In physics, the dissipation factor (DF) is a measure of loss-rate of energy of a mode of oscillation (mechanical, electrical, or electromechanical) in a dissipative system. It is the reciprocal of quality factor, which represents the "quality" or durability of oscillation. Electrical potential energy is dissipated in all dielectric materials, usually in the form of heat. In a capacitor made of a dielectric placed between conductors, the typical lumped element model includes a lossless ideal capacitor in series with a resistor termed the equivalent series resistance (ESR) as shown below.[1] The ESR represents losses in the capacitor. In a good capacitor the ESR is very small, and in a poor capacitor the ESR is large. However, ESR is sometimes a minimum value to be required. Note that the ESR is not simply the resistance that would be measured across a capacitor by an ohmmeter. The ESR is a derived quantity with physical origins in both the dielectric's conduction electrons and dipole relaxation phenomena.

In dielectric only one of either the conduction electrons or the dipole relaxation typically dominates loss.[2] For the case of the conduction electrons being the dominant loss, then If the capacitor is used in an AC circuit, the dissipation factor due to the non-ideal capacitor is expressed as the ratio of the resistive power loss in the ESR to the reactive power oscillating in the capacitor, or When representing the electrical circuit parameters as vectors in a complex plane, known as phasors, a capacitor's dissipation factor is equal to the tangent of the angle between the capacitor's impedance vector and the negative reactive axis, as shown in the diagram to the right. This gives rise to the parameter known as the loss tangent δ where Since the DF in a good capacitor is usually small, δ ~ DF, and DF is often expressed as a percentage. DF approximates to the power factor when is far less than , which is usually the case. DF will vary depending on the dielectric material and the frequency of the electrical signals.

In low dielectric constant (low-k), temperature compensating ceramics, DF of 0.1% to 0.2% is typical. In high dielectric constant ceramics, DF can be 1% to 2%. However, lower DF is usually an indication of quality capacitors when comparing similar dielectric material. ^ S. Ramo, J.R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics, 3rd ed., (John Wiley and Sons, New York, 1994). I recently found an easy and cheap way to test ESR (Equivalent Series Resistance) of electrolytic capacitors, in circuit, that might save some people a lot of time. It requires only an oscillosope and a simple signal generator. I had an oscilloscope that I was trying to repair (Intensity control had little effect. Horiz sweep was only halfway across screen at higher freqs. One power supply rail was too low and others were too high.) and I had already checked every electrolytic capacitor in several/many different ways (all in-circuit), and even compared each of the readings to those from an identical unit: Powered off: Looked at signature from component tester (single-curve tracer) across each cap, and from each end of cap to ground, did resistance check with DMM, did capacitance check with DMM, checked resistance from each end of cap to ground.

Powered on: Put scope across each cap, and scope from each end of cap to ground, used DMM and measured DC and AC voltages across each cap and from each end of cap to ground. ac unit for 2500 sq ft homeI did find some bad caps (and some other bad components) and replaced them. carrier hvac air handling unitsBut the problems were still there!goodman ac unit model numbers I had been wanting to order an ESR meter, but hadn't done it yet, and needed to get this scope repaired immediately. / and found a GREAT method for testing ESR of capacitors in-circuit that requires only a signal generator and an oscilloscope (and some cables), and had found and fixed the problem within about ten minutes!! Here's what I did (This technique is basically directly from Sam's repair faq site):

I used a signal generator and an oscilloscope to set up what I now call an "ESR Scope": At the output of the generator, I connected a BNC "tee" adapter. I ran one 50 Ohm BNC cable from the tee to a good (Tek 2465A) scope (with a 50-ohm BNC terminator on the scope input). On the other side of the tee, I connected another BNC cable that had alligator clips on its other end (It might have been a 75 ohm cable; shouldn't matter too much?), which I clipped onto the banana plugs of a set of cheap DMM-type probes. (Terminator note: I used a Tektronix 50 Ohm "pass-through" terminator, on the scope end of the BNC cable. But, you should also be able to use, instead, another BNC "tee" on the scope input, with an "endcap" terminator on one side and the cable coming in on the other side of the tee. A standard 10BaseT Ethernet 50 Ohm coax terminator (and 50 Ohm Ethernet BNC coax cables) should work fine. And they're available at Radio Shack, and probably Staples, et al.) I set up the signal generator to produce square waves at about 100 kHz, with about 100 mv peak-to-peak amplitude as seen on the attached scope, and no DC offset (A simple 555 timer circuit would do the job, too!).

Then, I turned the scope's v/div to 5 mv/div, with time/div at 1 microsec, with AC coupling of the input. Shorting the probes together gave me a display on the scope that was about one division high. It was basically a square wave, with large narrow peaks at each leading edge. But I only looked at the horizontal part's p-p amplitude. That's the whole setup! Just cables (and a terminator). I did also try it with a decade resistor box in series with the probes, just to see what it would look like. I could clearly see each one-ohm increase, on the scope display, with the probes shorted together as well as with the probes across a good electrolytic capacitor. When I applied the probes across a GOOD capacitor in-circuit, there was little, if any, change in the scope display, compared to when the probes were shorted (since, depending on the frequency, a capacitor should look more-or-less like a short circuit, to AC). But, when I tried it across a BAD capacitor, usually the display would be almost-totally off the screen.

And, there were some caps that looked marginal, making the display go from about one div p-p up to about 3 to 5 divs (which probably corresponded with somewhere between 5 ohms and 20 ohms of ESR, if I recall correctly.) Anyway, within just a few minutes I had found one more bad electrolytic filter cap in the power supply, two smaller bad electrolytics in the P.S., a bad one on the horizontal sweep switch's board, four bad ones near the middle of the main board, and a couple more that I can't remember right now. I made a note of each one. When I was all done checking, the first thing I did was replace the filter cap in the power supply, and then power it on and check the power supply rails' voltages. They were all normal again! Not only that, but the horizontal sweep problem and the Intensity control problem were both GONE!! That filter cap had checked out as perfectly OK, using every one of the other methods that I described above (all were "in-circuit", though), and compared OK to the other identical scope's same cap, in all of those cases.

But with this "ESR Scope" method, it was totally obvious, immediately. And the same cap on the other scope tested good, with this method (So, the earlier comparisons WERE bad cap vs. good cap, but showed nothing!). [I also noted that after the bad cap was removed, it tested bad in the same way that it had while it was in-circuit, with a basically identical scope display. And all of the other ones that I replaced also tested bad, when OUT of the circuit, even with the other methods.] This " ESR Scope " method isn't a perfect panacea, of course: There were some cases where, without an identical unit to compare to, the displays would have been difficult for me to interpet, and possibly misleading. (However, it *always* worked with every *electrolytic* that I tried it on, IIRC, from 10 uF 10v to at least 1000 uF 100v, with no need for an identical unit to compare to.) But, then again, I haven't played around with it enough, yet, either. I assume that adjusting the frequency for different capacitances might be helpful, especially if non-electrolytics were to be tested.