The primary function of a vehicle's exhaust system is to muffle the sound coming out from the exhaust port of the cylinder head and to direct the exhaust gas out the back of the vehicle.
The objective of a properly-engineered turbo exhaust system is to provide additional performance while still delivering adequate sound control. Unlike an all-motor exhaust system, a turbo exhaust system suffers no ill effects from going as big as possible. Essentially on a turbocharged vehicle, the turbine section acts as a very effective muffler.
The larger diameter exhaust pipes allow the back pressure to be significantly less than the factory exhausts system. As a result, the difference in exhaust pressure before and after the turbocharger is increased. The increase in the magnitude of the pressure difference allows the turbocharger to reach higher shaft speeds at lower engine operating rpms. As a result, boost response increases and boost pressures increase. More boost pressure at the intake manifold results more power at the wheels.
At least a full 2.5” exhaust system makes a turboed Miata breathe very easily. (IMO A 3 inch system is best, and you will see results by going from a 2.5 inch to 3 inch exhaust)
The first part of a turbo exhaust system is the downpipe. This replaces the exhaust pipe pre-catalytic converter. Downpipes help dramatically to improve exhaust flow and improve turbo spool up. They can also lower the engine-bay temperature when using stainless steel as opposed to mild steel which gives off more heat. Heat contained within the turbo system will increase power, while heat escaping to the engine bay will raise intake temps—which reduces power and isn't kind to rubber hoses or spark plug wires.
Next is the catalytic converter which must be retained if you plan on passing emissions. This is usually one of the more restrictive parts of an exhaust, since the exhaust must pass through the catalysis. If you want to improve your exhaust flow you’ll want to use a high-flow cat. High-Flow Cats usually have 200-300 honeycomb style catalysis that a relatively free flow through your car's exhaust system all while passing emissions. They usually cost around $150
A free flow catback exhaust system does wonders to help a turbo Miata breathe. The second biggest restrictor on the exhaust system is the muffler. A free-flowing muffler actually has a perforated internal core wrapped in the sound dampening material. Since the internal core itself is straight through, the muffler is not a restriction. The turbo itself acts like a damper on the exhaust pulses so it is possible to run a very free flow muffler without being overly loud. In fact a catback exhaust on a turbo Miata that was designed for a non-turbo Miata will most likely be a quite as stock. And likewise, a turbo exhaust on a non-turbo Miata will have virtually no sound dampening. A number of 2.5” Stainless Steel Turbo Catbacks are on the market today.
In other words, get a DP that matches your turbine exit. Taper it out to 3" all the way to the tailpipe and enjoy all the added efficiency.
A full 3" exhaust will provide massive performance benefits, look cool, sound great and impress all your friends