Power Supply Instability

Problem

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One of the most embarrassing things that can happen to a power supply = circuit=20 designer is to have their "finished" design go unstable during = manufacturing or=20 after delivery to the customer. This happens quite often and it is not = too=20 surprising. Switching-mode power supplies are one of the toughest = circuits most=20 engineers will ever have to stabilize. The reasons are:

The power supply can operate in different modes, such as the = continuous and=20 discontinuous current mode, presenting different control loop = parameters in =20 each mode.
The input voltage can appear in the gain of the feedback loop, = changing the=20 gain characteristics as the input voltage swings over the wide = operating=20 range typical of many applications.
Load variations affect the location of poles or zeroes associated = with the =20 output filter.
The effective value of components contributing to poles and zeros, = such as =20 inductors and the load resistance, can vary as a function of line and = load =20 variations.
The circuit can contain both real and complex right-half-plane = zeroes that =20 migrate as a function of line, load, and temperature.
Many of the components affecting circuit poles and zeroes are = nonlinear, =20 such as swinging inductors.
Many of the components affecting stability have large variations in = =20 tolerance as purchased and over operating temperatures and system = life, such =20 as electrolytic capacitors.
Long power source leads or added system filters, such as EMI = filters can =20 have a dramatic effect on system stability criteria. See Input=20 Filter Interaction.
Added load capacitance, including high quality decoupling = capacitors =20 shorting the ESR of the power supply output capacitor, which may be =20 contributing a stabilizing zero, can effect stability.
Minor loops inside the power supply, like those causing emitter = follower =20 oscillations or power MOSFET drive resistance instabilities, may go = unstable =20 over the range of purchasing tolerance or variations caused by = manufacturing, =20 temperature, and age. These can go unstable with little noticeable = effect on =20 output observables (except perhaps radiated EMI in the Megahertz = range), but =20 can alter the feedback loop by causing saturation of components or DC = level =20 shifts in interior states and can greatly degrade field = reliability.
Things like the magnetizing current in the magnetics can affect =20 stability.
Switching noise can affect stability and stability measurement. One = of the =20 industries first challenges with switching-mode power supplies was = trying to =20 measure small gain and phase signals in a noise environment much = larger than =20 the signal. See personal = anecdote =20 below.
Chaos can occur in these circuits. SeeChaos=20 and personal = anecdote below.

A common and totally inadequate defense against the above is often to = analyze=20 the circuit at nominal input voltages and load and verify the analysis = with a=20 measurement on the breadboard using a resistive load and laboratory = bench=20 supplies. No wonder switching-mode power supplies often break into = oscillation=20 during manufacturing or over the life of the product in the field.

Relevance

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Applies to any circuit with a feedback loop, but keeping = switching-mode power=20 supplies stable over the life of the product in all environments is far = more=20 difficult than most feedback loops.

Solvability

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No complete solution, but the risk can be reduced greatly. What is = needed is=20 a practical strategy of analysis, measurement, screening, and = follow-up. There=20 is a tradeoff between cost and risk in all of this. The elements of = such a=20 strategy are discussed under solutions.

Solution

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Planned strategy of analysis and test followed with a closed-loop = oven screen=20 and follow-up. The questions to answer are:

At what operating points should analysis be performed and tests = made?
Is there a useful screen?
Is this sufficient or is some follow-up necessary?

Analysis and Measurement

Nominal Measurements: You normally have to calculate one = gain-phase=20 plot and make one set of measurements so you can show your management = or the=20 customer that the system is stable with sufficient gain and phase = margins, even=20 though analysis and measurement at a single set of operating conditions = is high=20 risk. Typically the operating conditions are room temperature, nominal = input=20 and bias voltages, and either the expected or full load. This approach = is at=20 the lowest cost, highest risk extreme.

10% Increments: Another approach is measuring on a grid of=20 intercepting operating points. This results in combination explosion. = For=20 example, using 10% increments with input voltage, one bias voltage, = load=20 current, and temperature, you would have to calculate 14,641 gain-phase = plots=20 and measure the same number. Even if you could or would want to do = this, you=20 probably are not going to have the patience to examine each one = critically.=20 This is the other extreme, maximum cost, but not necessarily the = minimum risk,=20 because no one is going to critically look at this many calculations = and=20 measurements. You increase the increments, say to 25%, but this is = still 625=20 calculation/measurement pairs for the above example.

Coffin Corners: This approach, called the coffin corner = approach here,=20 is to calculate/measure at the worst case extremes only. For the above = example=20 this reduces the analysis/measurement pairs down to sixteen pairs for = the above=20 example. You've cut the cost, but you still have some uncomfortable = risk, since=20 you have not even measured at the nominal conditions that the power = supply will=20 most likely be used. To correct for this you add back in the min, nom, = max load=20 at nominal input, and the min, nom, max line at nominal load all = measured at=20 nominal bias and nominal temperature. This adds five more measurements = for a=20 total of 21 analysis/measurement pairs. This can be done, especially if = you are=20 using a computer controlled analysis/measurement system for this.

Coffin Corners Modified for Switching-Mode Power Supplies: The = above=20 may work for most feedback circuits, but for switching-mode power = supplies you=20 have a few more critical measurement points. The control loop = characteristics=20 change at the continuous/discontinuous current boundary. Typically a = second=20 order system in the continuous current mode reduces to a first-order = system in=20 discontinuous current, which is normally stabilizing. But other=20 stability-related things happen near this boundary, for example see the = Jang and Erickson = paper=20 in the discussion on Input Filter=20 Interaction.

Finally, power supplies are often overloaded or shorted, and you = don't want=20 them to go unstable under these conditions. Hence more = analysis/measurement=20 pairs are called for and often you have to increase risk to get the = number of=20 pairs down to a reasonable number. Can you cut the pairs and do = something else=20 to reduce risk?

Oven Screen

The oven screen described below has proven extremely successful in = finding=20 operating conditions where stability margins in a switching-mode power = supply=20 deteriorate.

In essence, a square-wave voltage is applied across the reference and = the=20 output voltage response is observed as the load current is swept from = no-load=20 to full-load for various input voltages, biases, and temperatures.

Figure 1 shows some of the waveforms that can occur on the = output.

3D"Screening =20

Figure 1: Oven-Screen Waveforms
Overdamped, ideal, = underdamped,=20 near oscillatory

The upper left waveform shows the overdamped response of a = conservatively=20 stabilized system where performance may be sacrificed for a robustly = stable=20 system.

The upper right waveform shows the ideal waveform. The output = replicates the=20 input waveform.

The lower left waveform shows the very beginning of ringing. Usually = damping=20 should occur within a cycle of the first overshoot/undershoot. Any less = damping=20 should be noted.

The lower right waveform shows a system about to go unstable.=20

The circuit is set up in an oven and for a given temperature, the = load is=20 swept for a fixed input voltage and bias voltage and any ringing or=20 oscillations noted, along with frequency, on a plot of Vin vs. Iout as = shown in=20 Figure 2.

3D"Oven =20

Figure 2: Oven Screen - Vin vs Io

A grid of input voltages for a fixed bias is set up and the load = sweeps made.=20 Then repeated for various biases, and then repeated for a grid of=20 temperatures.

Collapsing all the graphs on a single graph, such as Figure 2, shows = the line=20 and load conditions that are problem areas over the temperature = range.

Typically, it takes a half day to set up the circuit in oven, and a = half day=20 to make all the sweeps. Most of the time is waiting for the circuit to = reach=20 thermal equilibrium with the oven ambient.

The theoretical foundation of this approach assumes a system no = higher than=20 second order, which is rarely the case. However, since you try to make = the=20 circuit behave like a first or second order system, it seems to work in = practice. I have known a lot of power supplies to develop oscillation = in the=20 factory or the field, but never one that has passed this screen.

Variations. Inject white noise across the reference at various = injected=20 levels of noise. Noise can induce subharmonics=20 and chaos in susceptible circuit.

Practical Advice

The signal can be injected from a square-wave generator through a = blocking=20 capacitor if the reference internal impedance is sufficient to develop = a clean=20 square wave across it. If a noise filtering capacitor is across the = reference,=20 then it may have to be removed in order to get a clean square-wave = signal. More=20 sophisticated injection approaches can also be used. Make sure that if=20 capacitance or resistance at the reference node is modified, the = break-points=20 are outside the frequency range of interest. Always monitor the = injected=20 signal, to make sure it does not distort, as well as the output = signal.

Scope probes melt before 125C. Keep the probes outside the oven if = the range=20 will exceed the temperature rating of the probes, either hot or = cold.

Make sure the circuit in the oven reaches thermal equilibrium with = the oven=20 ambient before you make the measurements. This will take most of the=20 measurement time.

You can also make ripple, regulation, and other measurements of = interest at=20 various temperatures while you have the circuit in the oven.

Measuring your circuit alone is necessary but not sufficient to = guarantee=20 stability in the system. You need to include input filters, cable = impedances,=20 nonresistive and nonlinear load impedances, etc. in both your analysis = and=20 measurements.

Follow Up

Ultimately, your power supply must be stable in its operating = environment=20 over the life of the system. For that reason, an injection point and=20 measurement point are often built into the power supply and brought out = to=20 board and system test connectors. You have to be very careful that the=20 injection lines do not pick up noise and inject it into a critical = point in=20 your circuit. This approach lets you check your stability as the system = builds=20 and is deployed. An early version of this was the marginal test = capability that=20 was built into early computer power supplies that allowed the power = supplies to=20 be varied plus or minus some amount during maintenance tests in order = to weed=20 out weak integrated logic circuits. By observing the wave forms during = this=20 test, you could get a feel for the stability of the power supply.

One risk you will face is that some cost-reduction suggestion or = "improved"=20 part will be incorporated in your design during the manufacturing life. = These=20 often negate your hard work and make changes to your system that = degrade it,=20 including causing it to oscillate. You have to be continually = vigilant.

Personal Anecdote

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I remember in the mid 1960's when I was first asked for a gain-phase = plot of=20 a switching-mode power supply I designed. Fortunately, at that time I = believed=20 in limiting the gain of my feedback loops to 40dB and using feedforward = and=20 other compensation to minimize the effect of line and load changes, so = things=20 were manageable. Still, breaking the loop was a challenge. I used = batteries=20 with potentiometers for a true open loop measurement, or large = capacitors to=20 open the loop to AC signals, and was finally able to make open-loop=20 measurements. However, there was so much noise from the switching = frequency=20 that it was anyones guess what the amplitude and phase was near unity = gain. For=20 many years I had, and others had, gain-phase plots that they could show = people,=20 but anyone who had actually made a measurement didn't believe in them. = It was=20 then I developed the oven screen and learned to trust it.

R. David Middlebrook changed all this when he published a 1975=20 paper and expanded on it in a 1976=20 paper describing a measurement technique using a tuned voltmeter = that=20 eventually gave some credibility to gain-phase measurements of = switching-mode=20 power supplies.

When I and others started to use Middlebrook's techniques, it took = about 40=20 hours, starting with a simple RC circuit and graduating to = switching-mode power=20 supplies, to learn how to make them with confidence -- and they were = always=20 tedious to make.

The next breakthrough came in the late 1970's and early 1980's when = people=20 started to successfully put together systems based on instruments from = Hewlett=20 Packard, Schlumberger, Nicolet, and Bafco. Some of these systems took = man-years=20 to put together and debug -- and then gave mixed results.

In 1980 Dean Venable experimented with various systems, published=20 a paper and founded Venable=20 Industries that provided turnkey systems, including accessories and = documentation, for making these measurements. Venable Industries is = still a=20 leader in this field and Dean Venable has kept publishing papers on the = subject=20 (see references). = Some of=20 Venable Industries computer controlled systems have gotten quite=20 sophisticated.

In the late 80's, some of the major measurement companies like = Hewlett=20 Packard, figured out how to do it and gave some seminars, but it still = took=20 some figuring out to use their equipment.

Lately, some other companies, such as Ridley=20 Engineering, have entered the field with low cost approaches.

These developments have turned the once very difficult task of = measuring the=20 gain-phase of switching-mode power supplies into something manageable. = But you=20 still have to be careful. If the signal distorts on you, then things = are no=20 longer linear, and under these conditions even sophisticated equipment = can give=20 erroneous results. This is the most common mistake with the new = equipment. I=20 always monitor the input and output signals with an oscilloscope so I = can=20 either control distortion, or at least know not to trust the = measurements when,=20 as at some resonances, distortion is inevitable.

Finally, a comment on injecting white noise across the reference. I = noticed=20 the problem when one of my 25 KHz switching regulators developed a 12.5 = KHz=20 subharmonic ripple when in the system. When in the lab or on an = extender board,=20 there was no subharmonic. Thinking it might be related to noise, I = injected=20 white noise into the reference and other circuit nodes. When the = white-noise=20 generator hit a certain level, the subharmonic would appear. Increasing = the=20 level started what I now know as bifurcation to other harmonics, = probably on=20 the way to chaos, = which at=20 the time, I had never heard of.

On the Web

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Many of the pioneers and players in stabilizing switching-mode power = supplies=20 have websites.

Ardem Associates, R. David = Middlebrook's=20 website, describes a seminar that covers his techniques of loop = analysis and=20 measurement. The site includes Dr. Middlebrook's annotation=20 of his papers covering his techniques of analysis and measurement with = the=20 pioneering papers on measurement of switching-mode power supplies at = the=20 end.

Venable Industries = provides many uses of a network=20 analyzer and a list of his papers,=20 many with full text.

Ridley = Engineering's pages=20 provide additional information including his page on Design=20 Tips which gives some solid information on closing the loop. It = also has a=20 list of his papers=20 with some excellent annotations.

References

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References. A = short=20 bibliography of test paper abstracts related to stability = testing.

Legal=20 Statement

Do not use this information for design without = independent=20 verification of the information.