I recently purchased this cable. It is perfectly does what it is supposed to do. You can connect your smartphone to your TV via the HDMI connector, select an appropriate source for video signal and see a mirror the screen of your smartphone on TV. I had no problems at all, when I connected my S4 to my Samsung TV. As a gift, our smartphone consumes power from the USB port and TV no battery.
Surely someone would prefer a wireless solution for the same task, but it requires different equipment.