Your A & B make up the whole plot. The WP has 3 DF's. They are A+B+AB. I don't know what the sub plot is. I could be of more help if you provide the number of factors and resolution in the sub-plot.
I have attached a pdf of instructions for analyzing such a split-plot design. I call this an efficiency split-plot...The restriction has nothing to do with difficulty in changing factor levels, but due to the desire to increase the precision of the WP and the SP while minimizing resources. In the example attached, the experiment has 31 total DF's. The whole plot is created by factors S, P & V (full factorial). WP has 7 DF's: S+P+V+SP+SV+PV+SPV. The sub plot is created by factors T & t (full factorial). SP has 24 DF's: (T+t+Tt)(1+WP).
Y=WP+SP. Let me know if you have any questions.
"All models are wrong, some are useful" G.E.P. Box