Two op amps can ruin the stew

Op-amp circuits have a feedback loop, but sometimes it is advantageous to improve closed-loop performance by including another amplifier within the op amp's feedback loop. For example, a limited selection of high-drive-capability/precision-input op amps exists, and one option is to put a high-drive-capability amplifier in the op amp's feedback loop. Some ugly results of adding secondary amplifiers to a feedback loop are overshoot, ringing, and oscillation. Ringing and overshoot are the first signs of instability, and oscillation is the final sign, so understanding what causes and cures instability is important.

An op amp oscillates when the gain, A, and the feedback, β, achieve the following relationship:

(Figure 1). It might seem difficult to achieve a gain magnitude of 1 at exactly –180° phase shift, but, in most cases, the op amp automatically reaches this magnitude. Op-amp output stages become nonlinear near the power rails, thus reducing their overall gain and satisfying the condition for oscillation.

You determine stability by calculating the phase shift at the 0-dB crossover frequency. The open-loop-gain/phase plot in the op-amp data sheet applies to the primary amplifier. The secondary amplifier operates in closed-loop mode, so you have to measure its phase shift not only close to the 0-dB crossover frequency, but also at a point at which the circuit still has some loop gain. When primary and secondary op amps have nearly identical unity-gain bandwidths (0-dB crossover point on the gain/phase plot), the circuit oscillates. I have verified this fact with many dual op amps, and it has always proved to be true.

The trick to obtaining stability is to use two op amps with dissimilar unity-gain bandwidths. A rule of thumb is that the ratio of high-to-low unity-gain bandwidth must be greater than five to ensure stability. This separation of the unity-gain-bandwidth points ensures stability because the high-unity-gain-bandwidth op amp cannot accumulate much phase shift before the loop gain becomes zero. Increasing the bandwidth of an amplifier to increase stability may seem weird, but remember that amplifier poles residing near infinite frequency introduce negligible phase shift at the 0-dB crossover point.

Most circuits use a high-bandwidth second op amp, but feedback systems are linear, so either op amp can be the high-bandwidth guy. When the circuit requires a high-output drive amplifier that has just adequate speed, the primary op amp becomes the high-bandwidth op amp.

When a feedback loop includes two op amps with similar unity-gain bandwidths, oscillations occur. You must separate the unity-gain bandwidth of the op amps by a factor of five (rule of thumb) to prevent oscillations. Bandwidth data is not a guaranteed specification, and a phase-versus-frequency calculation is nonlinear, so you can't rely on the rule of thumb as more than a mathematical starting point. You must verify all assumptions in the lab, and you must leave significant margins to accommodate parameter changes.

Circuit stability increases when the closed-loop gain increases, because the loop gain decreases. Circuit stability decreases when the secondary-amplifier gain increases, because the loop gain increases. You usually select the primary op amp because it has precision or low-noise specifications. You usually select the secondary op amp because it has excellent voltage/current drive specifications.

Author Information

Ron Mancini is staff scientist at Texas Instruments. You can reach him at 1-352-569-9401, rmancini@ti.com.