When ever i install an antivirus I get disconnected from the internet?

As if you are using windows 7 and avast antivirus, I think the antivirus blocking all the applications which you are using.

You might need to know which applications you are using. Some antivirus lets the users decide the behavior or permissions of a application, after installing antivirus they asks you the permission to connect to the internet. If that application is trusted, you know that application you can allow the application or in case you can block it.

Windows Firewall is also blocks certain application that are related to 3rd party application. If the application given by the Microsoft that is the trusted software so in this case windows firewall allows that application to access internet with out any intimation. If that application related to 3rd party, you were asked to connect to internet, in here windows firewall asks you the permission if that is trusted or you know that software you can grant access.

All internet security software's have permission grant access feature. In here we need allow each application to grant access to internet.