Matching DOF

https://www.youtube.com/watch?v=hi_CkZ0sGAw

Of bigger sensor to smaller one is done by using crop-factor and aperture (f-stop). For example:

Full frame camera with f4 will have the same dof as camera with crop factor of 1.6 if we divide f value with crop factor.

f4 / 1.6 = f2.5. 

For micro 4/3 the crop factor is 2 so

f4 / 2 = f2.

This will change the exposure, so we can counter that with changing the ISO.

Full-frame ISO
--------------- = Equivalent ISO
(crop factor)^2

If full-frame ISO is 400 then for camera with crop factor 1.6

400 / (1.6)^2 = ISO 156

or crop factor 2

400 / 4 = ISO 100

so

full-frame focal length / crop factor = Cropped focal length
full-frame aperture / crop factor = Cropped aperture
full-frame ISO / (crop factor)^2 = Cropped sensor ISO

Limitations ↓

For a lens that says 105mm / 1.5 you would need asp-c lens 70 mm with f0.9 (there is no such lens)

1/2” sensor ↓

For a small camera with 12.7mm sensor (5.41 is crop factor), what lens would be the same as asp-c with f2 and 50mm lens at ISO 200?

So f2*1.6 = f3.2 to get the full frame aperture. 
Full frame ISO would be 1.6^2 * 200 = ISO 512

Small camera ISO would be 512/5.41^2 = ISO 17 (impossible?)
Small camera aperture would be f3.2/5.41 =~ 0.6 (impossible?)
And the lens would be 50/5.41 =~ 9mm (possible)

Small required ISO could be bitten with build in ND filters, but aperture on for example sony PXW-Z280 stock lens is F1.9 - F16 (5.6 - 95.2 mm zoom).