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Plain Lucky we don’t live in a PSpice World!

We should keep that in mind, that all we need to do sometimes is to just sit back and allow nature to do its 'thing.' We have a natural ally in nature. Design problems actually really start, only when we have somehow managed to adopt what is in effect a schematic confrontation with natural forces. Luckily, nature doesn't have 'convergence' problems, like PSpice often does. All this may sound like some vague debating point in some esoteric man vs. machine philosophy panel discussionbut it is actually just plain design common-sense. Appreciating these finer aspects of nature can help us succeed with a host of seemingly mundane or challenging engineering pursuits. And it's almost faster than getting our grand simulator engine to essentially mimic nature itself.

As a seemingly trivial example, we all know that when an object heats up, the air around it moves upward trying to cool it down. Eventually, we achieve thermal equilibrium. But have you noticed that oddly enough, higher the dissipation, lower the thermal resistance (expressed in degC per Watt). This is because the rising air turns “turbulent” under higher dissipations, in an effort to help us even further. This phenomenon, once understood, is actually exploited in creating special pin fin heatsinks that try to provoke turbulent air flow even at lower dissipations. You can try “Pin Fin Heatsinks” and “Equations of Natural Convection” at www.pcim.com for more information. Carrying our learning to the extreme, small miniature fans are sometimes mounted on high dissipation ICs blasting air perpendicularly at very close quarters onto the exposed hot surface. This is called 'impingement air flow', and it leads to a further and really dramatic reduction in thermal resistance. A good read on this technique is available at the ETD library of Lousiana State University.

Now let's take a typical switching converter. If we apply a voltage across an inductor during the switch ON-time, we get a corresponding increment in current from the basic equation V=LdI/dt. But then we turn the switch OFF. Now we will find that a certain voltage automatically appears across the inductor. Its magnitude may be undefined initially (as during initial power-up), but what we can be sure of always is that it is of reverse polarity to the voltage we applied during the ON-time. If we think hard, we realize that our contribution as engineers is simply that we managed to create a circuit schematic (or 'topology') where we allowed nature to develop this reverse inductor voltage. But if for example, in a typical converter, we put the diode in the wrong way, (or forget the diode altogether!) we may just be preventing this voltage reversal, causing instantaneous combustion.

From V=LdI/dt, we also see that to get the increment in current during the ON-time to exactly equal the decrement, every cycle, we need the quantity 'V multiplied by time' during the ON-time to be equal in magnitude to the same quantity during the switch OFF-time. In fact, that is the fundamental volt-seconds law of power conversion. It leads directly to the expression of duty cycle in terms of input and output voltages.

But what drove nature to strive to do all this? To put it bluntly, we are lucky we don't live in a 'PSpice world.' Luckily, most natural processes tend to converge in our world and without 'user intervention!' We can foresee that if the current doesn't decrease to exactly the same instantaneous value it had at the start of the cycle , then every cycle there will be a small net increase in current. After a million switching cycles (nowadays that could take just one second!) this 'small' net increase will not be so 'small' anymore. Ultimately, we would probably never achieve a measurable or stable 'steady state' on the bench. And any 'switch' we may develop will ultimately combust under these escalating currents. Keep in mind that if it is not current, the switch will certainly fail due to excess voltage. Because nature goes all out to help us, even increasing the reverse voltage (if that is schematically possible) to force a 'reset' (i.e. convergence in effect). Too bad if we didn't leave any available doors open to allow nature to step in to help us out here. On the other hand, we would be hard pressed to make a typical PSpice-based converter circuit stabilize without explicitly implementing closed-loop feedback.

Note that the voltage reversal can be considered from the electromagnetic viewpoint as a result of Faraday's Law of induced EMF (or Lenz's law). It is interesting to recognize that not only 'transformer action' would not be possible without this law, but no stable DC-DC inductor-based topology could exist either. Because Faraday's law is simply the volt-seconds law in another guise (or vice versa). Without Faraday, we have no volt-seconds law either. And without this, there would be no switching power conversion for one!

But what has all this to do with PSpice? Well, on a more subtle level, and in the same spirit of things, nature also tries to lend an additional helping hand by imparting 'parasitics' to every component we use. These actually help many processes converge eventually (or stabilize), even if we have partially overlooked some crucial design aspect or abnormal operating condition. Yes, these parasitics do seem like a nuisance usually, but they have the potential to even temporarily stabilize an inherently flawed new topology. Of course we usually don't want to operate a converter that depends on parasitics for its functioning. Though we do something similar when implementing ZVS ('Zero Voltage Switching'). Parasitics often just 'soften' an abnormal or excessive application condition though we may not realize it (that's until we run PSpice!). As a trivial example, the ESR helps limit the inrush current into the input capacitor. We also know that even the small trace inductances leading to the input capacitor can help dramatically reduce shoot-through (cross-conduction) currents in synchronous buck converters.

Let us also consider what happens if we suddenly overload a normal non-synchronous buck converter … say by placing a dead short on the output? The duty cycle is still way up initially, not having had time to respond. So the converter 'thinks' the output voltage is still high and since its duty cycle is unchanged, it actually continues to try to deliver the normally required output voltage. But we know for a fact that the actual voltage on the output terminals has been forced to zero by the short. So where did the excess volts disappear? In fact, the full calculated output voltage momentarily appears across the diode and the DC resistance of the inductor. And the current must therefore increase (overload current) such that the following equation is satisfied unequivocally during the initial moments of the short: Vd + I*DCR=Vo, where Vd is the diode forward drop, and DCR the DC resistance of the inductor. So in a fault condition on the output, the DCR of the inductor and the diode drop actually both help in reducing the overload current. 'Good diodes' (with low forward drop) make the overload currents even higher. Note also, that in the latter case, it is not only the fact that we have a diode drop that helps reduce the overload, but the fact that this drop actually increases with increasing current, thus effectively helping out when needed the most. In fact, this effect was belatedly replicated by placing a series resistance (ohmic) term in the PSpice diode model.

Do write me at sanjaya.maniktala@nsc.com and copy Steve at sohr@cmp.com if you want to express convergence of views on this topic. But it's also OK, even if you want to momentarily explode and vent yourself after reading my little viewpoint. Just as long as we all manage to ultimately stabilize the resulting situation! And quite naturally so!

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