We show that observables in QED-type theories can be realized in terms of a combinatorial structure called chord diagrams. One advantage of this combinatorial representation is that it simplifies the study of the asymptotic behavior of corresponding Green functions. Particularly, using the new representation, there is no need to use the standard approach of singularity analysis. This relation also reveals the unexplained correlation between the number of Feynman diagrams in Yukawa theory and the diagrams in quenched QED.