Why do amino acids hydrogen bond rather than ionic bond when they are forming secondary structures in proteins?
(this should be a comment)
I think you are not quite understanding the concept of partial charged or charged. The N atom in the polypeptide chain (so the N in the peptide bond) is partially charged! to be in an ionic state it should have 4 bonds instead of 3. 
 The peptide bond which is formed(above) just contains a N atom which is bounded to three other atoms. The oxygen atom is also partially charged but not charged! read this about H-bonding and partial charge