# Gas station without pumps

## 2013 June 26

### Kemet tech reports on capacitors

Filed under: Circuits course — gasstationwithoutpumps @ 08:46
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I was looking through the tech reports from Kemet about capacitors, to see whether there was anything else useful, besides the report that explain why capacitors don’t have their rated values that I mentioned in my previous post about DC bias.  I found one very beginning tutorial that may be useful for the Applied Circuits course: What is a Capacitor.  It talks about the standard RLC model for a capacitor, with series resistance and inductance and parallel resistance for leakage current.

It also does a pretty good job of talking about the different dielectrics used. I was not aware that barium titanate (class 2 ceramic capacitors) had dielectric constants of 3000 to 8000—I can see why it is so popular since tiny areas and thick layers are sufficient to get high capacitance.  They don’t mention a few of the classics from my youth (like mica capacitors), but you’d have to really be into old surplus to find those nowadays.  The low dielectric constant insulators are still in heavy use for high-frequency signal applications, because there are a number of problems with the ceramics and electrolytics in those applications.

I read CARTS – Spice Models with Temperature-Bias-Frequency Concerns also, because I was interested in how they modeled the DC bias concerns, but they didn’t really address that in the modeling, despite the title.  The temperature and bias dependence are handled by a proprietary tool that sets the parameters of the various RLC models for a given fixed temperature and DC bias, which does not at all capture the dynamic nature of DC bias and allow it to be simulated.It may be a useful tool for people designing fixed-voltage power supplies and using bypass capacitors, but it doesn’t really model bias effects in variable-output supplies or circuits with varying bias.

The report Why 47 uF capacitor drops to 37 uF- 30 uF- or lower is still a better presentation of what goes wrong with ceramic and electrolytic capacitors.

I looked at Avnet Power Forum – Capacitor Selection for DC-DC Converters, which is a series of slides from a lecture, not a full tech report.  It has some interesting material on DC-DC converters, which would be useful for a class on power supplies (or for anyone actually using a DC/DC converter), but is not really relevant for the Applied Circuits course.

CARTS – Can ESR Be Too Low describes the instability problems that can arise when using a capacitor that has low series resistance with a power supply controller designed for a capacitor with high series resistance.  The discussion was interesting to me, but relies on the reader knowing a little control theory, and so is mostly unsuitable for the Applied Circuits course.

There are lots more papers on the Kemet page, but most of them seem from their titles to be too specialized for the Applied Circuits course.

### Capacitance depends on DC bias in ceramic capacitors

Filed under: home school — gasstationwithoutpumps @ 06:56
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I think I now understand why my Colpitts oscillator oscillated at a different frequency than I expected, and why the 4.7µF capacitor appeared to be a 4.0µF capacitor when I measured it. The problem is most likely the DC bias on the capacitors.

It turns out that cheap ceramic capacitors have highly variable capacitance, depending on temperature, DC bias, and AC voltage applied.  There is a pretty good explanation of these effects from Kemet, a capacitor manufacturer: Tech Report 2008-03: Why 47 uF capacitor drops to 37 uF- 30 uF- or lower.  The paper talks about several different voltage, temperature, aging, and frequency effects of both electrolytic capacitors and multiple-layer ceramic capacitors (MLCCs).

There is actually some interesting physics going on.  They explain that there are 4 different polarization mechanisms that can cause a material to exhibit a higher dielectric constant: electric, atomic, dipole orientation, and space charge.  These correspond mainly to the magnitude of the movements of charges.  The most important of them for the ferromagnetic ceramics used in MLCCs is the dipole orientation.  What happens with DC bias is that many of the dipoles are already aligned to the electric field, and so fewer of them can rotate as a result of any AC signal added to the DC, resulting in a lower effective dielectric constant and hence lower capacitance.

The effect depends mainly on the magnitude of the electric field.  A capacitor with a low voltage rating has a thinner dielectric, and hence exhibits this drop in capacitance at lower voltages than one with a high voltage rating.  They give an example of a 22µF capacitor with X5R dielectric dropping fairly linearly to about 18µF  (–18%) at 30% of its rated voltage then more steeply to  9µF (–60%) at 80% of its rated voltage.  The effect depends somewhat on which dielectric is used, but they don’t give the details in this survey.  This effect looks like a good reason to use a 3 times higher voltage rating on ceramic capacitors than the voltage you actually plan to use.

They do talk about the rating system for MLCC dielectrics (those mysterious codes like Y5V and X7R).  It turns out that these are talking about the temperature dependence of the dielectric.  The first letter gives the low temperature limit (X=–55˚C, Y=–30˚C, Z=+10˚C), the middle digit gives the upper temperature limit (2=+45˚C, 4=+65˚C, 5=+85˚C, 6=+105˚C, 7=+125˚C, 8=+150˚C, 9=+200˚C), and the last letter gives the capacitance deviation over the temperature range (A=±1%, B=±1.5%, C=±2.2%, D=±3.3%, E=±4.7%, F=±7.5%, P=±10%, R=±15%, S=±22%, T=+22/–33%, U=+22/–56%, V=+22/–82%).  Note: these ratings are for Class 2 and Class 3 dielectrics: Class 1 dielectrics use a different scheme for specifying temperature coefficient,which they also provide (those codes look like C0G or M3K, not starting with X, Y, or Z, and specify a temperature coefficient in PPM/˚C).

So an X7R capacitor has a ±15% variation over a temperature range of –55˚C to +125˚C, while a Y5V has a +22/-82% variation over –30˚C to +85˚C.  Now I see why the TI datasheet for the LM3668 Buck/Boost converter says “Multilayer ceramic capacitors such as X5R or X7R with low ESR [are] a good choice for this as well. These capacitors provide an ideal balance between small size, cost, reliability and performance. Do not use Y5V ceramic capacitors as they have poor dielectric performance over temperature and poor voltage characteristic for a given value.” Apparently, the high temperature dependence also results in high voltage dependence, which could be a real disadvantage in a capacitor used for smoothing out ripple in a DC power supply.

Unfortunately, I’ve forgotten exactly which capacitors I ordered last year, and I don’t have the original packaging.  Based on the price (I bought the cheapest at Digikey), they probably have X7R or X5R dielectrics, which appear to be the popular ones with a good tradeoff between size and performance. These shouldn’t shift much with temperature, but the voltage dependence may still be large enough to explain the effects I’m seeing.

If the problem is indeed the DC bias on the capacitors, then I should be able to control the frequency of the LC oscillator by replacing the ground connection between the capacitors of the Colpitts oscillator with an adjustable voltage source.  I used a potentiometer and a unity-gain buffer to provide a voltage source that was between the 2.5V virtual ground and the 0V power rail.  When the voltage source was at virtual ground, the frequency of the oscillator was 7.4kHz, but when the voltage was –2.44V relative to virtual ground, the frequency was 8.6kHz, a 16% change in frequency or a 26% drop in capacitance.  The change was fairly smooth with the bias voltage and was reversible and repeatable, so I’m reasonably convinced that what I was seeing was indeed a DC bias effect on the capacitors.

I had not been aware that the DC bias effect was so large in ceramic capacitors.

## 2013 June 25

### LC resonance

Filed under: home school — gasstationwithoutpumps @ 20:17
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Since the inductors looked ok in Fitting L and R values, I decided to check the capacitors and the LC tank circuit using the same technique. That is, I put the device under test (DUT) in series with a 100Ω resistor, fed the output of the Bitscope Pocket Analyzer function generator into pair, and measured the RMS voltages across the DUT and across the resistor with a Fluke 8060A multimeter.

This is supposed to be a 4.7µF capacitor, but seems to be a bit low.  It looks like a pretty pure capacitance, though, with no series (0Ω) or parallel (∞Ω) resistance. I only did the full set of measurements for one capacitor, but I checked a few values in the middle of the frequency range for the other, and it seems to have about the same capacitance.

I then made a tank circuit like the one in the Colpitts oscillator, with the AIUR-06-221 inductor in parallel with a pair of the (nominally) 4.7µF capacitors in series.  This should resonate at $\frac{1}{2 \pi \sqrt{LC}}$= 7kHz, with L=220µH and C=2.35µF.

The LC tank resonates at about the expected frequency (7.4kHz instead of 7kHz), but to model the data well, I had to add series resistors for both the inductor and the capacitor.  The series resistor for the inductor seems a little low and the inductance a little high, and the series resistance for the capacitor quite high, but trying to fit four parameters to the rather limited data makes errors like these probable.

It is certainly the case that the LC tank is resonating at the expected frequency, so now all I have to figure out is why the 180˚ phase changes that determine the oscillator frequency and that I measured with an external oscillator (in Colpitts LC oscillator) are not at or near the resonant frequency.

## 2013 June 2

### Nanopore capacitance

Filed under: Uncategorized — gasstationwithoutpumps @ 20:48
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I recently wrote about the noise in nanopores, as a thinking-out-loud exercise to clarify for myself what the noise sources were and what the consequences of changing the concentration of salt ions would be. Today I did another, smaller exercise, thinking about how much capacitance the membrane of a nanopore device has and whether it would have any effect on the measurements.

I was going to try to use the standard parallel-plate capacitance formula, using the area, the separation, and the dielectric constant. The nanopore devices used at UCSC have a lipid bilayer closing a 1 µm hole between the two wells of the device, giving a plate area of about 785E-15 m2, but I don’t know the thickness nor the dielectric constant for the lipid bilayer, both of which undoubtedly depend on what lipid is used.

Since I’m mainly interested in a ballpark estimate, I looked up the capacitance of lipid bilayers on the web and found

O Alvarez and R Latorre
Voltage-dependent capacitance in lipid bilayers made from monolayers.
Biophys J. 1978 January; 21(1): 1–17.
PMCID: PMC1473368

which gives a measurement of capacitance (at 0 volts) of 0.65 to 0.81 µF/(cm)2 for various lipids.  For the nanopore, that would give a capacitance of 5–6fF, far less than the capacitance of the wires connecting to the electrodes in the wells, which are probably in the pF range.  So for practical purposes, we can mostly ignore the capacitance of the lipid bilayer, and regard the nanopore as a variable resistor, with a resistance of about 10GΩ.

## 2013 March 12

### Exploding electrolytic capacitors

Filed under: Circuits course — gasstationwithoutpumps @ 08:58
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Yesterday, during my office hours in the lab, a couple of the students finally did something I’ve been expecting all quarter: blew up an electrolytic capacitor.  Luckily no one was hurt.  The problem was the expected one: hooking up the capacitor backwards.  In this case it was a little more subtle: the capacitor was being used in the low-pass LC filter at the output of their class-D power amplifier, and they had hooked the negative lead up to ground, instead of to their negative power rail.  They actually managed to blow up two of the capacitors (the second much less dramatically) before getting the right power connection.

I looked around on the web to find a good explanation to give the class about electrolytic capacitors (most just say “don’t hook it up backwards” but don’t explain what is really going on)—I thought I knew how the electrolytic capacitors worked, but was not 100% certain, so I was glad to find the following explanation that matched my understanding exactly:

Electrolytic capacitors by Hans Egebo.  The following is just an excerpt from http://www.hans-egebo.dk/Tutorial/electrolytic_capacitors.htm, which has more to say about the capacitors—Hans does make the mistake of claiming that the US uses MF for µF and MMF for pF, but I don’t know any electrical engineers who still use those archaic abbreviations—I’ve seen them in some old books, but I think that the usage went out of style in the 1950s.  I’ve taken the liberty of Americanizing the spelling in the excerpt.

#### So, how to build a large capacitor?

One way to make a large capacitor is to take two long strips of aluminum foil (=large plates), put strips of isolating materials between them, and make a nice compact roll. Capacitors up to around 1µF can be made this way, but they are physically big, so if we want even higher capacity, we need to look for other things than plate area. It happens that we know of a very thin and very voltage resistant type of isolation material: Aluminum oxide. If we cover a strip of aluminum foil with a thin oxide layer, we have one plate and a very thin dielectric. Problem now is to make the other plate come close enough to the other side of the oxide layer. The thing that comes really close to anything is a liquid, so if we submerge our oxide covered plate in a conducting liquid, the liquid forms the other plate, and we can make a very large capacitor. A conducting liquid is called an electrolyte, see?

#### But there are problems

Nothing comes for free, so this type of capacitor has its drawbacks. Some have practical solutions: Instead of having liquid sloshing around inside the capacitor, an electrolyte-soaked paper is used, some modern types are even virtually solid. Others become restraints we have to live with:

The oxide layer is made by an electrolytic process; the foil is submerged in some liquid and current is passed through the liquid into the metal, forming the oxide layer. This is an advantage and a disadvantage: The good news is that the dielectric layer has self-healing capabilities, so if a weak spot occurs, the resulting leakage current will more or less rebuild the isolation. This is the reason electrolytic capacitors can regenerate if you raise the voltage over them slowly. The bad news is that the process is reversible! If you reverse the polarity, even the slightest leakage will begin to tear the dielectric down, resulting in more leakage, which tears away more dielectric, which—well, you get the picture. This is the reason you need to observe polarity strictly when using electrolytic capacitors.

Another problem is the presence of the electrolyte itself: Excess heat, either from inside or outside sources, will eventually start to evaporate the liquid, building up pressure, which may very well result in a violent leak, even an explosion. And as if that was not bad enough, once the electrolyte escapes, it will interact corrosively with other parts of the equipment, because all electrolytic liquids are more or less corrosive.

Finally, even if our electrolytic capacitor escapes a violent demise, its very construction gives it a limited life-span. Given time, the dielectric may deteriorate beyond regeneration, resulting in a high leakage current, or the electrolyte will eventually dry away, reducing the capacity by several orders of magnitude. This is the reason that people who restore antique radios will often be faced with the need to replace electrolytic capacitors.

#### Three sure ways to kill an electrolytic capacitor:

• Overvoltage: If the specified voltage is exceeded, current will leak through the isolation, not in a slow way that might regenerate weak areas, but violently, creating hotspots where additional break-down occurs. The danger of explosion is imminent.
• Reversed polarity: As described, the inverse of regeneration = self destruction, will occur. If the applied voltage is near the normal (right polarity) working voltage, break-down is quick and violent. The effect of a low inverse voltage might be reversible.
• Heat. Heat shortens the life of an electrolytic capacitor. A good rule of thumb is that every 10° C over 85º will cut the life expectancy in half.

Electrolytic capacitors are a very cheap and easy way to get high capacitance, but their somewhat low reliability and limited lifespan have caused problems, particularly if poor manufacturing practices are used in making them.  Almost all computer manufacturers ran into trouble between 2002 and 2007 with improperly made electrolytic capacitors from Taiwan (see the Wikipedia article on “Capacitor plague”) which used the wrong electrolyte.

It is possible to get bipolar electrolytic capacitors (where the aluminum oxide coats both plates) that are not subject to the reversed polarity explosion (though they can still fail due to heat or overvoltage).  Using bipolar electrolytic capacitors in the circuits course would add several dollars to the parts cost, since the larger bipolar ones cost about \$1 each, and would not reflect normal practice, as bipolar electrolytic capacitors make up only about 1% of the electrolytic capacitor market (based on the number of parts listed at DigiKey).