Try these for other wave shapes, for example a
squarewave. Integrating a square wave should give a triangular wave.

.. image:: pics/RCintegration.png
	   :width: 300px
.. image:: pics/RCdifferentiation.png
	   :width: 300px
