High Pass and Low Pass Filters

I wrote an introductory class on using some National Instruments products, including LabVIEW and the Virtual Bench, for the Urban Workshop. National Instruments produces tools for engineers to build electrical and mechanical systems, and to test electrical circuits. While writing the class, one of the other instructors suggested that I use high and low pass filters as an example of an electrical circuit that you could study with National Instruments tools.

I've found that high and low pass filters can be difficult to explain in the class, so I wanted to practice my explanation here.

High and low pass filters are basic electrical circuits that filter a signal based on its frequency. A high pass filter will allow signals with high frequencies to pass and reduces the power on low frequency signals to prevent them from passing through the circuit. A low pass filter will do the opposite - it will allow signals with low frequencies to pass, but it will stop high frequency signals from getting through the circuit.

Let's consider a high pass filter first. This filter is built by putting a capacitor and resistor in series as shown in the diagram below.

High pass filter. (Image source: http://www.instructables.com/id/Passive-Filter-Circuits/)

A capacitor is made of 2 metal plates separated by a non-conductive material. You can think of capacitors like batteries that charge up whenever voltage is input to the circuit, and they can just as quickly discharge when there is a load on the circuit. A capacitor has “capacitive resistance” which is greater at low frequencies than at high frequencies. As an analogy, compare a capacitor to a pool of cornstarch in water (colloquially known as “oobleck”) - if you walked slowly through the pool, your feet would sink into the pool of cornstarch/water. Your low frequency walk induces a high capacitive resistance in the oobleck and you move slowly. However, if you ran over the surface of the pool, the cornstarch/water would appear more rigid and you would not sink. Your high frequency run induces a low capacitive resistance and you can move very quickly. Walking is equivalent to a low frequency signal, and the cornstarch/water slows you down, or applies resistance to the signal. Running is equivalent to a high frequency signal where the cornstarch/water does not slow you down or apply any resistance to the signal.

In a high pass circuit, the signal enters at V_in, and encounters the capacitor first. If the signal frequency is high enough, then the capacitive resistance of the capacitor is low and the signal can move through to be read at the terminal marked V_out. If the signal frequency is too low, the signal does not pass through the capacitor to the rest of the circuit.

Low pass filter. (Image source: http://www.instructables.com/id/Passive-Filter-Circuits/)

Now let's consider the alternative in a low pass circuit. The signal again enters at V_in but it encounters the resistor first. if the signal has a low frequency, then the capacitive resistance of the capacitor is high. The signal wants to follow the path of least resistance so instead of flowing through the capacitor to ground, it will flow to the terminal marked V_out. We can read the signal at V_out and that's what makes this a low pass circuit. However, if the signal has a high frequency, then the capacitive resistance of the capacitor is low and the signal moves through the capacitor to ground, and we cannot detect it at the terminal marked V_out.

You can calculate at what frequency a low pass circuit will go from allowing the signal through, to blocking it. (This calculation also works for high pass circuits.) This frequency is called the cutoff frequency, and it is calculated as shown below. The examples I used in my class use a 1000 ohm resistor and a 10nF capacitor, so the cutoff frequency is approximately 15.9 kHz.

Sources:

http://www.learningaboutelectronics.com/Articles/High-pass-filter.php

http://www.electronics-tutorials.ws/filter/filter_3.html

http://www.electronics-tutorials.ws/filter/filter_2.html