In this study, we demonstrate a co-fired magnetoelectric (ME) laminate consisting of piezoelectric/magnetostrictive/piezoelectric layers with unipoled piezoelectric transformer structure. The ME transformer was characterized by quantifying the voltage gain variation and resonance frequency shift as a function of applied DC magnetic field. We delineate the magnetic tunability feature by considering the magnetoelectric coupling and delta-E effect, where E represents the modulus of magnetic material. The ME response of the composite structure was found to be 473 mV/cm.Oe exhibiting DC field sensitivity of 100 nT under AC field of 1 Oe at 1 kHz. At a magnetic bias of 60 Oe, the transformer exhibited large frequency tunability of the order of 1.4 Hz/Oe. These results present significant advancement towards developing on-chip magnetic-field-tunable devices.