Passive Filters

We can build some very simple filters out of a capacitor and a resistor. A filter will block some frequencies, while admitting others.

Better filters can be made out of op-amps.

Low-Pass Filters (LPF)

A low pass filter will admit lower frequencies and block out high ones. This can help us smooth out our signals and get rid of high frequency noise.

We can make one by hooking up our capacitor and resistor like this:

When set R=500Ω and C=2nF, and hook up an AC voltage source, the voltage we see at $V_{o}ut$ depends on the frequency of our source. Here is a plot of the frequency response of the filter, on a logarithmic scale from 10Hz to 10MHz:

As we can see, the filter blocks the higher frequncies.

Since a square wave is made out of a superposition of many sine waves, the low-pass filter will block the sine waves with higher frequencies. Our input and output will look like:

File:RC LPF square wave.jpg(C=200uF, R=500Ω)

High-Pass Filter (HPF)

A high pass filter will block out lower frequencies while letting high frequencies through. The output will respond more strongly to changes in the input signal, such as that coming from a motion detector.

We can make a simple high-pass filter by hooking up our capacitor and resistor like this:

The frequncy response of a filter with R=500Ω and C=2nF looks like this:

This time, the filter blocks the lower frequencies.

When we put a square wave though the filter, the resulting waveform looks like this:

File:RC HPF square wave.jpg(C=200uF, R=500Ω)

Notice that when the input voltage drops to zero, the output voltage becomes negative. This is because the capacitor is discharging, and forcing the current backwards.