Damping the input filter, there are a number of possible ways to do that. We'll first do that in a sort of a heuristic manner, and then we will follow an optimized damping approach. Damping is something that we have already seen earlier in the context of damping, a or a converter. And one approach to damping the input filter is to make sure that we have enough dissipation in the filter, if you wish. And we can just simply add a resistance in parallel with the output capacitor on the filter. What is that Rf resistance going to contribute to the output impedance? How is it going to affect the output impedance? Well, at the resonant frequency of L and C, what is the output impedance of L and C? What is the output impedance that we had seen Z naught for the undamped filter? It's infinite, right, that output impedance becomes infinite. The resonance, and this is parallel resonance between Lf and Cf, you see infinite impedance. If you just place Rf in parallel, you bring that down to the value that's equal to Rf. So this is going to give us immediately the value of the measure of the Z naught being equal to Rf and current frequency of the filter gate. And you can just pick Rf to be small enough to meet the condition that it's much smaller than either Zd or Zn. Now, of course, there is a problem with this as is, loss, right? So this, as shown right here, has a problem with the loss and we're going to fix that in just a second. But before we do that, you have another approach to the damping the filter which places this Rf in parallel with Lf. What do you say is the output impedance here that we have all the filter at the corner frequency f sub f. In this case, here, this is an alternative way of damping. It's going to be, again, equal to Rf, right? So if you short the input and look at the output impedance of the filter, you'll still see a resonance at ff between Lf and Cf. And all you are going to be left with is going to be Rf. What do you think about this approach to damping the input filter in terms of losses? L sub f at DC is very small impedance, right? It's going to be reduced down to just whatever the binding resistance of the inductor actually is. Ideally, if there are no losses on Lf, if that one resistance is very small, the vast majority of the DC current will, in fact, be going through this path right here, so this is Ig. The Ig is going to be approximately going through right here or entirely going through right here as long as any the series resistance of the inductor is very small. So this is, from the point of view of losses, a better situation compared to putting this in parallel with a capacitor. Because in parallel with a capacitor, we have entire DC voltage V sub g across it, and we have tons of current going through sub f and a lot loss on it. So the same value of Rf would be placed in a more favorable position in parallel with Lf, then in parallel with Cf. All right, now the parallel of Cf is a fairly popular approach, and it actually has some advantages compared to the approach that we have down there. In particular, it has advantages in terms of one other aspect that the filter has to meet. Why do you think we would actually prefer this compare to this from point of view of what the purpose of the filter is in the first place? What is the filter for? The filter is for attenuating the ripples coming from this side, right here, to that side. The purpose of the filter is to attenuate the switching ripple. So if you look at this case, right here, we have Lz situation, right here. We have a second order response, and as you go up further in frequency, the attenuation is going to be increasing at what rate? 40 DB per decade, right? So every decade in frequency, you have a second order filter present right here. So you have 40 DB per decade improved attenuation as you go up. How about this case right here? Putting this Rf right here, nicely damps the filter, but it reduces the attenuation. The attenuation, instead of being 40 DB per decade is going to go back down to just 20 DB per decade. Because at the high frequencies, this becomes an open circuit, and you look like an Rf type filter. A single first order filter with 20 DB per decade attenuation increasing as you go up in frequency. So filtering is now compromised by adding Rf and parallel with Lf. All right, so you have advantages here in this version with respect to losses, you have this advantages with respect to attenuation. So if you go back to this case right here, you say well, I like to have second order attenuation. What can I do to mitigate the losses? Yeah, you put a DC blocking cap in series and you take care of that, right? So putting an extra capacitor in series is really what gets you back into not having this in losses on the damping component, and retaining the second order attenuation property of the filter. All right, and so that's really the essence of what we have right here. So this is the filter with damping, and I will take that as a starting point into the discussion next time. We'll figure out how exactly to choose components Rf and Cb to accomplish effective damping of the filter, and do that in an optimal manner.
