Since the driver was written with VISA commands, you probably only need to make a couple of small modifications. The first is to set the serial port parameters (baud rate, etc) and possibly add a termination character to the VISA Writes. You might want to download a driver written for both GPIB and RS-232 to see how the first is done. The HP34970A is a good example. Check your manual to see whether a serial write must have a termination character. This is typically a CR or LF. Just like a VISA property node is used to set port parameters (in VISA Configure Serial Port), there is also a property node to set the Serial End Mode for Writes. Add this property to a copy of VISA Configure Serial Port and put this in the Initialize vi of the scope driver. Then all you should have to do is select the correct com port in the VISA Resource Name.
