The Effect of Internal Resistance on an Energy Harvester with Cubic Resistance Load

The objective of this paper is to study the effect of the internal transducer resistance on the dynamic behaviour and the output power of an energy harvester when it is attached to a cubic load resistance. It is seen that by considering the internal resistance, the dynamic equation of a conventional nonlinear energy harvester changes so that it is not easy to separate the linear damping from the cubic damping. An analytical model is presented for an energy harvester with an internal resistance in series with a cubic load resistance. Then, a comparative study is conducted between three different cases, representing three different levels of the internal resistance for energy harvesters, respectively, with the values of 0.2Ω, 2.8Ω and 6.8Ω. For each case the performance of the system with cubic resistance is compared with its equivalent in three different conditions. The three conditions are as follow: purely linear system, referring to the condition that the load resistance is linear and there is no internal resistance in the system; linear system, referring to the energy harvester with internal resistance in series with linear load resistance; and purely cubic system, referring to the system with cubic load resistance and negligible internal resistance. The comparisons between systems are carried out for both variable amplitude and variable frequency input excitation. It is seen that, similar to the linear systems, the internal resistance of the energy harvester provides an upper limit for the electrical damping of a device with cubic load resistance. By increasing the amount of the internal resistance, employing the cubic damping to increase the output power of system becomes less effective since the system behaves in a more linear manner.