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| Elliott Sound Products | Part 2 - Passive Power Factor Correction |
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If you haven't done so already, please read Part 1 of this series first. There are many basic concepts that you need to understand, and it would be silly to repeat the information. There will be some duplications, but only as needed to make sure that what you read here makes sense.
Although vastly inferior to active power factor correction (PFC), passive systems are still used in some cases. The passive approach has the advantage of simplicity, but is often comparatively large and heavy, and cannot approach the performance of an active PFC scheme. One advantage of a passive correction scheme is that it is may not be necessary to add extra EMI (electromagnetic interference) components, although that depends on the method used and/or the quality of the PFC inductor.
I have discussed active PFC in Part 3, and passive PFC has also been mentioned elsewhere on the ESP site. Off-line switchmode power supplies (SMPS) have been with us for many years now, with the best known example being the standard computer power supply. For a long time, these have presented an awful load to the mains supply, drawing current only briefly at the very peak of the AC mains waveform. This applies to both desktop and portable PCs, as well as many other external supplies used in their millions worldwide. Off-line means that the power supply circuit has a direct connection to the AC mains without an intervening transformer.
There is another form of PFC known as passive power factor correction. While simple to implement, it is no longer cost effective when compared to active systems. It's difficult to achieve a PF better than about 0.7 but it's still useful for low power applications. In all of the great many lighting power supplies I've looked at over the past few years, I've not seen a single example of passive PFC, other than the valley-fill circuit explained below. For LED tube lights, it may be included 'accidentally' if the fluorescent ballast is left in circuit, but since most now have active PFC this is redundant.
This article only discusses the basic PFC circuits. There are many enhancements that can be made if the cost is justified, including harmonic traps and series and parallel resonant filters. These are seriously expensive to implement, and will not be found in any consumer goods. For a large, high power machine, the additional cost becomes very small compared to the cost of the machine itself and (perhaps more importantly) the on-going costs incurred because of the otherwise poor power factor.
Resonant filters can become very expensive, largely because of because the amount of capacitance needed. For example, 100mH and 100uF is resonant at 50Hz (close enough), but 100uF of capacitance rated for 275V AC (single phase use only) is a physically large and costly component. In some configurations, the capacitor and inductor will also have to carry a significant current, and this demands much larger (and more expensive) parts.
In all the cases shown below, the mains voltage is 230V AC at 50Hz. There is a resistor of 0.8Ω in series with the supply, which is roughly the impedance of the mains wiring to an average house. I made no attempt to emulate the normal 'flat-topped' voltage waveform in these simulations, because the extra distortion makes current waveform distortion measurements meaningless.
There are many different ways that passive PFC can be incorporated, but only a few are common enough to warrant discussion. The correction scheme depends heavily on the load, the type of equipment and customer expectations. For an industrial power supply, reliability and performance are the most important, with cost and size/weight somewhere lower on the scale. For any consumer item, cost and size/weight are the common driving factors, with reliability below that and performance well down the list. This will occur because most consumers have no idea what constitutes 'good performance' regarding power factor, so the design will be sufficient to meet applicable standards but no more.
It's informative to have another look at a capacitor input supply, this time with all values scaled to those used for the other examples shown. In particular, look at the current waveform and power factor. The power delivered to the load is higher for this circuit than any of the others, simply because the rectified DC voltage is higher because there are no in-line impedances to limit the current.
Figure 1 - Capacitor Input Filter Power Supply
The current peaks of 6.5A cause considerable stress on the power supply, especially the diodes and the filter capacitor. The capacitor ripple current is a little over 1.8A RMS, which is a rather tall order for any electrolytic capacitor. Even the tiny 0.8Ω mains wiring resistance manages to dissipate over 3W, and this is wasted power. Note, too, that the RMS input current is a great deal higher than you'd expect for a 200W (nominal) power supply. In a perfect world, input current would be less than half that shown, and the peak current would only be 1.3A instead of 6.5A.
Figure 2 - Capacitor Input Filter Current Waveform
The above circuit and waveform is the base-line against which the alternatives may be compared. For low power applications (below 50W) this arrangement is still very common, but as worldwide regulations start to impose greater restrictions on waveform distortion (harmonic generation) and power factor, it will eventually disappear for all but the lowest power devices. In a few years at most, I'd expect that simple capacitor input filters will not be permitted for anything above ~10W or so.
For low power applications, there's a rectifier circuit known as a 'valley-fill' rectifier. It's simple to implement, but is only suitable where a very high effective ripple voltage on the DC output can be tolerated. This limits its usefulness, but it is found in some low-end LED lighting circuits, and is also suitable for some CFLs and similar lighting products where the high ripple voltage is not likely to cause a problem.
The power factor improvement is much greater than one might expect, and a PF of a little over 0.7 is typical. The current waveform is still quite distorted though, and it's unrealistic to expect too much from such a simple circuit. THD measured 82% in the simulation of the circuit shown. While hardly anything to crow about, it's still better than having over 150% distortion or more.
Figure 3 - Valley-Fill Power Factor Correction
Essentially, the two capacitors are charged in series, but discharged in parallel. This means that when the peak of the applied AC falls, so too does the output voltage, until it reaches a voltage that's roughly half the AC peak (162V less a few diode voltage drops) and is actually the voltage across the capacitors in parallel. The output 'DC' therefore has half the applied voltage of ripple - 158V peak-peak in the circuit shown. As you can imagine, the applications for any rectifier/filter with this much ripple are limited.
It's interesting to see the current waveform, and it is shown below. The 2.2 ohm resistor helps to reduce the sharp peaks that sit on the top of the waveform. Higher values reduce the peaks more and reduce distortion, but result in higher power dissipation in the resistor, wasted power and less power to the load. While it might seem that adding a small inductor (say 10mH) instead of the resistor would be able to eliminate the spike on top of the waveform, it's not as effective as one would hope. The added cost and bulk isn't worth the small gain obtained.
Figure 4 - Valley-Fill PFC Current Waveform
If examined closely in a simulation (it's not shown here for clarity), the 'DC' voltage varies from 158 to about 318V - that's a lot of ripple. The mains current waveform looks pretty bad, but it's much, much better than that shown for the standard rectifier and capacitor supply. The power factor is far better than expected, and although there are still some significant harmonics (which result from the distorted waveform), THD is far better than the previous version as well.
As noted though, this type of supply is only suitable where the high ripple is tolerable, and you won't find it used much any more. It's basically an idea that came too late, because cheap PFC ICs that are a great deal better in all respects came along only a short while after this circuit was first used. Until I started working with LED tube lights, I'd never seen it before, and now, only a few years later, I don't see it used in any of the new designs. The latest LED lamps are now using active PFC which is far better than any form of passive PFC can hope to be.
The next version is interesting. It's not especially good, but doesn't have the extremely high peaks of a standard capacitor input filter. It has the advantage of only needing a fairly small inductor, but still requires the addition of another diode and capacitor. It does have one significant potential point of failure though!
Figure 5 - LCD (Inductor/ Capacitor/ Diode) Power Factor Correction
The first electrolytic capacitor is the most likely to fail in this circuit, because it has a high ripple current. With the values shown above, the ripple current is over 1.36A RMS, and that's a very big ask for a low value electrolytic cap with limited surface area to radiate heat. If you look at data sheets, you'll see that the maximum RMS ripple current for a 22uF 400V electro is around 760mA, but that has to be derated for low frequencies. The derating factor can be as much as 0.3 for 100-120Hz ripple, meaning that the maximum ripple current is only around 228mA [6]. Long-term survival is unlikely unless the expected output power is reduced significantly.
Figure 6 - LCD (Inductor/ Capacitor/ Diode) Current Waveform
The current waveform looks pretty bad, but THD is below 100%. I know it seems strange to imagine that over 90% distortion is 'good', but this is one of the many limitations of passive PFC. Small value parts just don't work well, and it's a constant battle to get performance that's acceptable. This isn't a circuit that I've seen used in any commercial product so far, but it does exist and there is quite a lot of information on the Net if you care to find out more.
Although you might imagine that having the inductor on the AC or DC side of the rectifier bridge would give entirely different performance, this is only partly true. Steady-state performance (some time after the circuit has been powered up) is virtually identical, other than the differences shown below. In particular, the current waveform is very similar, with only a couple of relatively minor changes.
Figure 7 - AC Inductor Power Factor Correction
By placing an inductor in the AC before the bridge, we introduce a low-pass filter. High order harmonics are progressively attenuated, and the current waveform has no sharp discontinuities. The results are not wonderful, but are certainly far better than we get with no inductor at all. Unfortunately, the inductor needed is a fairly bulky component, and is not inexpensive.
By placing the inductor on the DC side of the rectifier bridge, the result is similar to the 'choke input filter' that was sometimes used in the valve era. While it might seem that it would behave very differently, that's actually not the case. As you can see from the waveforms below, the results are almost identical. There are disadvantages to both arrangements.
Figure 8 - DC Inductor Power Factor Correction
This scheme has been used in PC (personal computer) power supplies for some time, although up until recently it was only found in the 'better' versions. It's reasonable to expect that passive PFC for PC power supplies will disappear in the not-too-distant future because active PFC is so much better and the cost penalty is disappearing rapidly.
Figure 9 - AC Inductor (Red) & DC Inductor (Green) Current Waveforms
When the inductor is on the AC side of the bridge rectifier, there is some ringing between the inductor and any EMI filter capacitor that's used (visible as a broad waveform around 0V - red trace). If there is no capacitor, the inductor will ring at its self-resonant frequency. This is much higher than the frequency obtained with a capacitor - possibly high enough to cause EMI compliance issues. With the values shown, the ringing frequency is 1.59kHz. On the positive side, the inductor carries no DC, so core saturation is easier to avoid without making the inductor any larger than necessary.
Placing the inductor on the DC side of the bridge means that it has a substantial average DC current, so it will normally be a bit bigger than the AC version. While there is no ringing, the characteristic DC level peak at switch-on can be pronounced. This is a phenomenon where the inductor and filter capacitor create a low frequency resonant circuit. With the values in Figure 8, this is around 23.2Hz. The DC response at power-on is shown below.
Figure 10 - Power-On Voltage Surge, Choke Input Filter
Note that the voltage peak shown occurs with the full 470 ohm load connected. The load doesn't change the peak voltage, but it does decay faster with heavier loading. This reaction is extremely common with choke-input filters, but was never an issue with valve rectifiers because their conduction is zero when power is applied, and starts slowly as the heaters come up to temperature. The peaking effect has always been a problem with semiconductor diodes used with a choke input filter. Changing values around doesn't help very much.
For example, with a 10H inductor and 47uF cap, the peak voltage is reduced to 240V DC, but the steady state voltage is then much lower too. The 'rule of thumb' for choke-input filters is that DC output is 0.9 times the AC voltage, and in this case the simulation shows 205V DC which is pretty close. An unexpected and rarely reported effect of a choke input filter (using a large inductor/ choke) is that the input current is a squarewave! The power factor with a sinewave voltage and squarewave current is around 0.9 - unlikely though that may seem.
When the inductor is sufficiently large (but much too large for any commercial product), the inductor current is continuous, which is to say that it never falls to zero. Under this condition, inductor current is a squarewave as noted above. Smaller inductors provide 'discontinuous mode' operation, where inductor current falls to zero for each AC half-cycle. To achieve continuous mode in the Figure 9 circuit requires an inductor over 1H, along with a smaller filter capacitor. To achieve good results requires a larger inductor, with around 10H being optimum for the load shown - the filter cap can be reduced to as low as 4.7uF. In fact, the capacitor become almost irrelevant, and even reducing it to 47nF only increases the ripple voltage by about 3dB (compared to the ripple with 4.7uF).
Needless to say, no-one is going to install a 10H inductor into any product if it can be avoided, because it will be huge, very heavy and extremely expensive. If you wanted to get rid of the peak completely, the inductor has to be even larger than 10H - 22H with a 10uF filter cap gives a smooth voltage rise with no peaking, but no-one is going to install a choke that big! Even with such a small cap, the DC voltage and ripple are exactly the same as with the small choke and large capacitor.
As it turns out, steady state DC voltage and ripple are virtually identical, regardless of where the inductor is placed. To avoid the high peak voltage, it is preferable to have the inductor in the AC line, not in the DC supply - unless you like the idea of a massive inductor of course. While some circuits won't be bothered by the voltage 'surge' with inductors of a manageable size, it requires that switching transistors/MOSFETs have a higher voltage rating than strictly necessary. Since overall performance is much the same anyway, there is no sensible reason to have the inductor in the DC supply.
Don't expect to find harmonic filters in any consumer product. This is the sole territory of industrial equipment that has to meet specifications, standards, and customer expectations. Cost is always important, but no sensible buyer will purchase equipment that saves a few (hundred, thousand?) bucks at the time, but costs far more to operate than the alternative. Both line frequency and harmonic filters essentially have to be designed for the job - there are no off-the-shelf modules that you can add as needed. Filter circuits can be very effective, but may be quite intolerant of load variations and/ or have poor transient response. They are usually unaffected by noise, and do not rely on high frequency switching so don't cause any EMI problems.
Harmonic filters can be in-line, or designed as harmonic 'traps', where the harmonic current is dissipated in suitably sized resistors. For 50Hz mains, typical filter frequencies would be 150Hz, 250Hz and 350Hz (3rd, 5th and 7th harmonic respectively). Naturally these are different for 60Hz. Harmonic traps will use a series resonant circuit, that is effectively a short circuit for the tuned frequency. By dissipating the harmonic energy in resistors, it is removed from the mains supply. These filters have to be extraordinarily robust - we are used to equipment that draws a few amps up to perhaps 20A or so, but industrial equipment can be rated for hundreds of kilowatts. The currents and voltages involved are very high, and will easily destroy anything that isn't rated for continuous duty at the power levels encountered.
I do not propose to go into any detail of resonant filters or harmonic traps. This is not the kind of thing that 99.99% of readers will ever be involved with, and it's hardly a topic for DIY. Suffice to say that both energy suppliers and their larger customers will go to extreme lengths to protect their infrastructure and the quality of the supply.
There is a way to create a high power factor rectifier that is the basis for nearly all current active PFC circuits. The basic circuit is shown below, and simply involves removal of the filter capacitor. The rectified DC has 100% ripple, so any circuit that follows has to be able to deal with that and behave just like a resistive load.
Figure 11 - High PF Rectifier
The above circuit is almost perfect. No current waveform is shown because it just looks like a sinewave, and of course it's perfectly in phase with the voltage. The power factor is shown as 0.99 so that it's in line with the others on this page, but it's really 0.998 - so close to unity that it's of no consequence. Distortion is only 0.35%. All we need to do now is add circuitry that can cope with the huge amount of ripple, and draw current that is exactly proportional to the voltage.
This is the basis of active PFC - circuitry designed to act like a resistive load as closely as possible. It must be able to provide a stable DC output - regardless of input voltage - that can be used by a conventional DC-DC converter to change the voltage to that needed by the load. Sounds simple if you say it quickly enough. 
Although the days of passive PFC may be numbered for low-medium power applications, it's expected that some industrial applications will have power demands that simply cannot be met economically (and reliably) by active systems. Understanding the basic principles goes a long way to help people make informed choices, or at least to realise why a particular piece of kit has selected one form of PFC over the other.
I hope that this article has provided the reader with some insight into the workings of passive PF corrected power supplies. While the circuitry appears very simple, the design of an effective correction system is actually very complex. Everything interacts with everything else, and the laws of 'unexpected consequences' cannot be ignored. No, I'm not sure how anyone can expect the unexpected in a useful way.
Just deciding where to place a PFC inductor has some potentially serious implications, as shown in this article. If you are unaware of the power-on voltage-boost phenomenon with a DC choke input filter, it's very easy to destroy the switching power supply due to the over-voltage condition, and it's likely that additional circuitry will be needed to prevent it from causing a problem.
One area that I didn't cover here is inrush current ... you can find out more by reading the article. This is also something that causes many problems, and these also fall into the 'unexpected' category. While traditional loads (such as incandescent lamps) may have an inrush current of 10 times the normal operating current, a switchmode power supply (with or without PFC) can draw an inrush current of 50-100 times the running current.
I have direct experience with this problem, and I've had to advise installers of the need to limit the number of devices on a single circuit breaker, and/or to use a so-called 'D-Curve' breaker that imposes a delay long enough to allow high starting-current devices to start. Fortunately, my lab setup is such that I can test and record measurements of waveform distortion, harmonics, inrush current (I had to design and build my own tester for that) and many other things that savvy customers want to know before purchase.
So, that finishes Part 2 of this series. You can now have a look at Part 3, which explains how active PFC works. Active power factor correction is here to stay, and it will only get better as IC designers refine their circuits even further. In the 5 years or so that I've been looking at PFC power supplies (primarily for LED lighting products), I have seen dramatic improvements, and they just keep getting better.
See 'Further Reading' below for some in-depth material.
Part 1 - PFC Introduction
Part 3 - Active PFCFurther reading ...
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