In this section we consider the frequency response of an RC lowpass filter.
The filter circuit, shown in Figure 
, consists of a resistor
and a capacitor in series with the function generator. The function generator
has an internal resistance of 50 
which you must take into account
in the analysis. Recall that the voltage 
is two times the voltage displayed
on the front panel of the function generator. The output
of the circuit is taken to be the voltage across the capacitor.
Figure: RC Lowpass Filter Circuit
The behavior of the circuit as a function of frequency may be deduced
from considering the impedance of the capacitor for different frequencies.
For example, at DC (f=0) the capacitor is an open circuit. Therefore, no
current flows through any of the elements since they are all in series
with the capacitor. Since the current through the resistances is zero,
the voltage across them is zero. KVL applied around the loop shows that
. If the frequency is arbitrarily large (
) the
capacitor becomes a short circuit and therefore the output voltage 
.
As the frequency increases from DC (f=0) the capacitor goes from being an
open circuit to being a short circuit. As a consequence, the output voltage
goes from 
to zero. The circuit produces its greatest response at
DC. As the frequency is increased, the response drops. As the frequency is
increased further the response drops to zero. Low frequencies pass, high
frequencies are cut. It is a low-pass filter (LPF).