Antenna for broadcast AM reception on ARM Radio SDR
Ok, doing a little work with the calculators found here and here, I came up with an idea that I think you might like.

Materials:


14ga-18ga "fray wire"  
9" section of 4" PVC pipe  
Power drill with ~1" hole saw &amp; 1/4" bits  
3/4" pvc pipe (at least a foot)  
3/4" &amp; 4" PVC pipe end-caps  
1+ zip tie(s)  
Magnet wire (about 150')  
Some BBs, iron powder, etc.  
50ohm coax cable (to reach the receiver
A 3' or taller frame to hang it all from


If you ground one end of your primary (50ohm) winding on the input transformer, you can then run an unbalanced coax line to a "loaded quarter wave" antenna that can be made resonant with a 50ohm impedance for our band of interest. FYI: AM broadcast band reaches across nearly 2 full octaves of bandwidth (0.5MHz-1.7MHz), so it's not very well possible to receive the whole band resonantly with a 'fixed' antenna.

Construction:


Strip the last 1-2" of the coax from the antenna end;  
Solder a 1' length of the 'fray wire' to the coax center conductor;  
Drill a 1" hole in one of the 4" pipe caps;
Insert the piece of 3/4" pipe through the hole; glue on one 3/4" cap; fill with BBs/iron filings; then slip on the other 3/4" end cap (so the 3/4" pipe filled with metal can slide up &amp; down through the 4" pipe cap, but can't escape).  
Glue the end caps on the piece of 4" PVC pipe, leaving 6" of 'bare' pipe between the caps;  
Drill a pair of 1/4" holes near the piece of 3/4" pipe on the 'top' 4" cap (we'll call the 3/4" pipe section the "tuning slug," as that's its function), to attach the rest of the 'fray wire' to for hanging the inductor (whole PVC pipe assembly becomes a 'tunable inductor' once it's done).  
Solder the free end of the first 1' section of 'fray wire' to a stripped end of your magnet wire, then glue to the side of the bottom 4" PVC end-cap;  
Wrap the magnet wire around the 'bare' 4" PVC pipe (between the end-caps) for about 150 wraps (or 150' of wire, both are 'close enough'), keeping the wrappings evenly spaced (or evenly overlapped) across the 6" length.  
Solder another section of fray wire (about 1' long) to the top end of the (now wound) magnet wire &amp; glue to the side of the top 4" cap; then loop the fray wire through the 2 1/4" holes and tie/glue in place for stability.  
Attach the free end of this top wire to the mounting stand, so that the shield of the connected coax at the bottom can nearly contact the ground.  
Solder a short "ground lead" of bare wire to the coax jacket (when in use, this wire should be grounded to a ground plane as near to the antenna as possible)  
Attach a zip-tie "pretty tight" around your tuning slug, so by sliding the zip tie up/down the length of the slug, you can adjust how much of the slug's metal filling is inside the coil (and thus, control the coil's inductance).


OK, that took a bit more explaining "on paper" than I expected in my head, but if you get this far, you should be ready to "fire her up." Start out with the tuning slug mostly outside of the inductor, then tune to a high-frequency band AM signal in your area &amp; adjust the tuning slug for best reception. More slug in the coil = lower frequency tuning for the antenna, so if you can't get the high-frequency station to tune in 'great' at any slug position, try tuning to a lower station; if that works, remove metal filling from the slug as necessary.