Given S different species and M sites . Where in every site species are unique (not repeated within the site,that is there are no 2 individuals from the same species in the same site , but can be repeated across sites) . N random sites picked as a sample , and species occurrence rate counted in every site in the sample. Applying Shannon index across sites gives me different numbers, I am unable to find an upper bound for the index .
How can I normalize Shannon Index in this case ,or at least found the upper bond for the index ?

Given S different species and M sites . Where in every site species are unique (not repeated within the site,that is there are no 2 individuals from the same species in the same site , but can be repeated across sites) . N random sites picked as a sample , and species occurrence rate counted in every site in the sample. Applying Shannon index across sites gives me different numbers, I am unable to find an upper bound for the index .
How can I normalize Shannon Index in this case ,or at least find the upper bond for the index ?