S5-4.2 Op-Amp Applications

What this is and why it exists

The previous topic built two amplifiers. This one changes only the network around the device and gets an adder, a subtractor, an integrator, a differentiator and an oscillator.

That is the point worth carrying away. The feedback network defines the function. The amplifier merely makes the network's rules hold.

The vocabulary

• Summing amplifier — several inputs feeding one summing point, giving a weighted sum.
• Difference amplifier — an amplifier whose output follows the difference between two inputs.
• Integrator — a capacitor in the feedback path, so the output follows the running total of the input.
• Differentiator — a capacitor at the input, so the output follows the rate of change.
• Sample and hold — a switch and a capacitor that freeze a value for something else to read.
• Comparator — the device run with no feedback, so its output goes to one rail or the other.
• Hysteresis — two different switching thresholds, one for rising and one for falling.
• Schmitt trigger — a comparator with positive feedback, which is what creates that hysteresis.
• Triangular waveform generator — an integrator and a Schmitt trigger wired into a loop.

The mental model

Start with the summing amplifier, because it is the cleanest demonstration. Several resistors meet at the inverting input, which the ideal rules hold at zero volts. Each input therefore drives its own current, and none of them interfere. The currents add at that node and pass through the feedback resistor. The output is a weighted sum, and the weights are resistor ratios you choose.

The difference amplifier subtracts instead. It is the first step towards rejecting noise that appears on both wires of a pair. Go further in this direction and you reach instrumentation amplifiers.

The integrator puts a capacitor in the feedback path. A steady input gives a steadily ramping output, which is exactly what integration should do. The ideal version has a problem that ruins it in practice. Any offset at the input, however small, is a steady input, so the output ramps until it hits a rail and stays there. The practical version puts a resistor across the capacitor. At direct current the resistor dominates and the circuit becomes an ordinary amplifier with modest gain, so it cannot ramp away. At signal frequencies the capacitor dominates and it integrates. Knowing why that resistor is there is the difference between a circuit that works and one that latches up.

The differentiator is the mirror, with the capacitor at the input, and it has a mirrored problem. Its gain rises with frequency, so it amplifies high-frequency noise enthusiastically. The practical version adds a resistor in series with that capacitor, which limits the gain where you did not want any.

Sample and hold freezes a value. A switch closes to charge a capacitor to the input, then opens, and the capacitor holds while something else reads it. It is the front end of every converter in the next topic, so it is not an aside.

Now remove the feedback entirely and the device becomes a comparator. Any difference between the inputs is amplified enormously, so the output slams to one rail or the other. It is simple, and it misbehaves on a noisy input. Near the threshold, noise pushes the input back and forth across it, and the output chatters.

The Schmitt trigger cures that with positive feedback. A fraction of the output is fed back to the non-inverting input, which moves the threshold in the direction that opposes another change. So the level that trips the output high is different from the level that trips it low. Noise smaller than that gap cannot cause a second transition. This circuit recurs everywhere in digital interfacing, so it is worth being able to design rather than merely recognise.

The triangular generator wires two of these into a loop. The trigger's output is a square wave that drives the integrator. The integrator ramps one way, hits the trigger's threshold, and the square flips, so the ramp reverses. Watching the triangle and the square appear together makes the loop obvious in a way the schematic does not.

What you should now be able to explain or do

Design a summing amplifier for stated weights. Explain why the ideal integrator saturates and what the parallel resistor does about it. Explain the differentiator's noise problem and its cure. Describe how a sample and hold circuit works and where it is used. Design a Schmitt trigger for a stated hysteresis, and explain how the integrator and the trigger together make a triangular wave.

Check yourself