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 Since the impedance of an ideal voltage source is zero, the impedance Zi is easily seen to be a parallel resonant tank. L1 is in parallel with C1! The impedance of such a network is, of course, just a peak like the top of a pyramid. Since damping eliminates the high Q resonance, Zi follows fairly close to the asymptotes, and with Q = 1, never exceeds the asymptotic peak Ro1 =D'SQRT(L1/C1). Zo, meanwhile, is a series LC tank, with an impedance that looks like an inverted pyramid which is the way they are built in the southern hemisphere [maybe not.] At any rate, we will also be damping this resonance, in fact to Q = 1/2, so again the asymptotes will suffice! Now, the point where the asymptotes meet is at Ro2 = (D'/D)squared x SQRT(L2/C2). But, the minimum impedance of Zo, which occurs at the same place, is 2 x Ro2 since Q = 1/2! Note that Zo has been reflected through the M = D/D' "transformer" in the canonical model. This is why Ro2 contains a (D'/D)squared term! Remember that this ideal and imaginary transformer represents only the Vout/Vin = D/D' action of the non-isolated switching converter. When an isolation transformer is used in an actual design, one must account for it by reflecting all power components to the primary side, as shown elsewhere on this site. [see Conversion to Simple Converter page] Note also that the Io generator has an infinite impedance, so we don't include it in our calculations. A real load has a finite impedance, but it is dangerous to rely upon it for damping. Usually the input impedance of our load circuit is unknown, undetermined, and variable over time. We will make sure our circuit is a stable regulator regardless of AC load impedance by employing shunt damping. The only thing left to explain is The Line.  The condition on Zi vs. Zo is, as we have seen, necessary for good response. Violating this condition produces a sluggish power supply at best. The second condition on Zi is that it should be much less than the line RD'/Msquared, where R = Vo/Io. This condition ensures that the RHP zeroes present in the undamped converter are pushed into the LHP. The resulting response is minimum phase, two pole, easily compensated, and exhibits enough power gain-bandwidth to satisfy a tough spec. Meeting these two impedance conditions is easy when you order my Laminated Design Guide! It will show you how to turn your required spec into values for L1, C1, L2, and C2, while choosing an appropriate D. Only $25US! Simply click on the shopping cart!  Background | Tips | Engineering vs. Science | | Isolation of the Cuk Converter | Historical Perspective | | Return Home | Safety First | Lesson in Ethics | The Consequences of Bad Design | Real World Applications | Deals | e-mail me! | |
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