An analytical solution for the sheath dynamics of an asymmetrically driven capacitively coupled plasma is obtained under the assumptions of time-independent, collisionless ion motion, inertialess electrons, and uniform current density. Modeling is performed considering that the plasma is driven by a nonsinusoidal radio frequency (rf) current which can be resolved into a finite number of harmonic components. Together with different sheath parameters the equation for the bulk plasma impedance is also obtained to calculate the overall plasma impedance and the overall rf voltage. Assuming equal plate areas the solution for a symmetric discharge is also obtainable from this model. We have found that the even harmonic components of rf voltage and impedance are always present, even in a symmetric discharge. Experimental results are shown to be in qualitative agreement with the theoretical model. The values of normalized rf voltage and impedance harmonics assume lower values as the asymmetry of the plasma chamber decreases.