## What You Need

What you put into the circuit:

- One capacitor with capacitance C (in
*F*). - One resistor with resistance R (in
*Ω*). - An input signal (ours came from a function generator).
- An oscilloscope (for testing).

What you get out of the circuit:

- A filtered output signal.

## How to Build the Circuit

### Where do the parts go?

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.

### Test to make sure it works.

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

### Calculate the cutoff frequency.

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*.

### What does the cutoff frequency mean for the signal?

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.

### The output signal is phase shifted from the input.

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.

#### BUT HOW DID YOU GET THESE RESULTS?!?!

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.

## TL;DR

- The high pass filter can be made as follows:
- Input - Capacitor - (Output) - Resistor - Ground

- High pass filters filter out signal with frequencies below the cutoff frequency (1/2πRC).
- Since the cutoff is strictly determined by R and C, choose the appropriate resistor and capacitor to cutoff frequencies where you want to
- The output signal is phase shifted from the input.