Operational Amplifiers

Op amps are versatile ICs containing a hundred or so transistors that can perform a vareity of mathematical functions. For this reason, they are the building blocks of many signal processing circuits. They have two inputs, an inverting (-) and noninverting (+). A positive voltage source and negative voltage source or ground are connected directly to the op amp, although these are rarely shown on circuit diagrams. There is a single output, which is almost always connected to the inverting input with a negative feedback loop.

Op Amps have almost infinite gain, high input impedance, and low output impedance. Because of this, they serve many useful purposes in analog circuits. Some of these properties are discussed in the context of the following examples.

All of the example circuits can be analyzed by observing the following simple rules.

1. The output does whatever is necessary to make the voltage difference across the inputs equal to zero.
2. The inputs draw no current.
3. The output voltage does not depend on the output current.

Even though there is a lot going on inside the op amp, these rules describe its "black box" integrated circuit behavior. Ideal op amps are modeled with infinite gain and infinite impedance - real op amps only approximate these model properties. Likewise, while our model assumes infinite voltage gain, the limiting output voltage magnitude is about 1.4V lower than the magnitude of the supply voltage (this is due to diode drops in the op amp). Some of these effects should be observable if we apply a square wave input. At the rising and falling transitions of the square wave the voltage changes infinitely fast and while they're fast, op amps can't change instantaneously - there should be a slightly non-vertical slope produced in the output. This can be measured by the slew rate (with is the change in voltage over the change in time).

Inverting Amplifier - This configuration copies an inverted and scaled version of the input signal to its output. In doing so, the circuit isolates the circuit that produces the input reference from the circuit that uses the output by virtue of our op amp's impedance relationships.

Non-Inverting Amplifier - We can accomplish amplification without inversion if we re-configure the circuit slightly.

By setting R₂ to zero (short circuit) and R₁ to infinity (open circuit to ground), we get a non-inverting, unity gain amplifier - the unity-gain follower. This is an important use of operational amplifiers. The high input impedance of the amp draws virtually no current and so acts as an impedance buffer. One could, for instance, use a voltage divider to step the voltage used to drive a resistive load down without worrying about impedance loading the divider. The op amp lets you track the input voltage without drawing significant current.

Integrating and Differentiating Amplifiers - By using a capacitance, the op amp can compute the integral and differential of the input voltage. In the first example, we see that the output voltage is the integral of the input voltage.

And by switching the capacitor and the resistor, the output voltage is the derivative of the input voltage with respect to time.

Adder - This circuit produces and output equal to the negative weighted sum of the respective inputs. One can imagine that with the right input resistances, we could construct a form of D/A converter with in which input "bits" are amplified by an amount proportional to their position in a binary word.

Comparator - This setup is used to determine which input signal is greater. When the inputs are equal, there is no output. When the inverting input is greater, the op amp becomes saturated and output voltage is equal to the positive voltage supply. When the inverting input is greater, the output voltage is equal to the negative voltage supply. There are TTL comparators available that would be recommended for this purpose, but the mighty op amp can do it in a pinch.