Explain the operational amplifier used as a comparator, including its very high gain and the two output states

What this dot point is asking

SEAB wants you to explain how an operational amplifier (op-amp) is used as a comparator: how it compares the two voltages at its inputs, why its very high gain forces the output to one of two extremes, and how a sensor divider and a reference voltage make it switch at a chosen level. The central insight is that an op-amp with no feedback amplifies the difference between its inputs so strongly that the output is always slammed either fully high or fully low.

The answer

The op-amp and its two inputs

An operational amplifier has two inputs and one output:

• The non-inverting input (marked $+$).
• The inverting input (marked $-$).

The op-amp amplifies the difference between these two inputs. It also has a very high open-loop gain (the gain with no feedback), often a hundred thousand or more.

Why the output saturates

Because the open-loop gain is so enormous, even a tiny voltage difference between the inputs is multiplied to a value far larger than the supply voltage. The output cannot go beyond the supply rails, so it is driven hard against one rail or the other. The result is that the output rests at only two values, not a smooth range:

• If the non-inverting ($+$) input is higher than the inverting ($-$) input, the output goes high (near the positive supply).
• If the inverting ($-$) input is higher than the non-inverting ($+$) input, the output goes low (near $0\ \text{V}$ or the negative supply).

Used this way, with no feedback, the op-amp is a comparator: it compares two voltages and gives a clean two-state output.

Comparing against a reference

To make a useful sensing circuit, one input is held at a fixed reference voltage (often set by a potential divider or a variable resistor), and the other is fed by a sensor divider whose voltage changes with light, temperature or another quantity:

• When the sensor voltage rises above the reference, the output switches to one state.
• When it falls below the reference, the output switches to the other.

The reference voltage sets the exact level at which switching happens, which is how a comparator decides "too bright", "too hot" or "too high".

Why a comparator is useful

A sensor divider gives a slowly changing analogue voltage, but many circuits need a sharp on-or-off decision. The comparator turns the gradual sensor voltage into a clean high-or-low output that can directly drive a transistor, a relay or a logic input. It is the bridge between analogue sensing and digital switching.

Examples in context

Example 1. A frost alarm. A thermistor divider feeds one input of a comparator and a reference set just above freezing feeds the other. As the temperature drops past the set point, the comparator output switches and sounds an alarm. The sharp two-state output means the alarm comes on decisively rather than fading in, which is exactly what a warning needs.

Example 2. A light-activated switch. An LDR divider compared against a reference switches a lamp on at a chosen darkness. Because the comparator output is clean and full-swing, it can drive a transistor and relay directly. The reference, set by a variable resistor, lets the user choose precisely how dark it must be before the lamp comes on.

Try this

• Cue. State the output of a comparator when its inverting input is higher than its non-inverting input. The output goes low (near $0\ \text{V}$), because the output is high only when the non-inverting input is higher.

• Cue. Explain why a comparator output saturates rather than varying smoothly. The op-amp's very high open-loop gain multiplies any small input difference beyond the supply rails, so the output is driven fully high or fully low.

• Cue. State the purpose of the reference voltage in a comparator sensing circuit. It sets the level the sensor voltage is compared against, fixing the exact light, temperature or value at which the output switches.