Parametric frequency conversion have seen a renewed interest, specifically in superconducting quantum circuits at GHz range. These nonlinear convertors are typically narrow band and one may wish to extend their frequency range. Here, two coupled resonators are investigated: a loop-within-loop structure, whose gap is coupled by short, a diode, or simply left open. While simulations and experimental results are limited to GHz range, the concept is general. On their own, the loops exhibit natural frequencies of ca, f=1.5 GHz and f/2=0.73 GHz, respectively; the coupling modifies the resonance frequencies and increases its bandwidth. In one example, signal is fed from one loop and is received by the other. In another example, the input signal is provided across a coupling diode and is received by either loops. It is shown that in the case of nonlinear coupling, the frequency bandwidth can be as large as 3 GHz. Such bandwidth is associated with a very narrow temporal response of less than 150 ps, suggesting coherent effects through high-harmonic excitations at the near-field.