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3 HOURS
Resistors

Resistors are ubiquitous in electronics and arguably the first "real" electronic component we will be dealing with. They are the little pill-shaped stripe-y things found on most circuit boards. These parts in and of themselves don't do anything remarkably complex, but are vital in purpose. Over the course of this lesson we will learn what resistors are, how to 'read' them, special ways they can be used, and all about a special type of resistor called a potentiometer. Finally, we will bring everything together and make an audio mixer.

## Lesson Materials

In this lesson we will be making a Simple Stereo Mixer. I will also be demonstrating how resistors work by making a paper resistor.

While it is optional, if you want to follow along at home and make a paper resistor you will need:

(x1) pencil (preferably 6B, but a #2 will work)
(x1) Paperclips
(x1) 6" x 9" envelope (or piece of paper)

For the Simple Stereo Mixer project you will need:

(x2) 10K dual log potentiometers
(x4) 1K resistors
(x3) 1/8" stereo jacks
(x2) Knobs
(x1) 4" x 2" x 1" project enclosure
(x3) Stereo cables
(x1) Split back sticker paper (for printer)

A resistor is an electronic component that limits the flow of electrons. In doing so, it dissipates energy in the form of heat. Put into plain English, electricity has to struggle to flow through something with a high resistance. In doing so, it works up a lot of energy and converts this into heat. It's a little bit like how your body heats up when you do vigorous exercise.

You can think of a resistor kind of like a fixed workout routine for electricity. It provides a known amount of resistance to a circuit, and the electricity always has to do the same amount of work to get through it.

The amount of resistance that a resistor offers is measured in Ohms. The symbol for ohms is the Omega symbol from the Greek Alphabet.

In terms of electronics, the resistor reduces electrical current by a precise amount. If you consider that in a circuit you typically have a fixed input voltage, and resistors offer a fixed amount of resistance, you can then use Ohm's Law to determine how much a resistor will limit current. This is useful in a number of scenarios, including working with LEDs, which will be covered in the diodes lesson.

To measure ohms with a multimeter, turn the dial to the Ω symbol and selecting the proper range (unless you splurged on an auto-ranging multimeter). To determine the correct range, you will need to be able to 'read' the resistor, which we are going to get to in a moment.

In a circuit, a resistor's symbol looks like a zigzag line. It typically has its value written next to it.

## Make a Resistor

To better understand how resistors work, let us make our own resistor.

All we will need is a pencil (a #2 will do fine, but a 6B is better), a sheet of paper, and some paperclips.

Take a 6" x 9" envelope and turn it sideways, and then rub a pencil back and forth along the edge. Create a one inch wide band of graphite along this edge. Once you are think you are done, keep going. The more graphite you can put down onto the paper, the better your resistor will work.

Attach paperclips to the probes of your multimeter using jump cables.

Attach one of these paperclips to one corner of the strip.

When you touch the other paperclip anywhere on the strip, you will notice that you get a resistance reading. Congratulations, you have made a resistor.

Now, attach the second paperclip to the opposite corner.

My resistor gives a reading of about 500,000 ohms. I arrived at this because the multimeter is reading in the 2000K (hundred thousandths) range. Thus, it is giving a reading of 500K ohm. Your resistor should roughly be in this range. If your resistor reads much greater than this, add more graphite to increase its conductivity.

All resistors operate along the same principle. The paper resistor I have created offers the same resistance to a circuit as a standard carbon film resistor capsule.

We can determine what sort of resistor we have by looking at the packaging.

Telling its current rating can typically be established by the size of the resistor. This is something you will figure out intuitively in time, and not remarkably important for the kind of low-current circuits you will be working with when getting started.

Determining how much resistance a resistor offers is a little trickier and can be established by deciphering the colored stripes from left to right towards the tolerance marking. You will typically see four stripes, but you may also encounter resistors with five.

Resistors with four stripes are the most common. These will likely be the type you are working with most.

When reading a resistor with four stripes, the first two stripes are combined together to form a number between 1 and 99. The third marking is the multiplier. The last marking determines the tolerance, which will be discussed further in a moment.

For instance, in the following example, the first two lines represent 1 and 0, which is combined together as the number 10. This is then multiplied by 10,000 (which is the multiplier). The result is 100,000Ω.

However, when a resistor is 1,000 or more ohms, we measure it in kilo-ohms. A kilo-ohm is basically equal to 1,000 ohms. So, 100,000Ω is shortened to 100kΩ. Basically, it is 1,000 ohms times 100. All we are essentially doing is removing three zeros from the number, and replacing them with with k.

If that was confusing, let us look at another example. This resistor has the same initial number of 10, but a multiplier of 1,000. When multiplied together, these numbers yield a resistance of 10,000Ω or 10KΩ.

Now, let's say the first two numbers were to change, and the multiplier were to decrease. In this example, the first two colors when combined create the number 68. When multiplied by 10, we get the number 680. Since 680Ω is less than 1,000, we just call this resistor 680Ω.

One last thing, if there is a million or more ohms, we then measure in mega-ohms. For example, this resistor is worth 1,000,000Ω. This is shortened to 1MΩ.

Resistors with 5 stripes are a little less common, but just as easy to read. Let us briefly consider how to read them. Like the 4 band resistor, you first find the tolerance marking on the far edge, and then read left to right towards the marking.

However, where they differ is in that the first three stripes get read as a single number, and the fourth stripe is the multiplier. So, in this case, we can determine the first number is 100 and it gets multiplied by 1,000, giving us a resistance of 100K.

The fifth stripe is the tolerance marking.

## Tolerances

Just like you and I, resistors are not perfect. However, they strive to be as good and as consistent as they can. This is where the tolerance band on the resistor comes in.

A resistor with a gold band has a resistance with a +/- 5% tolerance or - you could say - margin of error. What this means is that the resistance can be over or under its value by 5%. So, if you had a 100K resistor and measured with a multimeter, it could read anywhere from 95K to 105K.

For all of the circuits we will be building here, such approximate values will do fine. We often think of electronics as an exact science, but the truth is that there is a bit of wiggle room in most of what we make. As you begin to dive deeper into electronics you will realize that there is enough fluctuation in circuit building to allow for experimentation and creativity. While this might be a lot to process right now, bury this idea in the back of your head for later.

Anyhow...

Four band resistors have a typical tolerance of +/- 5% and this is indicated by a gold band on the far right.

Five band resistors have a typical tolerance of +/- 1% and this is indicated by a brown band on the far right.

## Variable Resistors

A variable resistor is a resistor whose value varies within a set range.

Some of the most common types of variable resistors you may encounter include photocells which change in relation to light, bend sensors which change in relation to being flexed, and FSR (force sensing resistors) that change resistance when you apply pressure upon their surface. You also might encounter a host of other variable resistors that change in relation to heat, moisture, and gas, to name a few.

Most importantly, there is the potentiometer. This is the most common variable resistor and utterly ubiquitous in your day-to-day life. Every time you use a slider or knob on an electrical device, you are using a potentiometer. For instance, every single mechanical light dimmer you have ever used is a potentiometer.

Potentiometers come in a wide range of resistances, and have a physical actuator that sweeps from 0 ohms resistance to whatever value is marked upon it.

The inside of a potentiometer does not look remarkably different from our paper resistor. In fact, it is basically just a miniaturized version of what we have made. Instead of moving a paperclip, there is an actuator knob or sliding lever that moves a conductive element over an electrically resistive surface.

By connecting a wire to either one of its outer terminals, and another to the center terminal, we can wire a potentiometer as a variable resistor.

In a schematic a variable resistor looks like a normal resistor with a line reaching around and pointing back at itself.

You may also be wondering why the potentiometer has three legs, when two seems to be enough to work as a variable resistor. We will get to that in a moment, but first, I need to introduce an important concept.

## Voltage Dividers

Let's mirror a potentiometer for a moment and add a third paper clip close to the center of our paper resistor. Now, if we were to connect voltage across the outer terminals and use a multimeter to measure from either of the outer terminals to the center terminal, you may notice something interesting. The voltage reading we are getting is about half of the supply voltage. By "dividing" the resistor in two, we have created a voltage divider.

Resistors can be placed in series to make voltage dividers. These voltage values are in proportion to the values of each resistor. The resistance value of the two resistors is less important in determining the voltage than the ratio of values between the resistors.

If you run the simulation, you will notice that two 10K resistors in series between 5V and ground will have the same voltage rating at their midpoint as two 100K resistors between 5V and ground. This is because there is an equal ratio between both sets of resistors.

On the other hand, if we were to change the resistors of these voltage dividers to have uneven values, the voltage will increase or decrease.

By changing the 100K resistor connected to power to 47K, the voltage reading increases. This is because there is less resistance between the positive terminal and the midpoint than from the midpoint to ground, so voltage can flow more easily from power. On the other hand, we have decreased the value of the 10K resistor connected to ground to a value of 4.7K. In this scenario the voltage decreases because electricity can flow to ground more freely than power.

These two gnarly looking metal tubes are actually giant resistors used as voltage dividers for converting the electrical system in a military jeep from 24V to 12V. While crudely effective, it is by no means the best way to do this. Resistors work by converting energy to heat, which is a wildly inefficient way to solve the problem of voltage conversion. Additionally, unlike the massive resistors pictured above, standard resistors are not rated to handle the current that a typical circuit requires. Trying to power electronics through a voltage divider will in all likelihood release the 'magic smoke' from one component or another.

## Potentiometers

When we connect the end of the resistor to power and ground (respectively) and move the probe along the paper resistor, you may notice that the voltage changes.

If it wasn't clear by now, let me reiterate what is happening. The paper resistor is functioning as a giant variable voltage divider.

It should now be apparent what the third connection in the potentiometer is used for.

As the potentiometer's knob is turned, the wire connected to the center pin is swept along, creating two discrete resistance values between power and ground. This pins is basically functioning like the middle paperclip in the paper potentiometer example. It allows us to change the voltage as it is turned one or another.

In the following wiring configuration the voltage will increase when the potentiometer is turned clockwise, and decreased when turned the other way.

It does not matter what the resistance of the potentiometer is, when wired in this manner, the center pin on all potentiometers will be adjustable between 0 volts and the supply voltage.

In a schematic, a potentiometer looks like a resistor with an arrow pointing towards the center.

## Tapers

While the sweep in the potentiometer varies the voltage, not all sweeps are the same. There are two types of sweeps you will encounter, and they are typically referred to as a potentiometer's taper.

A linear taper has a linear response curve. What this means is that when you sweep the potentiometers actuator through it's full range, the resistance will increase or decrease steadily.

This type of potentiometer is most common and used in most things.

On the other hand, a logarithmic (or "log") taper has a response curve which looks like a logarithmic curve (or in layman's terms - this dude's smirk --> ¯\_(ツ)_/¯ ).

The reason you would want this type of potentiometer is largely for adjusting audio volume. Loudness is not linear, but logarithmic. If you were to use a linear potentiometer for adjusting volume, it would go from being really quiet to really loud very suddenly. By using a logarithmic potentiometer, you can follow the curve of the music and have a more gradual increase in volume.

Thus, stereo volume knobs tend to be logarithmic. Although these potentiometers are not prevalent, they are common enough that you will encounter them. In fact, we will be using them when we build our audio mixer.

## Making an Audio Mixer

To demonstrate resistors in use, we are going to make a passive stereo audio mixer. When I say stereo, I am not talking about your home entertainment signal, but an audio track with a separate left and right channel.

This mixer will allow us to combine two stereo tracks into one single track, while adjusting the volume of both tracks individually and together.

We will also go over techniques for mounting electronics in an enclosure. Since this is primarily a class in electronics and not building enclosures, it is not necessary that you mount your electronics in exactly the same way I do. However, I recommend trying to follow along.

## Mixing the Signals

A stereo signal is two channels (left and right) which are actually two separate audio signals with a shared ground.

If we want to combine two stereo signals into one, we will need to mix together the left channel of each stereo signal, and the right channel of each signal.

The easiest way to do this is to combine them together using resistors.

If you connect each respective left channels to a 1K resistor, and the other end of each resistor together, then you have effectively mixed the left channels together. The right channels can be mixed in identical fashion. You are left with a two channel stereo mixer.

This schematic shows the left channels and the right channels being connected together through resistors.

The three boxes that look like strange renderings of potted flowers are actually audio jacks with their barrels connected to ground. The triangles next to each jack represent a channel. Also, notice the strange half-loop to the right of the 1K resistor that is third from top? That loop represents a 'hop' in the schematic and means not to connect those wires together. Otherwise, any time lines intersect, they should be connected together.

This is the simplest audio mixer you can make, but hardly the best one.

## Volume Control

Simply combining the signals though does not give you any volume control.

To add volume control, we use potentiometers.

The potentiometer is connected in such a way that it functions as a voltage divider between the incoming signal from each channel and ground. Thus, depending on how much the potentiometer is turned will determine how much voltage the signal will be allowed to have when it passes through the center pin to the mixing resistors. The output voltage from the center pin is basically the volume of the signal.

Keep in mind, the input signals volume can always be decreased in this manner, but never increased, since it is only adding resistance to the signal and no additional power.

## Dual Potentiometers

You may have noticed that by using a potentiometer for each channel, the right and left channels of the same stereo track were being controlled individually. Since you likely want each track to maintain equal volume levels on both the left and right channels, you will need something to control both channels at once.

To do this, you will need a dual (or "ganged") potentiometer. This is essentially two potentiometers built into a single package and controlled by a single shaft.

By using a dual potentiometer, we are able to control both tracks at the same time. In fact, dual potentiometers are largely manufactured exclusively as stereo volume knobs, and typically have logarithmic tapers.

Ours is logarithmic and you can tell this because it is labeled with an "A" instead of a "B" in front of its printed value rating.

## Label

Before you start, download and print out the attached files onto a sticker sheet.

Sticker sheet with split-back perforation is ideal (as you will see in a moment).

## Label the Enclosure

Typically enclosures are made as after thoughts for electronics projects. In most of these projects throughout this class we will be starting with the enclosure. Not only that, I am going to show you how to build them well. There will be no soap dishes with wires sticking out of them in this class. If you want to ignore my methodology and go your own way, that is your business. However, I intend to show you how to do it correctly.

First of all, aesthetics are important and you should always make things that look reasonably good. Why invest a lot of time making something if it's hastily jammed haphazardly into a travel soap dish as an afterthought? The nicer you can make this, the less likely it will be to get thrown away some day.

Secondly, understanding the constraints of the enclosure means that you have clearly planned ahead and know what needs to get done. This actually makes it easier to build and debug the circuit.

To begin, trim the labels down with scissors and peel the top label such that the far ends still have their backings on. This is where having split-back sticker paper comes in very handy because you can peel only a little bit of the label at a time.

The reason for doing it this way is because the enclosure's mounting screws will ultimately be hidden under the label. At the end, you will need to be able to get underneath the corners of the label to fasten the case shut. It is only at this point that the label will be fully applied.

Stick this partially peeled label to the enclosure's lid.

Also, while you're at it, stick the input and output jack labels to the sides of the enclosure.

## Drill

Now it is time to drill holes in the enclosure for the potentiometers and jacks using the label's drilling guides.

Find the cross hairs on each of the labels and make drilling guides by tapping them on center with a hammer and nail. When working with metal enclosures, you will want to get a proper center punch, but for soft materials like plastic (and possibly aluminum), this is good enough.

Drill pilot holes in each of these indents using a 1/8" drill bit.

Next, widen the holes for the potentiometers in the lid with a 9/32" drill bit (the unofficial drill bit of most potentiometer mounting holes).

Widen the audio jack holes on the sides of the enclosure with a 1/4" drill bit.

## Positioning Holes

Notice how the potentiometers have little rectangular tabs protruding upward on one side. This tab is meant to be inserted into a hole in the enclosure which is to prevent the entire body of the potentiometer from turning when the shaft is rotated. In order for this to work, we need to make these holes in the enclosure.

To figure out where to drill these holes, insert each of the potentiometer's shafts into the mounting holes upside down. Make note of where the tab is.

Drill in the spots where the tabs are positioned with a 1/8" drill bit.

## Shorten the Shafts (optional)

This part is optional, but recommended if you are overly concerned with aesthetics like I am.

If you mount the potentiometers and place the knobs onto the shafts, you will notice they are riding a bit high. On account of this you can easily see the tab mounting hole and parts of the label which are supposed to be hidden. In order to hide these things, you will need shorten the potentiometer shafts to lower the heights of the knobs.

Doing this is easy. Measure to figure out how much the knob needs to be lowered, and then using a hacksaw, cut that much metal off of the potentiometer shaft.

You will immediately notice an appreciable difference.

Repeat the process for the second knob.

## Wire the Input Jacks

Connect a black wire to the tab on the stereo jack to the terminal electrically connected to the barrel.

Connect a red wire to one of the tabs connected to an internal connector.

Connect a green wire to the other tab.

Which tab the red and green wires get connected to are less important than that both jacks are wired exactly the same. So long as the green and red wires are always connected to the same tabs on all of the jacks, the left and right channels will not get crossed.

## Wire the Output Jack

This jack should be wired similarly to the input jacks, but instead of connecting one red and one green wire to each of the terminals, we will be connecting two of each.

## Wire the Inputs

Now we will wire each input jack to a potentiometer.

The ground wires should go to the bottom left tab of each respective potentiometer.

The red wire should get connected to the top right tab.

The green wire should get connected to the bottom right tab.

## Resistors

Solder 1K resistors to each of the center terminals on the potentiometers.

Trim away the excess lead on the side of the resistors soldered to the potentiometer, but leave the other leads connected on the side of the resistors that has yet to be soldered.

## Attach the Output Jack Signal Wires

We are going to start attaching the output jack by connecting the red and green signal wires.

Slide 1" of heat shrink tubing onto each of the jack's signal wires. The color is not remarkably important.

Solder a red wire to one of the resistor leads coming from the 1K resistor connected on the top center of the potentiometer. Then, attach the other red wire to the other 1K resistor connected to the top center of the other potentiometer.

Solder the green wires in a similar fashion to the 1K resistors connected to the lower center pins.

When all of the wires are connected to resistors, trim the excess leads and insulate them with shrink tube.

## Wiring Ground

Connect the ground wire from the jack to any of the pins on the left side of either potentiometer.

Finally, use another black wire to solder together all of the pins (top and bottom) on the left side of both potentiometers. These are all ground pins, and should all be connected with one another and the black output wires on all three jacks. If you miss connecting any of the ground wires together, this likely won't work right.

## Test It Out

Once all of the ground wires are connected, the circuit should be complete.

Before you mount it in the enclosure, test it out fully and make certain it works.

## Mount the Components

Remove the all of the mounting nuts from the potentiometers and jacks.

Insert the components into the enclosure, and then twist back on all of the mounting hardware to lock everything in place.

## Seal the Deal

Use the enclosure's mounting screw to fasten the lid firmly shut.

Finally, peel the remaining back off the label, and stick it down over the mounting screws.

Normally, we wouldn't cover the mounting screws with the label because it will prevent us from reopening the case later.

However, in this case it is okay because this is a passive mixer. Being passive means it uses no external power source. The only electricity is coming from the audio signal themselves. Thus, we will never need to open the case to replace a battery, nor will we likely ever need to repair anything.

## Finishing Touches

Twist the knobs entirely to the left.

Line up the knob's indicator marks with the appropriate marking on the label, and then fasten the knob in place using it's set screw.

## Give It a Go

You should now be done, and able to mix together to separate stereo tracks.

Keep in mind, this is one way to make a mixer using resistors, but not the best way to make one. The resistors result in some loss of volume. This is particularly problematic if you decided to build one with more tracks.

This method also might result in crosstalk between the tracks, which can become a problem if any of the audio is going through a special effect circuit. There would be nothing stopping the effect from getting applied to all tracks.

The best way to make a mixer is to make an active one using Op Amps. This method both prevents volume loss and cross-talk. This is far beyond what we have learned so far, but by the end of the class you will have learned enough to research and build one on your own.

## CLASS PROJECT

Share a photo of your finished project with the class!

Nice work! You've completed the class project