Operational Amplifiers (Op-Amps)

This article covers the basics about operational amplifiers (op-amps).

The ideal op-amp

The op-amp has two inputs (+ and -), and one output. Because of the very high gain of the amplifier, it usually must be used in a feedback configuration. By sending back an inverted (negative) portion of the output signal into the input, the overall output is reduced. At first this might seem like a bad thing to do. After all, why would you want to cut down the signal in your amplifier? The reason behind this is that by using a high gain amplifier and a feedback loop, you can reduce signal distortion and provide a very linear response.

When you are using an op-amp in a feedback configuration, its best to think of the op-amp as changing its output to make the input voltage difference equal to zero. This may be a bit difficult at first to completely grasp, but beginners should just look at a few op-amp circuits to see what is going on. Eventually it will start making sense.

The following diagram shows the op-amp in a typical negative feedback configuration. Because we are assuming that this is an ideal op-amp, if the positive input is grounded, so is the negative input (remember that the output will change to force the input voltage difference to zero). This leads us to the conclusion that the output voltage is equal to the voltage across Rf, and the input is equal to the voltage across Ri. Because we are assuming the input current to be zero, that means that the current through Rf and the current through Ri must be equal, but of opposite signs (remember from Kirchoff that the sum of all currents into a node must be zero). We can therefore write the following equation:

        Vo/Rf = - Vi/Ri

        Which is more commonly written as:

        Vo = -(Rf/Ri)Vi

Note that if you do not assume the op-amp to be ideal, these equations become a great deal more complicated.

Overall, this means that our circuit will multiply the input by -Rf/Ri to create the output. Because of the negative sign, this is called an inverting amplifier. The output will be the opposite sign from the input, and will be scaled by the proportions of the two resistors.

The input impedence of this amplifier is simply Ri, since the inverted input is effectively grounded.

Real World Op-amps

In the real world, op-amps do not have quite an infinite gain (100,000 to 1,000,000 is more typical), and they do draw a small amount of input current (a few nano-amps). As long as you do not attempt to use circuits that are affected by these less than perfect specs, you should not run into any difficulty.

Never attempt to use positive feedback. This will drive the op-amp immediately into saturation, and your circuit will not work. If you need a non-inverting amplifier, use a circuit like the following: (note that the - and + terminals are reversed from the previous circuit, otherwise this would be positive feedback)

In a practical circuit, do not attempt to use a feedback resistor that is too low of a value, otherwise the op-amp will not be able to generate enough feedback current to operate properly and strange things may result. A feedback resistance of 1 meg is typical.

Note that most op-amps will not produce rail to rail (+V to -V) outputs, but instead will start to clip at about 1.5 volts away from the supply. If you have a +/- 9 volt supply, the output can't go more than +/- 7.5 volts.

A real world op-amp usually requires a bypass capacitor. This is a small capacitor (a 0.1 uF ceramic usually works fine) placed between +V and -V, as close to the chip as possible. This doesn't mean you need to sandwich the cap under the chip, but typically it should be right next to the chip on the circuit board. Sometimes your circuit will work fine without a bypass cap, but other times it will howl and scream due to uncontrolled oscillations.

Your choice of op-amps will depend on your particular circuit requirements. The basic 741 op-amp is one of the most popular chips in the world. It has a reasonable performance and is very low cost, making it ideal for hobbyists. For most audio circuits it works fine, but if you need better frequency response, you may need to select something with slightly better characteristics (and a bit larger price tag).

Using a battery

Op-amps require a dual voltage source. You can just use two batteries to power the device, or you can be a bit clever and use only a single battery. Remember that voltage is all relative. If you make a voltage divider out of two resistors that are equal, the voltage in the middle will be half of the voltage between the two ends. So, let's assume we have a 9 volt battery, and we connect two 1 K resistors to the battery in series. The midpoint where the two resistors connect to each other will be at 4.5 volts. What if we take this midpoint as our voltage reference? In other words, we assume that this is our zero point. The positive lead of the battery is therefore at +4.5 and the negative lead is -4.5 volts. Hmmm... sounds like a dual voltage power supply to me, eh?

In practical circuits, it is best to include bypass capacitors between this midpoint and ground (0.1 uF ceramic caps will work fine for most circuits). This helps to keep the reference at a stable voltage, so that it is not affected by noise and signal variations.

A disadvantage of this method is that the resistors are always drawing power just to create the voltage reference. In the above example, a 9 volt battery connected to a 2k resistance (two 1k resistors in series) draws i=V/R=9/2K=4.5 mA.

If the external devices are drawing more current, smaller resistances may be necessary to keep the voltage divider stable. This will, of course, increase the amount of current required in the voltage divider. For most audio circuits (like guitar effects) 1K works fine.

Op-Amp circuits

There are more practical circuits for op-amps than you can shake a stick at. Obviously, I can't even hope to present them all here. So, here are just a few.