The impedance of R1= R and the complex impedance of C1 is given by and the output voltage is given by:

And the ratio between output and input voltage for this circuit is thus:

(1) |

If we multiply the equation above with 1 or in this case with we finally get the transfer function:

(2) |

Now, any complex number can be written in a number of ways. One of the most common ways to write a given complex numkber C is: . This is actually a vector in O(0,0) with a certain length and a certain angle. The Modulo of the complex number C is the length, while the Argument of of the complex number C is the angle of the vector.

The Modulo is given by:

(3) |

And the Argument is

(4) |

(5) |

With the result of (5) we can write the transfer function (2) a complex number C and we can calculate the Modulo and the Argument from it. The Modulo is given as:

| (6) |

Transfer function of a single stage RC filter. |
Transfer function of a single stage RC filter, log. |

The argument can be calculated as follows:

(7) |

We can plot the results from the function above in graph:

Transfer function of a single stage RC filter. |
Transfer function of a single stage RC filter, log. |