In order to investigate the energy harvesting performance of the DCR-MTM structure, firstly, an optimization procedure consisting of 10 steps was applied. A total of 6 resistors are integrated into the gaps on the rings of the structure consisting of double circle rings (Fig. 6a). The absorption characteristic of the resistor-integrated DCR-MTM is examined considering the resistor values that are the range 1000–10000 Ω in 1000 Ω increments. The graph of the absorption data obtained is shown in Fig. 6b. DCR-MTM structure has absorption percentages of 49.3, 63.5, 69.1, 73.6, 75.8, 78.2, 78.7, 79.7, 81.3, and 808 % at the frequencies 4.83, 4.84, 4.87, 4.87, 4.87, 4.87, 4.87, 4.87, 4.87, and 4.86 GHz for each resistor value, respectively. Similarly, the 2.44 GHz resonant frequency value has an absorption percentage of 768 %. The obtained absorption data proves the absorption maxima at 9000 Ω resistor value. According to these results, the value of the resistor is accepted as 9000 Ω. The optimization result shows that the DCR-MTM structure has potentials to be used in the energy harvesting applications. Subsequent calculations are performed with this resistor value.

To analyze the power obtained from the DCR-MTM design, the loss and power parameters are calculated in the 2–6 GHz frequency range. The results obtained from these parameters are displayed in Fig. 7. The proposed MTM design has \({Z}_{min}\) and \({Z}_{max}\) ports that are identified the floquet port. These ports are excited by the domain solver that depends on frequency. The power stimulated (PS) is the sum of all the stimulated powers per port. For ports \({Z}_{min}\) and \({Z}_{max}\) with active excitation, the stimulated power is obtained from the power that is delivered to the port by the EM signal. The default values for excitation amplitudes are set in the normalization overview. To begin with, for one excitation the PS power is 0.5 W at every port, and their sum gives 1.0 W. The sum of all powers per port is defined by the Power Accepted (PA) that is the net power flow accepted by DCR-MTM design from floquet ports. The sum of the power that is reflected from the structure back to the generator is defined as Power Outgoing (PO) for all ports.

In the first step, the total power in the proposed DCR-MTM structure can be calculated with the formula \(PS=PA+PO\). The Loss in Lumped Elements, Loss in Dielectrics, and Loss in Metals are the loss parameters. The power and loss parameters are expressed in Watt, which is the unit of power in the International System of Units. The losses in the metal resonator, dielectric substrate, and metallic ground layers constituting the proposed design are expressed by the Loss in Lumped Elements, Loss in Dielectrics, and Loss in Metals parameters, respectively. In the 2.44 GHz resonance frequency, PS, PA, and PO are calculated as 0.5, 0.32, and 0.171 W, respectively. At the 5.0 GHz resonant frequency, these parameters have 5.0, 0.343 and 0.156 W values. The differences between the sum of \(PA+PO\) and \(PS\) are 0.009 and 0,001 W for the 2.4 and 5.0 GHz resonance frequencies, respectively. This slight difference is described as the power radiated by the excited DCR-MTM. The loss parameters are calculated as 0.1843, 0.0098, and 0.0547 W for 2.44 GHz, and 0.2032, 0.0075, and 0.0969 W for 5.0 GHz, in the order given above. According to the calculation data, the maximum power transfer to lumped elements for 2.44 and 5 GHz occurs at 9000 ohms with 0.0547 and 0.0969 W. The total power transfer of all resistors is 0.1516 W. The parameters harvesting efficiency (HE) and absorption efficiency (AE) are defined to analyze the harvesting capacity of the DCR-MTM structure. AE is the percentage of PA to PS (Eq. 1), indicates the percentage of the incident wave power which is successfully absorbed by the DCR-MTM.

$$\text{A}\text{E}=\left(\frac{\text{P}\text{A}}{\text{P}\text{S}}\right) \text{x} 100$$

1

The consumed power in resistive (PR) loads can be used for conversion efficiency. HE is demonstrated in the Eq. 2. The HE is the measure of the percentage of the PS that is successfully transferred to the resistive loads.

$$\text{H}\text{E}=\left(\frac{\text{P}\text{R}}{\text{P}\text{S}}\right) \text{x} 100$$

2

AE parameter, which defines the absorption quality of the proposed DCR-MTM structure, reaches 64 and 68% maximum value for 2.44 and 5.0 GHz resonance frequencies, respectively. HE parameter has a total harvest percentage of 30.32% for 2.44 and 5.0 GHz resonance frequencies. Obtained AE and HE parameters can be considered adequate for WLAN harvesting applications in the 2–6 GHz frequency range. The harvested energy can be transformed to the external circuitry by regarding the impedance matching between the proposed DCR-MTM design and external circuitry. The proposed DCR-MTM design allows AC-DC energy conversion thanks to its simple resistor and resonator structure. This design can be an alternative for low energy requirements like portable systems.