Stuff we learned:
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Nominal duty cycle of 0.23 is reasonable, so L = 240uH is reasonable!
Turns Ratio Calculation
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Therefore, for an N:1 turns-ratio transformer, N must be less than 7.2. Conveniently, we will pick N=7, so our transformer should have a 7:1 primary to secondary turns ratio
Peak Primary Current, Ipk
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Peak primary current is supposedly calculated using the following formula (from here):
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Dmax = 0.5 (from above)
Vin_min = 90V (from above)
fsw = 55 kHz (from above)
Lp_max = 240uH (calculated from above)
But then why is there a 2 term in the denominator? We’re not using RMS, these are DC values
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At aroudn 7:15 in this video: https://www.youtube.com/watch?v=VGZyqmAHMw0He mentions that the Duty Cycle of 0.48 should be multiplied by 2 for some reason?? IDk |
From this other source, there’s no 2 in the equation:
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When you also try to derive the equations yourself with V = L dI/dt and tON = D*1/f, you don’t get a 2
So we will assume there is no 2 involved:
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Ipk = 3.4A, which is very high….
Looking at the InnoSwitch datasheet, these are the rated I_limit values
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With this in mind, we should use INN4076 (or higher) with the 4.7uF BPP configuration
Transformer Core Selection
We will semi-blindly trust the area product method shown in this video:
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Ac is the area of the core [mm^2]
AW is the area of the winding space [mm^2]
E = max energy the inductor needs to store = 0.5*L*Ipk^2 =0.5 * 240uH * 3.4A = 1.3872 mJ
Bpk = saturation flux density of the core, which is determined by the material of the core. We will use a ferrite core (since it low losses), at which the common saturation limit is 300mT
J = current density in winding, which as a rule of thumb is given as 3A/mm for copper wire (from the video), so we will use that as well
PF = packing factor, which accounts for what percentage of the available wiring space is actually fillable by wire, since things like insulation take up space. The video estimates 50%, or 0.5, so we’ll use that too
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Then 'A' (which is Aw*Ac) is 6200 mm^4, so we try to find a transformer where Ac (area of core) multiplied by Area of Winding (Aw) is similar
180W uses this: https://www.digikey.ca/en/products/detail/tdk-corporation/PC95PQ32-30Z-12/9607321
60W uses this: ATQ23.7 (not on digikey)
Alternatively, let’s follow the calculations from here:
We need these parameters:
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Skin depth, based on their formula, is:
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where Awire is in mm^2, so we want to pick a wire with a MINIMUM cross-sectional area of 0.25mm^2, or 0.0025cm^2, or 2.5cm^2*10^3
To verify this is correct, we use https://www.allaboutcircuits.com/tools/skin-depth-calculator/ , and see:
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So then plug into area of circle formula:
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We see minimum wire area is also ~0.25mm!
According to Table 4-9 in chapter 4, we the MINIMUM wire size we can use is 23-AWG
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Then calculate Irms, which they give as:
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We can simplify the equation to just:
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Then, follow their steps for determining the right transformer to use
Assuming alpha (proportion of power loss due to copper resistance) is also their value of 1% (which is just 1 in their equation for some reason), then we find Kg = 0.0213 cm^5
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So then go to chapter 3 of their guide, and find a core with a similar Kg (but slightly larger, just so that there’s more area to work with)
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For EE cores, nothing is within good range  Also nothing good for EC:  Nothing for ETD:  Nothing for ER:  For EFD ferrite cores, best is EFD-25 = 0.01911 or EFD-30 - 0.03047  For EPC ferrite cores, EPC-27 = 0.024036 is very close too!  For EP ferrit cores, EP-20 = 0.02892 works  For PQ ferrite cores (what they use in examples), we see PQ20/20 = 0.0227  |
So the ‘valid’ cores, in order of ascending Ku, are: PQ20/20, EPC-27, EP-20, EFD-30
Looked on Digikey and found the below options, then downloaded a spreadsheet format for all the valid options so it’s easier to filter and calculate stuff.
Spreadsheet: https://docs.google.com/spreadsheets/d/1O1wjWdbnPksTQmW_tAbk-rAPtSNWPjp_Yc3J71V07ag/edit#gid=1019363053
https://www.digikey.ca/en/products/detail/epcos-tdk-electronics/B65875A0000R087/3914436
EPC-27: (does not exist on digikey)
https://www.tdk-electronics.tdk.com/inf/80/db/fer/ep_20.pdf
https://www.digikey.ca/en/products/detail/epcos-tdk-electronics/B66423G0000X187/3914948