**DISCLAIMER:** I don't know how dependent this answer is on specific hardware.
`airmon-ng` will enable a monitor interface without disrupting your wifi connection. Install `aircrack-ng` then run something like (I'm assuming wlan0 here):
sudo airmon-ng start wlan0
Which will typically create a `mon0` interface to the same physical card.
You can also try to do it with `iw` (I'm assuming you are using phy0 here):
sudo iw dev #this will show you the relation between phy's and interfaces
sudo iw phy phy0 interface add mon0 type monitor
Where you will create a `mon0` interface to the same physical card. See (< for more details on using `iw`.
As far as hardware goes, I usually run Atheros cards, but I've seen both of these techniques work on Broadcom cards as well, with the notable difference that when I had a `mon0` interface to a broadcom card, `airodump-ng` couldn't change the channel.