comma or no comma after "Note that"

Please advise if a comma is needed after “that” (condition + effect, right?), and kindly provide the reason(s) why there should be no comma or a comma.

The sentence goes this way:

Note that if C =1, W will become zero.


I wouldn’t use a comma there. If you read this aloud, there is no need for a pause.


Thank you, Alan. I just want another opinion because some authors would insist that a comma should be inserted after the conjunction “that.” Do you have a rule or other reasoning besides saying that there is no need for a pause when we read the sentence aloud? I need a reasoning that is more profound and established so that I can explain it to them why there is no need for a comma. All I can say is that the “if” clause is a restrictive one. I hope that you have other possible explanations on this matter.

I already found the answer in the Chicago Manual of Style. Many thanks, Alan!