# PWM in a switching power supply

• posted

Hi,

First of all, I'm trying to figure out how switching power supplies work (the ones in PCs). I've found very basic info, but I want more technical stuff. If anyone has some good links please let me know. These are questions I have yet to find an answer for.

Anyway, here's my question. One thing I read was that the output voltage of the supply is fed back to the PWM which changes it's duty cycle accordingly to keep the output voltage constant. But I thought that the input-to-output ratio of a transformer is fixed. If the PWM is outputting 100V at 20KHz to a 10:1 transformer, you get out 10V at

20KHz, right? What does it matter what the duty cycle is? It's still 100V at 20KHz. What am I missing?

Second, why does a switching power supply break without a load?

Third, in all my years in electronics, I have never used a choke, now I see them all over these power supplies. Can someone clue me in about what they do, and why they are in these things?

I appreciate any info at all. Thanks a lot.

• posted

Yes, the _instantaneous_ output voltage of the transformer is still 10V.

The output of the transformer is feed to some form of filtering -- usually a series inductor and parallel capacitor -- and the output voltage then found across the capacitor is the _average_ of the input voltage. So... 10V instantaneous output from the transformer at 100% duty cycle gets you 10V across the capacitor... 50% duty cycle would get you 10V instantaneous output from the transformer for half the time and 0V for the other half of the time, so this averages to 5V across the capacitor... etc...

(This is somewhat simplified; in actuality the voltage change a little due to diode drops, active device losses, etc. -- the feedback loops jiggles the duty cycle until the right regulated output voltage appears, though.)

Because the designers are either (1) ignorant or (2) cheap. :-)

OK, actually, not all switchers have no-load problems. What happens -- and this is for the most basic example you could come up with, something like a simple buck converter -- is that during the time that the transformer (or inductor) is being fed current, flux (current) builds up in it. When the switch controlling this current is turned off, the current (flux) in the core starts dropping. The rate at which it drops is proportional to the load... bigger load (lower impedance), faster current drop. With a "big enough" load, the current goes all the way to zero. On the next switching cycle, the current ramps up again to some current, then ramps down to zero, etc. -- this repeats forever.

Now, with a small load, while the current does drop, it doesn't go all the way to zero before the next switching cycle. Now current ramps up again and -- if one isn't careful in design -- the current ends up higher than it was at the turn-off point of the last cycle. It drops a little again (but not to zero), and now at the next turn on the current is driven even higher. Sooner or later, the inductor saturates, which tends to look almost (but not quite) like a short circuit to the driver. That driver starts having massive current run through it, heats up, and sooner or later dies.

Hence, there's some minimum load that causes the switcher to change from discontinuous to a continuous mode of operation, and for loads lighter than this you can get into trouble.

If you think about it for a moment, it's clear you could simply detect the current in the core and quit driving it when you start to approach saturation -- this simple solution is what "current mode" switchers do, and they usually don't have no-load problems. In fact, if you think about it even more, even in the case with regular "voltage mode" feedback, since the current in the core is increasing, the output voltage will as well, so the feedback regulator should keep clamping down on the duty cycle so as to avoid saturating the core. The problem here is that the 'transfer function' of the power supply from input to output is different when it's operating in this 'continuous' mode rather than 'discontinuous' mode, and it takes more effort to build a feedback network that can keep the entire 'loop' stable in both modes (and without starting to become slightly sophisticated in your feedback network, making a power supply no-load stable often degrades the step response, which isn't desirable). Hence, for both the sake of cost (the extra feedback network circuitry) or merely ignorance on the part of the designer, some power supplies turn over and die when run without a minimum load.

Ummm... you know what capacitors do, right? You 'feed' them a current and this causes charge to accumulate within them such that a voltage appears across them? Inductors are their 'dual' -- you 'feed' them a voltage and this causes flux to accumulate within them such that a current flows throughout them. Hence, just like a capacitor, inductors can be used to store energy. With an inductor, by varying the duty cycle of a voltage across it, you can 'charge up' the inductor to some arbitrary average current and then 'dump' this into a load to get a corresponding voltage. This makes it easy to make regulated _voltage_ power supplies, whereas a similar approach with capacitors would get you a regulated _current_ power supply.

I'd suggest checking out Abraham Pressman's switching power supply book. It's not cheap, but it's written by a guy who seemed far more intent on building working power supplies than doing more theoretical research. It does of course have some math in it, but even someone with one semester of caclulus will probalby be able to follow it.

---Joel

• posted

W_Tom,

Uh, no, it doesn't! If I give you a periodic signal of a certain frequency, it doesn't matter WHAT it 'looks' like, its Fourier spectrum will ONLY contain the fundamental frequency and harmonics. Changing what it 'looks' like (e.g., the duty cycle of a square wave) only changes the magnitudes of the harmonics.

Overall most switchers lose far more efficiency in the switches than they do in the core.

Some do. :-) Although you could convince me that such switchers are, by definition, poorly designed.

Where do you get this stuff? Some generic "everything you wanted to know about electronics" encyclopedia? A lot of what you say is factually correct, just not at all relevant to the discussion at hand.

Someone who's an expert at filter design could very well not know the first thing about switcher design. They're pretty disparate areas of design, and really only start to overlap somewhat when you discuss output filtering, resonant designs, etc.

• posted

OK, I got it, the output is filtered to create a stable voltage that is the average of the duty cycle. But now I'm wondering, what is the purpose of the transformer? If you want to convert 100V to 10V, why not filter the output straight from a PWM with a 10% duty cycle? What's the difference?

Thanks a lot.

• posted

Duty cycle changes the energy of frequencies (sine waves of different frequencies) that, together, form a square wave. Learn about Fourier series (from math books) to better appreicate the concept. As duty cycles change, then more energy may appear in a higher frequency sine wave. Those higher frequencies dissipate more energy in the transformer. Best to have only a frequency at the ideal transformer frequency. But then duty cycle would not change to adjust output voltage. Less efficiency for better voltage regulation. This and other compromises are why the switching power supply cannot have 100% efficiency.

Unloaded switching power supplies do not break. Some switching power supplies do not operate well in a no load condition; so power supply shuts down without damage. Characteristics of each design. Important is even how the transfomer is designed. Numerous design compromises are involved. Many switching power supplies work just fine under no load. Which ones? The long list of numeric specs should be provided for each switching power supply model.

Chokes permit energy at some frequency to be c> First of all, I'm trying to figure out how switching power supplies

• posted

If the transformer is a voltage output (produces some ratio of the primary voltage when the switches are on) and zero the rest of the time), then, yes, the peak output voltage is essentially independent of the duty cycle. but those kind of transformers also require an additional LC filter that outputs a voltage about equal to the average input voltage, not the peak. Holding the peak voltage for a smaller part of the cycle lowers the average voltage.

In supplies, where the transformer acts as an energy storage device (apply input voltage, till the primary current ramps up to some value, then cut the primary current, forcing the stored energy to reverse the winding voltage and go up till an output rectifier connects the transformer secondary to some storage capacitor). the average energy throughput depends on how high the energy each charge-discharge cycle, and how many cycles per second, and if the stored energy is all dumped each cycle, or only some of it (whether or not the primary switch is left off till the transformer dumps all its magnetic energy, or is turned back on while the dump is in progress).

Break? As in Kablooie? I don't know about that, but many malfunction, because the control loop gain is dependent on the load current. That is, the gain goes up as the load decreases. Stability requires that the loop gain fall as frequency rises, so that before the frequency is reached where the loop phase shift swings by 180 degrees (compared to low frequencies) the gain has fallen below 1, so that the negative feedback (converted to positive feedback by the extra phase shift) cannot generate a self sustaining echo.

There are just inductors. They store energy proportional to the inductance and proportional to the square of the current passing through them. Once you get up into significant currents, they become as useful and necessary for energy storage as capacitors. Whereas capacitors pass current in order to control the rate of change of their voltage, inductors generate voltage across them to control the rate of change of the current through them. If you want to absorb current pulses and stabilize voltage, you use a capacitor. If you want to absorb voltage pulses and stabilize a current, you use an inductor. And we are back to that averaging filter that is needed to smooth out the current from that pulsing voltage, variable duty cycle, constant peak voltage rectified transformer so that it can be connected to a storage capacitor where the voltage is to be regulated.

• posted

A switching power supply could easily provide those voltages without the expensive transformer. But a power supply must also perform many other functions including galvanic isolation. For computers, this breakdown voltage must exceed

1000 volts. Therefore the transformer (to send power to the load) and the feedback circuit (to regulate output voltage and other functi> OK, I got it, the output is filtered to create a stable voltage that is
• posted

That's correct and consistent with what I had posted. Those harmonics are the different frequencies. As those harmonics increase magnitude (contain more energy), then the transformer is confronted by other frequencies with more power. As noted earlier, this can cause increased energy dissipation in the transformer and elsewhere.

Meanwhile I did not even try to say where most energy is lost. Why do criticize me for something that was not even posted? To argue semantics?

An unloaded power supply must not be damaged by no load. Any power supply that is damaged by a no load condition is typical of something bought by a bean counter - the enemy of innovators, responsible manufacturers, and those educated in computer electronics. No load must not damage a properly designed switching power supply.

So what? That is not what I said and is completely irrelevant to what I did say. A filter expert need not know anything about switching power supplies. But a power supply designer better damn well understand the principles of filter design. Why does Joel read reverse logic into a post? Why post what is both irrelevant and not even stated? Joel is arguing semantics rather than trying to help or answer the OP. Don't let him confuse you.

• posted

if you very the duty cycle alway from 50%, you get an un-even charge and discharge in the coils of the transformer. this interaction produces is low output on the secondary. its gets much deeper than that, but it's just a simple starter for you to think about. just think of charging a cap for 10 secs, but only let it discharge for 1 sec. you will see that the charging current duration is very short after the first initial charge.

• posted

high freq is much easier to filter, uses much smaller caps.. also using a switching supply allows you to put the driving components in saturation or even used things like Power fets to put the path in near 0 ohm thus generating very little heat and making the power efficiency much higher and smaller components.

• posted

Energy is passing from transformer to filter only during the "on" part of the duty cycle, The larger the % on time, the lower peak energy that must pass during the peak to satisfy the average energy flow.

You could also move an automobile by setting sticks of dynamite off behind it a small percentage of the time, but the peak forces would have to be pretty high to make up for the average force needed to keep the car moving. The windings in the transformer and the switch on the primary side are also affected by the peak verses average energy flow. For this reason, one normally wants to have the duty cycle just hit 100% at full output load and minimum input voltage, to keep the minimum duty cycle under other conditions as high as possible.

Good question.

• posted

There are excellent resources for switching power supplies at all the major manufacturers (TI, Linear Tech, Maxim and others).

One of my favourite design notes is from Linear Tech:

(AN-73 [pdf] at

should the link not work). This shows the basic principle of the Switchmode power supply using a specific device as an example, with the coil used as (as noted) an energy storage device.

As to why some switching power supplies 'break' with no load, I would agree it could be poor design, although to be fair to the designers they may be designed for a specific load. Much depends on the specifics of the type : Topologies: Buck (Step down) Boost (Step up) Buck-boost (inverting, usually) SEPIC (step up and step down - for isntance, generate +5V from a nominal 6V battery that may have an actual range of 4V to 7V)

Mode: Current. Inductor (or switch) current is controlled directly Voltage. Output voltage is controlled directly Generally, current mode controllers are insensitive to *input voltage* variations and voltage mode controllers are insensitive to *output current* variations.

A switching power supply (actually, any regulated power supply) is a closed loop system that has various (and numerous) filter elements in the loop. To get regulation employs negative feedback (i.e. an output variation causes a change at the input such as to [partially] negate the output variation).

What makes negative feedback negative is the effective phase of the feedback signal. The filters in the loop add their own phase characteristics, and if not carefully considered cause sufficient phase shift in the loop to make the negative feedback positive - giving an oscillator if it happens at unity gain. This is one of the [many possible] things that can happen at no load.

Feedback loops of this type have many analogies - the most basic principles are found in servo theory. For an excellent app note on loop compensation (the art of keeping negative feedback negative) for a current mode controller, see

(AN-76, once more from
) For the filters, the relevant equations

Capacitive filters: Fx = 1/(2*pi*R*C) where R is the equivalent resistance of the ffilter and Fx is the Frequency at which the difference between input and output is 3dB, which is also the point at which the phase difference between input and output is 45 degrees. The phase and relative amplitudes may be either leading or lagging depending on the filter configuration (a leading phase filter is known as a zero, a lagging phase filter is known as a pole)

Forr voltage mode controllers, there is a 2-pole filter at the output, given by 1/(2*pi* [sqr(LC)]) where L is the output inductor and C the effective output capacitance. At this frequency, there is 180 degrees of phase shift at the output.

Each pole (or zero) has a phase response of 45 degrees per decade, and an amplitude response of 20dB per decade (alternatively, 6dB per octave). (Note to others - I realise the filters may be -45 or +45 and amplitude response could be rising or falling)

So there's a lot of terminolgy and a lot of fundamentals to learn to understand these things. I think there's plenty of reading noted here to be getting on with if you want to understand the subject :)

Cheers

PeteS

• posted

Peter discusses (among many good points) the feedback circuit in switching power supplies.

A power supply failed repeatedly in the field (I later learned was also failing in the shop; but the failure was ignored). The feedback optocoupler required a gain of 150. I also learned that finding gains of 150 was all but impossible. So the bean counters installed a lower gain optocoupler. Therefore the power supply would sometimes - rarely - but sometimes not power up and sometimes just shutdown arbitrarily. IOW the power supply was 100% defective

- but was shipped because it usually passed tests. With insufficient feedback, it was unstable - failed intermittently. Cost thousands of dollars to replace that defectively manufactured power supply.

Power supplies break for many reasons. This manufacturer blamed insufficient load to avoid admitting the real problem. I'll never forget nor forgive that company. They tried to claim it was due to insufficient load when even their own spec sheets said that load was sufficient.

Feedback is a concept taught in control systems. Like filter design, the power supply designer must also have fundamental comprehension of feedback control loops.

The user need not understand these technical issues. This is where manufacturer spec sheets, manufacturer reputati> There are excellent resources for switching power supplies at all the

• posted

Awesome! That really answered my question. Thanks for all the help guys, and the links!

• posted

Your "100V input" is typically going to vary between, say, 95-105V. Similarly, depending on just how heavy the load on the "10V" side is, the extra current will cause various losses so that your output would tend to vary between, say, 9.5-10.5V even with a perfect 100V input. (How well a power supplies copes with the former problem is called "source regulation" and how well it copes with the laters is "load regulation.")

You do occasionally see some really cheap 12V->24V or 12V->6V DC/DC converters out there that use a fixed ~50% duty cycle and figure the output will be "close enough."

• posted

Hi W_Tom,

Hmm... if you say so. That's sure not how I read your post.

Yes, certainly true, but not really relevant to what a beginner needs to know.

For a bench supply or even a PC power supply, I'm tempted to agree with you. For embedded applications in cut-throat markets (TVs are a very good example), it's hard to ignore the cost savings that can be achieved by not bothering to make your power supply unconditionally stable when you 'know' there will always be a minimum load around.

It's the consumer who pushes the bean counters to skimp on parts count and/or quality. Although the US is a wealthy country that can readily afford to pay a couple bucks extra for a better computer power supply, this isn't true in all parts of the world (e.g., China). It's not the kind of engineering work I want to do, but I can see the justification for designing these really awful PC power supplies that cost literally no more than \$10 but can readily blow-up if you look at them crosseyed.

Mnay people get along just fine with being able to analyze single section filters (both the main L-C 'power' filter and something cheesy like an R-C feedback loop filter). Now, you may consider than the "principles of filter design," but personally I would say that someone well versed in such "principles" is more like to be able to spout off about Chebychev filters, group delay, Butterworth pole positions -- that sort of thing -- than just what simple LC and RC filters do. (I realize many power supplies do have "fancy" filters in the feedback path, I'm just saying plenty of them don't and I don't think you really need to know that much about filter design to make a workable switcher.)

---Joel

• posted

Somewhere was an 85(?) page introduction (from linear.com) to switching power supply design. Up front was a flow chart that asked if one wants to design a supply? The Yes path lead to a message that asked, "Are you Nuts?" Power supply design is complex. As demonstrated here, one must have knowledge of filters, feedback systems, principles of power systems, EMC, UL approval, FCC regulations, etc. A beginner must first decide how much will be learn before his eyes disappear into the back of his head.

If consumer pushed bean counters to reduce costs, then Honda and Toyota would not be dominant and growing car companies. Bean counters typically increase product costs - at least in the long term. It explains why GM has so many problems. Cost controls increase costs. To reduce costs, obtain more customers, create new markets, increase market share, create jobs, create wealth, increase product efficiency, etc... all require the most important thing - innovation. The US is a miser as are most every other nation. To sell in the US or anywhere else, the power supply manufacturer must innovate - not cost control. Meanwhile the US does have standards that some other nations do not have - for power supply performance, reliability, safety, emissions, and .... Europe has even tougher standards.

Most supplies, to be profitable, must be designed to operate anywhere in the world - either as a universal supply or with different options for different regions. Just another example of innovation; the alternative being bankruptcy. Just another reason why (outside of niche markets), the power supply designs must meet fairly universal world standards.

Tell us about harmonics? Do we solve this problem with filters, or what else? Will a power supply create too much harmonics AND will it operate when line harmonics are high? I recall the Intel spec that even demands output transient response - another factor in a feedback control system design. Power supply design is not about costs. It is about innovation - where costs are only one small part of a profitable design. The only way to cut costs and remain competitive - innovation.

A large market for inferior supplies exists that create problems such as computer system damage and intermittent failures. All power supply outputs must even be shorted and still not damage the supply. This too has been defacto standard for many decades.

We have demonstrated how much is basic information on power supplies. IOW, "your nuts" in that flow chart should be appreciated. 85(?) pages in that introduction paper demonstrates how complex a switching power supply really is and why a properly constructed supply selling for only \$65 retail is a marvel of free market economics.

However when purchas> Hi W_Tom,

• posted

Regarding Joel's notes on filter sections, it is true that in many instances a relatively simple filter calculation may be done for a workable switcher, but that depends on a number of things.

For a voltage mode controller, a widely varying input makes life difficult and is where a multipole (4 or even 5 filter sections) may be necessary, with the same provision applicable to large load steps for a current mode controller.

Where one has both (the usual situation in a lot of embedded systems nowadays), then a thorough knowledge of filter theory is certainly an advantage when one must do their own switcher, even though one may use spice programs; the issue is to use the program effectively, a knowledge of what one is doing helps :)

There are a number of reasons for designing one's own, including space, efficiency, unusual output voltages (althoguh there are 'adjustable' bricks out there) and Vin / Vout functions that have a particularly wide range. As an example, I had to do one that had 10-14V in nominal,

1.2V out, at loads from ~0 to 45A, with load steps of 94% with the assistance of the vendors involved.

I deliberately did not even attempt to cover everything (that's a subject in it's own right that many spend entire careers on, and I thank them for their assistance :), but merely try to point out that the loop filter is a critical issue in the design of a switcher (although one may use the 'suggested application' in many cases) that requires some attention, and is critical to understanding failure causes.

Cheers

PeteS

• posted

The following thread I started a couple of days ago may also be helpful.

From: Terry Pinnell Newsgroups: sci.electronics.design Subject: Rating of PC power supplies? Date: Sun, 29 May 2005 07:10:38 +0100 Message-ID:

In particular, Franc Zabkar posted this link to a detailed schematic:

```--
Terry Pinnell
Hobbyist, West Sussex, UK```
• posted

To demonstrate the complexity of power supplies - the so many functions that must be part of a minimally sufficient supply: Take that example supply from