The tuned substrate self-bias in an rf inductively coupled plasma source is controlled by means of varying the impedance of an external LC network inserted between the substrate and the ground. The influencing parameters such as the substrate axial position, different coupling coils and inserted resistance are experimentally studied. To get a better understanding of the experimental results, the axial distributions of the plasma density, electron temperature and plasma potential are measured with an rf compensated Langmuir probe; the coil rf peak-to-peak voltage is measured with a high voltage probe. As in the case of changing discharge power, it is found that continuity, instability and bi-stability of the tuned substrate bias can be obtained by means of changing the substrate axial position in the plasma source or the inserted resistance. Additionally, continuity can not transit directly into bi-stability, but evolves via instability. The inductance of the coupling coil has a substantial effect on the magnitude and the property of the tuned substrate bias.