Mini-DP -> HDMI adapters

I am not sure if it belongs in hardware or accessories but I figure that it kind of belongs on both forums.

I have a bit of a Mini-Display port to HDMI adapter puzzle. With most monitors I can use the same adapter and everything works perfectly. I have mini-display ports on my Lenovo W530, T430 and Surface Pro 3.

However when I try to hook up my projector, it doesn't even recognize the projector as a screen while if I directly plug in the HDMI into my ASUS ROG 702VSK, the project works perfectly fine as a second monitor.

I did a bit of research on this and this is probably because the cable/adapter combination draws power from the projector rather than from the laptop and that's causing the combination not to work properly. How would I be able to tell? In the future, what kind of adapters am I supposed to buy in order to make sure that it works?

Finally, is there a way to open the adapter up and solder something so that it would work properly with the projector? The adapter works fine with my TVs and monitor.

 

So the high impedence Microsoft surface mini-DP->HDMI cable works with the projector but my other cheap adapter that works with every other TV and monitor doesn't.