Sometimes we wish to make comparisons between two groups but there are insufficient numbers available for sampling in one of the groups to give the study either reasonable precision and/or reasonable power and significance.
One solution is to increase the numbers investigated in one group and have fewer in the other, but it is not a direct 'trade-off'. The excel spreadsheet shows the numbers required in each of the two groups and the overall total to give the same power or precision etc. as two groups of the same size.
Below is a link to an excel spreadsheet (.xls) for calculating sample size when you have (or are likely to have) unequal group sizes.