Frankfurt Airport
 

If I arrive at 7:35 am is it impossible to make a connection at 8:20 am in the Frankfurt airport?

I am trying to go from Frankfurt to Dresden and avoid waiting at the airport all day to take the train on a weekday.

A 45 min margin is incredibly close for an unfamiliar foreign airport. If your flight is early and all goes smoothly, you might just make it. Something as simple as whether you are at the front or back of the plane could make all the difference.

I tend to stress during an entire flight about the exact arrival time if I have a tight connection. If the consequences of a missed flight are great, you should consider a schedule change. Give yourself a little room for error.

FRA is an awesome airport but 45 minutes is still really close. What if your plane is 15 minutes late arriving (which seems to happen all too frequently)?
Personally I'd take the train right from FRA to Wurzburg or Mainz and explore for a day, then return the next morning to take that 8:20am flight

I am not quite clear if you plan to take a connecting flight out of FRA to Dresden, or the train.

For flight, 45 minutes are definitley too tight. Besides, even if you succeed, if you have checked baggage it might now make it. As a rule, I give myself 1 1/2 hrs beween connecting flights when coming from overseas.

Now as for train: I checked www.bahn.de and there is a train almost every hour from FRA to Dresden. One leaves directly from Terminal 1 without a change at 10:54 and takes about 5 hours. Costs EUR77, 2nd class, EUR 121 1st class. Most other trains require taking the S-Bahn to Frankfurt main station (Ffm.Hbf.) and getting the through train there. Costs are the same.

I've done this type of connection at least once (all on LH) - I rushed through the airport to get to my gate then sat and waited. If you are flying Lufthansa, Singapore, or UAL you'll arrive into FRA pretty close to your outbound flight.

AA or other airline for your flight into FRA and you'll have much farther to go. For the DRS flight, chances are they'll bus you from the departure gate to a plane on the tarmac. I've seen a last min bus drive up to the plane a couple of times with last min passengers. Your best bet if your running late may be to contact a Lufthansa personnel upon arrival and ask them for help (i.e. radio to departure gate, etc).