How to Calm Hysterics in Op-amps
Ben Duncan explains instability... and he should know!
Ben Duncan continues in his role as expert repair man.
It's not at all uncommon to find recording set-ups which are unstable. In other words, some part of it has been turned into an RF signal generator. Other than outright bad design or thoughtless quality control, oscillation comes about when the equipment is hooked up to an unfortunate combination of the studio's inhouse spaghetti collection!
Sometimes, ultrasonic instability is rendered directly audible in conjunction with a tape machine's bias oscillator: the two signals beat and combine to produce an audible chord, or 'difference frequency' as it is known. For this to happen, the oscillation will normally need to be in the 100kHz area, but in the real world, instabilities happen anywhere between 24kHz, all the way up to 40MHz. If it's not rendered directly audible, a likely giveaway is the rough, distorted sound above 5kHz, or a rough hissing or sizzling sound, which is louder than the noise level you'd come to anticipate. On the factory side, you may also notice the aroma of cooked monitors and amplifiers.
In ideal circumstances, the negative feedback (NFB) looped around every stage in a mixer (and so on) is displaced exactly -180° from the input it's correcting, which is taken to be at 0°. In other words, the feedback is out of phase with the input. This much is true at low audio frequencies, but higher up the output phase gradually lags behind, towards -360°. Thinking of phase as a circle, this has exactly the same connation at 0°, for of course: 0° = 360°.
Figure 1 displays the phase behaviour typical of the IC op-amps used in todays consoles. Peering at the curve, do you notice how the phase hits -180° at 10MHz? Because 0° is our NFB reference, this curve, then -180° corresponds to positive feedback. The net result is lots of oscillation. However, an amplifier with this behaviour can remain perfectly stable given that we can contrive to keep the loop gain (inside the feedback loop) down to 0dB at this critical frequency (if not well below).
The difference between the frequency at which phase reaches -180°, so guaranteeing oscillation versus the unity-gain frequency we actually choose, is called the 'phase margin'. For example, if we set the unity-gain frequency for the device in Figure 1 at 0.6MHz, the phase lag at this point is 90°, so the phase margin would be 90° -180° = 90° margin. Next, Figure 2 charts the gradual peaking up in HF response as the phase margin is eroded. Judging by the shape of the curves, you won't be surprised to hear that any phase margin below 60° is looked down upon as being either 'conditionally stable' or 'latently instable' depending on whether it's in the sales catalogue, or in a critical review!
In turn, loop-gain is subject to both the gain band width product (GBW) of the op-amp, and the gain. Designing for stability basically means taking care to keep phase shift well below -180° at all likely loop-gains. The designer's euphemism for forcing amplifiers to be stable in this manner is compensation, though there have been occasions where it has been rather more brutal...
Assuming the unstable equipment is of manufactured origin, (not a prototype, or home-built in a non-standard layout), then compensation need only concern us insofar as it corrects for excess phase-shifts. What are the causes of these?
Figure 3 shows two locations where stray capacitance promotes a bad, lagging phase shift. In real life, the magnitude of CN (N standing for 'Nasty') needed to wreck the HF phase margin is surprisingly small, often as little as 10pF. In non-inverting stages (where the signal comes in via the +ve input), this is easily represented by inter-track capacitance around the device itself. This is likely to afflict manufactured products insofar as PCBs are often hastily re-designed in the push to get a new product on the market. Just as often, though, the PCB designer employed turns out to have had no knowledge or experience of analogue PCB design.
The same goes for normal inverting stages (the sort illustrated in Figure 3), but the massed ranks of mix amps in consoles are an especially bad case. Here, CN is much larger because of the long length of the mixing buss, strung alongside many pF/metre of stray metalwork. There's lots of scope for a big, bad capacitance to ground under these conditions. Nevertheless, in any self-respecting console, the designer will have accommodated this buss capacitance. However, if some mods have been made to the console, it's not unknown to find lengths of screened wire have to be installed, and it's particularly tempting for the tidy-minded amongst us, to tiewrap this to one of the busses. Beautiful and artistic it may be, but imagine the oscillation! The mixer either bursts into a screeching fit, or else sulks in a latent instability. This symptom, brought on by loss of phase margin, is often occasioned to leap into real histrionics only when you need it least.
The second root cause of troubles is cable capacitance, seen by the output as a capacitative load (CO). Anything above 470pF can precipitate instability; that's the same as 14m of Phonoflex or 6½m of Musiflex cable. The cause of this instability is the phase shift introduced as CL works against the op-amp's inductive source impedance, RIOS, at radio frequencies.
The first remedy is preventative: simply avoid excessive capacitance by keeping modified wiring away from mix busses, and by using low capacitance screened cables. For example, Neumann mic cable has a capacitance of about 600pF/metre. This is fine for its intended purpose, but it's bad news for top-end response and system stability, if used indiscriminately in line level interconnections. A quick look at your cable supplier's catalogue, or a phone call to the dealer will set your mind at rest, if curious. As a benchmark, any capacitance below 100pF/m is low, 100pF to 200pF is medium, and anything higher than 240pF is best skipped.
For the second go at a cure, we add a 'phase-lead compensation' capacitor, CF. Intuitively, this can be seen as 'pulling' the feedback signal back into phase (see the arrow in Figure 4), and/or balancing out the shifts created by CL and CN respectively. Rather than calculate from hazy parameters, like RIOS, the value of CF can be determined empirically, starting at 10pF. We then select on test the lowest value necessary to attain stability, plus 10% for luck. Values above 1nF shouldn't have to be used; if it seems that nothing short of a big capacitor will slug the oscillation, then the phase conditions are seriously astray, and you'll need to combine a more modest value of CF with other steps. Capacitors can be Mica, Polystyrene or class 1 'low-k' ceramic, and should be soldered directly across the feedback resistor.
The third technique is somewhat simpler for the average enthusiast. All we need do is solder a resistor (RO in Figure 4) in line with the equipment's output socket. This takes the breakpoint of the output's critical -180° phase condition down in frequency, and out of harm's way. It also has the habit of rolling off the HF response, just like CF. So once again, excessive values will affect things like cymbals.
Typical values for RO are 10R, up to 680R, and once again, the lowest successful value (plus 10%) is best. Needless to say, it's important to test for stability with the guilty lead or leads plugged-in; it's no fun finding out that the problem has reappeared when the equipment has been reassembled, and heaved back into place. The final question must be: how can we be certain that instability exists in the first place, and how can we be sure it's been cured? To answer both of these uncertainties, and in lieu of being able to hear, smell or otherwise positively detect 10.0MHz, the most important tool is the oscilloscope. If you don't have access to one, I promise that many hours of sweat and tears can be avoided by blagging or hiring one.
For those wanting to delve more deeply into this subject, recommended is the IC op-amp cookbook by Walt Jung, published by Howard Sams (1974).
Feature by Ben Duncan
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