does the diameter of the downpipe have to match the catback exhaust piping? for instance, can i put a 3.5in dp with a 3in catback exhaust?

 

here is a little thermal dynmaics for you that you can learn from any book.

air expands as it becomes hotter. the higher the temp of a certain cubic cm of air, the more pressure and volume it percipitates. the molecules are more active, thus producing more kinetic energy. with that said...im only touching base on volumetric effiecancy that comes into play here...but basically...for a turbo charged vehicle which relies on exhaust velocity, volume and temp as a direct perportion to the performance; a larger downpipe is better capable of allowing hot exhaust gases to travel with little resitance. same thing is true with the catback portion, because air can only travel as fast as its smallest point. so...thats why (for a turbocharged vehicle ONLY) a large, straight through system with little to no change in diamter and route of piping will produce better performance.

so...to asnwer your question...No it doesnt HAVE to match but...but as long as the difference between the downpipe and your catback system diameter isnt huge, you're fine with those perportions. assuming you own a turbo supra...those dimensions are fine.