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Conductance-voltage characteristics (CVCs) for non-symmetric tunnel junctionsbetween $d$-wave superconductors with charge-density waves (CDWs) and normalmetals were calculated. It was shown that they have a V-like form at smallvoltages $V$ and are asymmetric at larger $V$ owing to the presence of CDW peakin one of the $V$-branches. The spatial scatter of the dielectric (CDW) orderparameter smears the CDW peak into a hump and induces a peak-dip-hump structure(PDHS) typical of CVCs observed for such junctions. At temperatures larger thanthe superconducting critical temperature, the PDHS evolves into a pseudogapdepression. The results agree well with the scanning tunneling microscopy datafor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ and YBa$_{2}%$Cu$_{3}$O$_{7-\delta}$.

Charge density waves as the origin of dip-hump structures in differential tunneling conductance of cuprates: the case of $d$-wave superconductivity