How can anybody relate the physical signification between converter dynamics and switching frequency? Can anybody kindly explain in details? This is important for my project work.
Hi Arnab,
I am not sure about your intent, but herewith my two cents.
1 Higher switching freq yields better max bandwidth/accuracy product, in theory. This is quite trivial from delta sigma shaping theory. After all switching is intended to reach some voltage/current other than the given source voltage/current, and switches are just on or off. In delta sigma a first order delta sigma improves accuracy with a first order result. Put differently: double the frequency and in first approximation the accuracy is twice better.
The reason is simple: if a signal is between two levels only, selecting actively to be on or off at a certain frequency, the accuracy can only improve by extra time. This comes from the example formula (N1*V1+N2*V2)/(N1+N2)=Vx. With a number N1 of pulses towards V1, N2 pulses towards another voltage V2, the average (division by the total number of cycles) reaches some Vx. But per moment Vx is not really reached: sometimes V1 lifts the summation in one direction, sometimes V2 in another direction, both getting the averaged summation off. From this understanding it becomes trivial to see that a higher accuracy on Vx takes more N1 and N2 pulses, so that their relative contributions gets closer to the desired target Vx. Note 1: the equal sign should be an about sign, but I don't know where to find that on my keyboard. Note 2: V2 does not have to exist, reduction of the formula to one V1*N1 also does the same.
2 A converter switch arrangement is typically single bit. I am not active in the field, and I myself do know how a single switch converter could be used to achieve higher order switching (at the cost of speed) but I am not aware that designs are actually implementing such a scheme. No idea how to verify that though. If I am right the max performance remains stuck at first order shaping, on switch side.
3 In practice a switched converter will always have filter means that may be chosen at a higher order in spite of the shaping, and it will actually help to choose that. Better high frequency rejection, but not as much as higher order shaping with higher order filtering would yield.
4 Of course switching converters may be combined with trailing regulators/amps: the switched version in order to have high efficiency and a rough first target, the linear one to get high accuracy. This is a common scheme that I know.
5 Now the limitations: in practice the materials are just having limits all over the place. Three main ones:
- max flux in magnetic materials (above which the material saturates and probably kills your electronics quite rapidly). This forces the speed up
- switches have a finite on resistance so efficiency. This limits the efficiency in a hard way
- switch gates have a tremendous non-linear capacitive behaviour which puts a lot of strain (and efficiency limitation) on the driver stage. This forces the max frequency down.
In practice any design is therefore a combo of compromises.
If with "converter dynamics" you mean the converter frequency response (closed-loop and loop gain transfer function), it needs to be pointed out that time-averaged models that are usually considered in order to study the dynamics of switching-mode circuits are valid for frequencies below f_s/5 (f_s/10 to be conservative), being f_s the swithing frequency of the converter. You may find a detailed presentation (including several examples) of small-signal analysis of DC-DC converters in the original paper by Middlebrook, which can be found at the following link:
http://www.ee.bgu.ac.il/~kushnero/temp/guamicuk.pdf
Reducing sw freq will allow one to use smaller inductor. Smaller inductor usually helps during transients. Theoretically one should be able to use higher bandwidth with higher sw freq. so that is a plus. But in practise DC-DC converters have bandwidth somwhere between 100K-300K really. So if you are going from 1Mhz to 2MHz say loop bandwidth doesnt help much. What really helps in this case would be a smaller inductor. When a load transient happens, inductor current needs to increase fast to reduce voltage drop at output. A smaller L will allow to increase rate of increase of inductor current, and hence will help this cause. Thats my 2 cents.
Higher switching frequency leads to smaller, lighter, converters. Ultimately these converters are lower cost, because, over time, material costs rise, while process costs decline. A limitation is that the higher frequency requires core material development, and some better core shapes. Excess copper losses at higher frequencies, proximity effect and layer effect, are mythical where converter magnetics are concerned. As the industry learns that these effects decay to zero, where all windings have the same pitch and the same lay, then windings will only have I^2*R losses, where I represents rms current, and higher frequency has no effect on optimum wire diameter.
For an up-to-date dynamics model of peak-current loop control, see
http://www.planetanalog.com/author.asp?section_id=3049&doc_id=563894
This is a complicated subject, and there is no general agreement in power electronics about how to model something as simple as a peak-current control loop. But see the above series of articles for the most complete model thus far.
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