This instructable is intended to show you how to make several different filter circuits, in particular, low pass and high pass filters, along with a discussion of notch/trap filters and bandpass filters.
So what is a filter and why would you ever want to build one? Well, you might not end up building any of these circuits by themselves, but you may find yourself integrating them into more complex circuits. You already know what everyday filters do (e.g. air filters, water filters); electronic filters are no different. They take some signal, which in this case is a voltage signal composed of one or many frequencies, and filter out frequencies in a specific range.
High pass filters are circuits used to remove low frequency signals and allow high frequency signals. Low pass filters do the opposite and are used to remove high frequency signals and allow through low frequency signals.
High pass filters are often used in speakers to filter out bass from an audio signal being sent to a tweeter, which could be damaged by the low frequency bass signals. They are also used to remove DC offset or DC bias from a signal, which could otherwise harm amplifiers and other electronic devices. In contrast, low pass filters can be used to filter out high frequency signals in audio being sent to subwoofers that can't efficiently reproduce the high-frequency parts of the audio signal. They are also used in devices such as in the tone knob of an electric guitar (to filter out treble), or in analog synthesizers.
Two other filter circuits that we will briefly discuss are the notch and bandpass filters. Notch filters are used to filter out a very specific range of frequencies, for example to filter out interference of a particular frequency if you happen to live next to a radio station. Bandpass filters do the opposite and will filter out everything but frequencies in a narrow range, and are thus used in radios to tune in to a specific frequency.
What you put into the circuit:
What you get out of the circuit:
Your input signal is first fed into a capacitor that is connected at its other end to a resistor, which in turn is connected at its other end to ground. Your output signal should be read between the capacitor and resistor.
If you don't have access to a function generator or oscilloscope, you'll have to trust we tested the circuit for you correctly. We built our circuit as shown:
The red alligator clip carries our input signal (from a function generator), the black alligator clip lead to ground, and the green wire carries our output signal, which we sent to an oscilloscope for testing. As we went from low frequency signals to high frequency signals, the result we read on our oscilloscope looked like this:
The yellow curve is our input signal, and the blue curve is our output signal (note that while the yellow curve appears to remain the same, it is because we were changing the frequency scaling on the display of the oscilloscope). At low frequencies, you can see that the entire signal is filtered out and we get almost no output signal. As frequency increases, the output signal becomes larger, until it reaches a point at which it is nearly the same as the input signal. This point is called the cutoff frequency, and we will show you how to find it later. You should also note that the output signal can be phase-shifted from the original input signal, meaning that although the signals have the same frequency, they aren't necessarily "in step", so to speak.
Also, note that while we intentionally inputted signals of a uniform frequency at a time, the circuit will work for compound signals.
The cutoff frequency is generally considered the frequency at which the signal is attenuated (or filtered). This means that any signal with frequency below the cutoff frequency is considered to be filtered, and any signal with frequency above the cutoff is considered to be "left alone" or unfiltered. So what is the cutoff frequency?
where R is the resistance of your resistor in Ω and C is the capacitance of your capacitor in F.
If you take a look at the ratio of the amplitude of the output signal to the amplitude of the input signal over a wide range of frequencies, you will get something that looks as so
Note that both axes are log-scaled. This means essentially that if you move up from one light gray line to the next, your value is actually increasing by 10 times. This means that if you looked at this plot without log scaled axes, you would essentially see an almost vertical drop off at the cutoff frequency. Any signal or component of a signal that has frequency higher than the cutoff frequency, however, is unfiltered, to a good approximation.
We said earlier that the input and output signals are not "in step" and are actually shifted. This may be fine for some applications, but there are other applications where this may be important. The phase shift changes as the frequency of the input signal changes, just as with the gain, and the plot of this change looks as so
At low frequencies, the output signal is phase shifted by π/2, and at high frequencies the phase shift is almost zero. The cutoff frequency is important to the phase shift because it is the frequency at which the output signal is phase shifted by exactly half of π/2, or π/4.
If you really want to know, go check out the Theory section for more information about how the circuit works and how we calculated the gain and phase shift.