# D String Analog Filter

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## Introduction: D String Analog Filter

This instructable covers how to make a filter which will amplify only the D string of the guitar. This is usually D3, which has a frequency of approximately 147 Hz. Ideally what we want is a filter which will have a very fast roll-off, such that there will be minimal or no sound that gets outputted from the speaker.

## Step 1: Decide on Filter Type

The first thing to do when making a string filter is to decide what kind of filter you want to make. There are two types of filters that we considered, a Butterworth filter, and a Chebyshev filter. Both of these filters are good, and ultimately accomplish what we want. The upside of the Butterworth is that it is very simple to understand, and to implement. The downside is that the Butterworth filter has a slow roll-off for the gain, so it doesn't isolate the D string as much as we'd like. The Chebyshev filter is harder to analyze, but has a very quick roll-off. The Chebyshev was the filter that we picked for ours, but the choice is completely up to you.

## Step 2: Pick Speaker

In order to design the filter circuit, you need to know what kind of output you need to have. For your output, you'll have a speaker which you can buy from online, or a Radioshack if you have one nearby. The speaker you get will determine what kind of output voltage you will need to have, because it will take so much voltage to produce an audible sound. A good way to test this is to take a signal and hook it up to your speaker, and see how your speaker outputs sound. We tried to output about 2V to our speaker.

## Step 3: Input Guitar Analysis

Another good thing to do before you build your circuit is to determine how much voltage your guitar outputs. The input signal to your circuit comes from the audio jack that you plug into the circuit, so having a good idea of how much voltage it outputs will help you in the construction and testing in your circuit. Determining the amount of gain you will need from the circuit comes from the guitar and the speaker. Our guitar outputted 15mV, but some might output 100mV, or possibly more. The output will depend on what guitar you have.

## Step 4: Circuit Design - Chebyshev

Now that you've picked the type of filter you want to have, it is time to design the filter. For the Chebyshev filter, the simplest way to design it is to use this following website: http://www.wa4dsy.net/robot/bandpass-filter-calc. Since the Chebyshev filter is a more difficult to understand mathematically, this is an easier way for less experienced students to understand how to make this filter. We based ours off of the 4-pole filter engine. Just select the Chebyshev .1dB for filter type, and input your desired string frequency, 147 Hz for D3. For the capacitor values, you decide those. Any value from 1 µF to 1 nF should be good. We used 1 µF for ours. You also decide the bandwidth that you want to use for your circuit. A good way to calculate your bandwidth might be (X#[Hz] - Xb[Hz]). If your note is X, this will give you a bandwidth that ranges from one note up to one note down from your desired note. For D3, that is D#-Db, or 155.6-138.6. You can always go one more pitch away on both sides if you like, just to give a little more room in case your guitar is out of tune, or you can just tune your guitar before you test your circuit. The last part is the gain. Now that you know how much your guitar outputs, you can design a circuit that will give you a gain such that

(Input * gain) = Desired Speaker Voltage

If you need even more gain, you can always duplicate your circuit again, hooking the output of the first one to the input of the second one, and the output of the second one to the speaker.

## Step 5: Circuit Design - Butterworth

The basic design concept for the Butterworth filter is that you will have a low-pass filter, and a high-pass filter. This means that you will have one filter which will let everything below frequency X1 (low-pass frequency cutoff) have sound, and the other filter will let everything above frequency X2 (high-pass frequency cutoff) have sound. When designing this type, you want to pick your X1 and X2 to suit your string. This will mean that any frequency between X1 and X2 will output sound. (There still might be some sound outside of your frequency range, due to this filter type having a slow rolloff. This is to be expected, and is one of the reasons that a Chebyshev filter design is preferable.) For D3, you might pick D#3 and Db3, or maybe E3 and C3. The frequencies you pick will determine your resistor values for the low-pass and high-pass filters.

Pick a value for your capacitors. Something between 1µF and 1nF will work fine for your purposes.

For finding the resistor values you'll use, use the equation Fc[Hz] = ( 1 / (2*pi*R*C)), where your Fc is your X1 or X2 frequency, and you picked your Capacitor (C). For your low-pass filter, you'll design it using the image shown on the top, with the resistor on the top line. For your high-pass filter, you'll design it using the image shown on the bottom, with the capacitor on the top line.

All you need to do to connect these is just wire the output of one filter into the input of the other filter.

## Step 6: Build It!

The video shown above is a test of our circuit. To compensate for the recording equipment, we placed a thin paper sheet with sand on it above the speaker, such that you can physically see the sound waves displacing the sand. The amount of movement and displacement shows how loud the speaker is, even if it isn't always audible.

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