Source: https://patents.stackexchange.com/questions/17060/patent-life-of-a-pct-application-and-royality-thereof
Timestamp: 2019-04-24 02:47:29+00:00

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a. NP (of invention "1001") is first filed in a foreign country (non-US Country, on 1 Jan 2017) and then a PCT is filed(on 31 Dec 2017), when will patent life begin for invention "1001" in The US?
b. If NP was filed in The USA itself (of invention "1001", on 1 Jan 2017) and then the application is filed for PCT (on 31-Dec-2017), when does patent life for invention "1001" begin in this case?
b. If my NP was 1st filed in US , then PCT was applied, - will it re-enter a national phase and from that moment wait for 18 months for US publication of my invention? And when will patent lifecycle begin in this case?
20 years life of an invention begins from the date of it's non-provisional application, but it's royality period begins from its first filing date of PPA, equivalent foreign PPA, given that the PPA/equivalent PPA later gets granted.
I agree with chempatent1981's answer on the expiry. I shall therefore focus on the when damages might be due.
You have used the term "royalty period". However, as far as I know, that is not really a widely used term. Perhaps a more common description would be the period during which actionable infringement may occur.
After issuance but before expiry.
After filing and publication but before issuance and expiry.
After filing but before publication, issuance and expiry.
I shall touch on each in turn.
In the US, the starting point is that anybody who makes, uses, offers to sell, or sells a patented invention infringes the patent (and thus may be liable for damages) (35 USC § 271(a)). A patented invention is an invention claimed in a patent (which is, by definition, issued).
Thus, any acts between issuance of a patent until it expires may give rise to damages.
35 USC § 271(a) requires a patented invention. Before issuance, there is no patented invention. Any "infringing acts" are therefore not infringement, and therefore do not give rise to damages under 35 USC § 271.
However, 35 USC § 154(d) provides for provisional rights. To be clear, provisional rights have nothing to do with a provisional application (and in fact can only ever apply to a non-provisional application, since provisional application are not published).
Provisional rights arise from the date of publication (of either a US non-provisional application or an English version of a PCT application designating the US) until a patent is issued (35 USC § 154(d)(1)).
the invention claimed in the patent is substantially identical to the patent claimed in the published patent application (35 USC § 154(d)(2)).
If this occurs, an infringer will be liable for "a reasonable royalty".
There are no rights in this period. 35 USC § 271(a) does not apply because there is no patented invention. 35 USC 154(d) does not apply because there is no publication.
a. The US filing date is the PCT filing date. You can find this stated clearly in this useful web page http://www.bpmlegal.com/howtoterm.html (1st asterisk). 20 year life time starts from the filing date, so the clock starts ticking at 31.12.2017.
b. You have not specified if you are using the US filing as a priority or as normal US filing. You have two options: You can use the US filing of 01.01.2017 to start a normal US prosecution and at the SAME TIME use it as priority to file a PCT (at 31.12.2017). This is of course not very smart, because the US patent will expire on 01.01.2037 while the PCT-stemming national patents will have a filing date of 31.12.2017, hence they will expire 31.12.2037. Can you see the 20+1 game here? OR you can use the US filing (US provisional this time) as a priority document and file a PCT application on 31.12.2017. The provisional will be abandoned, after surving its purpose. You can use the PCT application for US entry and normal national patent. The only thing you gain this way is establishing an earlier date, even though, probably, your invention has not been fully developed. Is it more clear now?
The publication date is only making it more complex, leave it outside for the purpose of understanding how filing and expiration dates work. But if you want to clarify this further, I'll be happy to try and help you!
I am not familiar with royalties, but I am sure someone will fill the gap here.
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What is the difference between the filing and priority date, since it is the same date for this invention?

References: § 271
 § 271
 § 271
 § 154
 § 154
 § 154
 § 271