The op-amp as a comparator

Structure of the basic op-amp comparator

The op-amp comparator is the operational amplifier in its native open-loop configuration, with no resistive feedback path between the output and either input. A fixed reference $V_\text{ref}$ sits at the inverting terminal, the signal of interest $v_\text{in}(t)$ drives the non-inverting terminal, and the output is taken directly. The supply rails $V_{CC}^{+}$ and $V_{CC}^{-}$ set the upper and lower limits of the output voltage.

• inverting input ($-$): reference voltage $V_\text{ref}$;
• non-inverting input ($+$): time-varying signal $v_\text{in}(t)$;
• output: $v_\text{out}(t)$, the result of the comparison;
• supplies: $V_{CC}^{+}$ and $V_{CC}^{-}$, defining the output range.

The open-loop op-amp as a one-bit decision element

An ideal op-amp obeys the differential gain equation,

where $A_\text{OL}$ is the open-loop voltage gain, typically $10^5$ to $10^6$ at low frequencies. Without negative feedback, an input differential of a few microvolts is enough to drive $v_\text{out}$ outside the supply range, so the output is forced to one of two values:

The width of the linear transition between these two states is

about $240\,\mu\text{V}$ for $A_\text{OL} = 10^5$ and $\pm 12\,\text{V}$ rails. At the resolution of most biopotential signals this transition is invisible; the transfer characteristic is effectively a step.

The comparator with a sinusoidal input

A sinusoidal input crossing a fixed reference produces a square wave at the output. Its duty cycle depends on where the threshold sits relative to the input mean and amplitude.

For $v_\text{in}(t) = V_m \sin(\omega t)$, the output transitions occur at the times where $v_\text{in}(t) = V_\text{ref}$, namely

If $|V_\text{ref}| > V_m$, the input never reaches the threshold and the output remains at one rail. Setting $V_\text{ref} = 0$ gives the zero-crossing detector, in which the output edges coincide with the sign changes of the input. The amplitude of $v_\text{in}$ is then irrelevant; only the timing of its zeros matters. This is the standard front-end for a phase-locked loop, a digital tachometer, or a heart-rate counter.

Limitations of the plain comparator with a noisy input

Real biosignals carry broadband noise from the electrodes, the analogue front-end, and the surrounding environment. Far from the threshold this noise has no effect. Near the threshold, every small excursion of the input across the reference produces an output transition, and the comparator breaks into rapid chatter.

The plot shows a synthetic ECG-like signal with adjustable noise. The counter on the output trace reports the number of edges produced over a three-second window. Even moderate noise placed near the R-wave threshold can convert a single genuine crossing into ten or more reported edges, making the output unusable for downstream timing or counting.

Where the noise comes from

• drift of the electrode-to-skin half-cell potential, of the order of millivolts per minute;
• mains pickup at 50 or 60 Hz, partially rejected by a differential amplifier but never eliminated;
• electromyogram (EMG) artefact within the passband of the ECG channel;
• input-referred voltage noise of the first amplifier stage.

None of these contributions can be removed entirely by raising the gain or sharpening the upstream filter. The plain comparator has no mechanism to reject small fluctuations of the input around the reference, which is its principal limitation as a threshold detector for biosignals.