To get the ring you need a few things: 1) Nitrogen, 2) Oxygen, 3) Heat, The Nitrogen comes from the wood and charcoal being burned, Oxygen from the air and Heat from the combustion of the wood or charcoal. Under the right conditions (Combustion) the Nitrogen combines with the Oxygen to form Nitric Oxide. The Nitric Oxide bonds with the myoglobin in the meat to form the ring. Gas/electric smokers produce no Nitrogen during the heating cycle. None! And cannot produce a "smoke ring". It's a chemistry thing.
Now you can trick an electric/gas cooker into making a "ring" by burning wood or charcoal while you are cooking with your gas/electric oven (because that's what a gas/electric cooker is - an outdoor oven). The problem is that you can barely get enough Nitrogen with the amounts of wood or charcoal you can safely put in your gas/electric oven before you have a fire risk. The purpose is to make a nice meal not burn your house down.
The more Nitrogen you can introduce the better your chance of getting a "smoke ring" that's why I suggested crushing up charcoal to mix with your pellets. Charcoal is very rich in Nitrogen, better than even wood. BTW the ring stops forming at 160 degrees surface temp, so anything you're doing after 160 is a waste.
But all that is just for show. The "ring" only adds a visual component to your BBQ. It doesn't enhance the taste one bit.