# Active Band-Pass Filters

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## Introduction: Active Band-Pass Filters

This instructable is intended to show the reader how to design an active band-pass filter FROM SCRATCH!

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## Step 1: Standard Design Procedure

There is some design criteria that you need to first create before you jump into build your active filter.  You need to know these things before you begin your journey into the world of active bandpass filter (BPF) design.  This instructable can take as little as 2 hours from start to finish, assuming that you already are in possession of the necessary parts.  Filters are a major aspect of any system.  The ability to understand them and how they interact within the confines of other systems is very important to any circuit designer.

1. You need to know what power supplies you have on hand. Hopefully in your case, you are in the confines of a lab, and can choose a typical DC power supply.

2. You need to know which  frequencies you which to be passed, and the frequencies that wish to be rejected.  These will both be a band of frequencies that you pass (pass-band) or reject (reject-band).

3. You need to pick a center frequency.  This frequency will be in the middle of your pass-band, and will be where the bode plot (gain in dB vs frequency) is symmetrical.

4. You will need to pick a capacitor value.  For high frequencies you should choose a value around 100 pico Farads or lower, for low frequencies you should choose a value around 100 nano Farads.  If the resistor values that correspond with these capacitor values are too large or too small for the desired frequency, pick different capacitor values.

5. It is assumed during this instructable that you have a basic knowledge of laying out parts on a breadboard. (connect resistorA on nodeA to nodeB, connect capacitor B from nodeB to output pin, etc)

The picture in this step shows the basic frequency response of any band pass filter.

Let's get going!

## Step 2: Designing High-Pass Filter

The BPF that we are making will consist of a high-pass filter (HPF) cascaded in series to a low-pass filter (LPF).  Both HPF and LPF are Sallen-Key filters.  You may also start with a LPF and connect the output into the input of a HPF.  Looking at the pictures for this section, and following the step below, we can create our HPF:

1. Pick capacitor 1 (C1) so that it equals capacitor 2 (C2).  C1 = C2

2. Decide a cutoff frequency for your HPF (this should be lower than the LPF cutoff frequency).

3.  Then using the formula shown in the second picture we can decide which resistor value we will use for R1.  The frequency that they are referring to is the cutoff frequency decided in the previous step.

4. Then using the formula shown in the third picture we can decide which resistor value we will use for R2.

remember:

1. the symbol that R1 is connected to is ground
2. when we connect Vin, the negative pin must be connected to ground
3. when we measure Vout, the negative pin must be connected to ground
4. the ground (or common ground, shared ground between sources) for your sources must be connected to your ground
5. there is only one ground!
6. when putting your breadboard together, each element connects to two different points (or nodes) and make sure you properly connect them
7.make sure you understand the layout of your breadboard (whether the pins are horizontally or vertically connected)
8. to have fun and experiment with different values!

On to our LPF!

## Step 3: Designing Low-Pass Filter

In this section of our instructable, we will continue on to build our LPF!

1.  Pick a value for C1.

2. Pick C2, such that C2 = 2*C1.

3. Calculate R1 and R2, such that R1 = R2. and that R1 and R2 equal the formula shown.

Now we have the values for the first order filters we are using.  These filters are defined as first order because the magnitude of the signal reduces by half, every time the that the frequency doubles (one octave increase).

## Step 4: Connecting Our Cascaded System

This step is simple, we can connect the output of our HPF into the input of our LPF.  This can be done so with a wire from the output to R1.  This can be seen in the corresponding picture.

## Step 5: Now We Build Our Own!

What you'll need:

2 Operational amplifiers (I'll be using LM741's)

various resistors and capactiors to choose from

power supply

function generator (for testing)

oscilloscope (for testing

wires

My HPF:
1 LM741 op amp
R1 = 10k ohm + 1k ohm in series
R2 = 22k ohm
C1 and C2 = 100 nF (these were bi directional caps)
cutoff freq: 102 Hz

My LPF:
1 LM741 op amp
R1 and R2 = 150 ohm
C2 =  10 micro Farad in series with another 10 micro Farad (these capacitors were electrolytic (meaning that the polarity must be taken into account))
cuttoff freq: 235 Hz

refer back to steps 2 through 4, for the design layout of our system.

the first picture is my completed HPF
the second picture is my LPF
the third picture is my cascaded system, aka our BPF
and the video is me showing my signal.

Video description:

1. I show my BPF
2. I show my lab environment
3. I show my oscilloscope with a clear sine wave
4. I then demonstrate that when I turn down my frequency, the signal gets squashed!
5. and vice versa, I turn it back up, showing my clear signal, and turn it up more so, to show that my signal gets squashed again at high frequencies! ( f>300)

BPF with a pass-band from 102-235 Hz

## Step 6: Analyzing Our Signal

The input signal that I used can be viewed in the first picture:
It was a 110Hz 1 Vpp (volts peak to peak) sine wave.
At this frequency we expect to see a clear output with a voltage with the same relative amplitude.

Our output signal was just that.  A 712mV Vpp sine wave, with freq 110.07 (was fluctuating around 110Hz).
This can be seen in the second picture, showing a view of our oscilloscope.

## Step 7: Concluding Remarks

I hope you guys enjoyed yourself and weren't too intimidated by this project, and I hope you found it useful to your coursework.  Filters are a good way to become more familiar with circuits, and they serve as good hands on practice.

If you have any questions, please contact me at bogenschultz92@gmail.com, I'd love to answer any questions, or correct small mistakes you find in my instructable!  Have a great day!

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## 5 Discussions

"This step is simple, we can connect the output of our HPF into the input of our LPF"
I can see this because I'm holding it in my hand (Capacitor to Inductor = 800hz - 5000hz), I can see how the Highs begin cutting off at 5000k but I can't see how the lows begin cutting off after passing through an Inductor, isn't the "Inductor" killing off all of the Highs just limited (Reduced) from passing through the Capacitor, what's left ?

"Power Supply"
What has anything to do with a/the Power Suppy ?
Whether 1 watt or a 100 watts, it's the frequencies effected and not the Voltage or Amperages !

You need to know which frequencies to be passed...
For a Mid-Range Speaker, 500hz to 4000hz "seems" perfect and not 800hz to 5000hz, there is too much low end loss (You're throwing out 300hz for nothing, electrons out the side door ?) and 5000hz is some what too high for Mid-Range Speakers, Mid-Range is not Tweeterish ? !

"You need to pick a center frequency"
Well 3500 cut in half (/) is 1750, and 500 + 1750 = 2250 (4000 - 1750 = 2250) !

When I take the Band-Pass filters that I have the Numbers don't add up ???
(22uf @ 8ohms = 7350hz, not 5000hz, and there is no info on the Inductor, it's wrapped in copper, a little more than an inch long)

So 5000hz @ 8ohms = 3.975uf ?
I don't know the Inductor rating but what about the Capacitor rating (22uf @ 8ohms = 7350hz, not 5000hz), does the Inductor knock off the rest ???

How about [ Inductors and Capaitors for Dummies, in plain English ]

Frustrating ???

Rick - Audio Storm

The power supply was completely ignored. Single supply? Dual? So much left out. Of course, great to have effort, but no vetting by instructables?

Very easy read. I have 358's on order. Looking forward to combining a high-pass with a low-pass filter. The below referenced link for the TI PDF is still active. Although the TI PDF, for the novice; you will expect to learn about +/- voltage, and 0 volt reference. There are plenty of good blogs on the subject if you are interested. If you are working on an Arduino, like me, I expect to be using a "single" source reference value of +5V to 0V.

Interesting, thanks.

Texas Instruments have produced a nice document on how to design filters in 30 seconds.