# Radiofrequency Performance Analysis of Metal-Insulator-Graphene Diodes
## 3 Model-Based Performance Projection of MIG Rectifiers
### Power Detection  
A power detector operating at 1.225 GHz and 2.45 GHz was simulated to evaluate the performance of the fabricated MIG diode at zero bias for different RF input powers. The power detector was implemented as described in [16], using a impedance matching network to ensure power transfer through the diode and minimize signal reflections due to impedance mismatch. In this work, the experimental setup used for power detection as reported in [13] and simulated in [16] was considered, and hence, the results at frequencies different from 2.45 GHz should be considered as guidelines for performance projections in non-optimal matching scenarios. The topology of the MIG-based power detector can be seen in Figure 5, where the stages that are part of the circuit are shown. The power detector circuit included a 10 M\(\Omega\) resistor at the output, representing the multimeter connected  
Figure 4: Figures of merit of the MIG diode under study: (**a**) responsivity (blue) and nonlinearity (red), and (**b**) asymmetry versus voltage. to the circuit's output, which evaluated the maximum voltage value resulting from the applied RF input power. To evaluate the output voltage \(V_{\text{out}}\) of the power detector, a transient simulation was performed at each input power \(P_{\text{in}}\) for a given frequency. As an example, Figure 6a shows the transient response of \(V_{\text{out}}\) to an 10 dBm input signal, exhibiting that a steady-state was not achieved after 300 \(\upmu\)s. To determine a single output voltage, convergence was sought by adding a reference voltage to the output of the circuit, to improve the initial condition used by the CAD tool [23]. This reference voltage should be as close as possible to either the expected result (provided measurements are known) or to a previously found solution for other power levels. By using a reference voltage, voltage convergence was achieved, as shown in Figure 6b. The lower \(P_{\text{in}}\), the more cycles per second are required to be computed in order to achieve a steady-state solution. The power detector was simulated in transient analysis at different frequencies and input power levels ranging from \(-60\) dBm to \(20\) dBm. Figure 7 shows its response, depicting  
Figure 5: (**a**) Circuit used as a RF power detector (the dashed blue line encompasses the MIG large signal model including extrinsic elements); (**b**) bias tee, and (**c**) impedance matching network. Figure 6: DC output voltage as a function of time for an input RF signal with a power of 10 dBm. (**a**) Transient response. (**b**) Steady-state response. the variation in the output voltage \(V_{\text{out}}\) as a function of the input power \(P_{\text{in}}\). Figure 7a shows the good agreement between the simulation results obtained here and experimental data at 2.45 GHz, specially in the range from \(-60\) to 20 dBm. The measurement details have been presented elsewhere [13]. Since low-power level RF signals (i.e., below \(-40\) dBm) are expected in various practical applications such as wireless communications systems or energy harvesters, it is important to properly describe the experimental data in such a range. In contrast to [16], where the simulation results deviated from the experimental data at low \(P_{\text{in}}\), an accurate description of the measurements was obtained here by improving the convergence in the simulation framework, i.e., by increasing both the computational time and precision of the initial reference value for each transient simulation. The results for half the previous operating frequency, i.e., 1.225 GHz, showed lower \(V_{\text{out}}\) values at low \(P_{\text{in}}\), whereas minimum differences were obtained at high \(P_{\text{in}}\).