# Low-Profile Harmonic Transponder for IoT Applications
## 1 Introduction  
Nonlinear radars, created to help cars avoid collisions, can be traced back as far as 1973 [1]. In comparison to the conventional linear radar, the nonlinear radar has higher immunity to clutter interference and also to the presence of metallic targets. Therefore, nonlinear radars have been utilized for several applications in the past few years [2, 3, 4], such as wireless sensing [5]. Most often, nonlinear radars are harmonic. Thus, the radar performance can be advanced by improving the transmitter linearity [6], utilizing modulated waveforms for transmission [2, 7], and improving the receiver sensitivity [5]. On the other hand, this paper is focused on possible enhancements on the transponder end. Most nonlinear transponders are tailored to have a maximum response by attaching an appropriate antenna to the nonlinear element [8], which is, in most cases, a Schottky diode. The used antennas are usually grounded patches [9] or dipoles that need to be kept vertical and stiff [10]. Therefore, designing printable single-layer transponder antennas is essential. However, connecting the antenna to the chosen diode without matching or biasing considerations introduces higher conversion loss (CL) values, which limits the reading range. In the literature, the diode is matched to the antenna either by utilizing lumped elements [11] or using open and short circuit stubs, each necessitating a ground plane layer and occupying a large footprint [12, 13]. Further, using lumped elements results in greater losses, as well as increased transponder weight, and that causes low acceptance in the field for identifying small objects, such as insects and small amphibians. In the literature, having ground plane and matching with lumped elements prohibit the transponder printing, especially when utilizing the printable Schottky diodes as presented in [14]. Thus, designing a single-layer, compact, lightweight and efficient harmonic transponder is the key issue for the full deployment of the harmonic transponders, and the main scope of this paper. With respect to the harmonic transponder presented in the literature, it is recognized that diode conversion loss is the most crucial aspect for optimal transponder operation. However, to the best of our knowledge, no systematic analysis on the role of diode matching and biasing play in this process has been completed. We fill this gap by investigating the influence of diode matching and biasing on the transponder conversion efficiency by circuit and EM simulations besides the conducted experiments. In this regard, the paper's advances are listed as follows:  
* A compact single layer harmonic transponder is introduced. This transponder outperforms the similar state-of-the-art work from the electrical size and coverage point of views as pointed out in Table 1 of the submitted paper. * The equivalent circuit model of the introduced prototype is derived, and the circuit simulation matches very well with the EM simulation. The very good matching between the EM simulation and the circuit simulation verifies the effectiveness of the derived circuit model. * Simultaneously matching the diode at two harmonically spaced frequencies. For the harmonic transponders in the literature, the matching is addressed at only one frequency. Further, the proposed planar T-matching network is compact and does not necessitate grounded Vias for the diode matching. * Diode biasing circuit is developed, and the corresponding prototype is theoretically and experimentally verified to be compared with the proposed matching solution. In this regard, the zero biasing HSMS-2850 Schottky diode is chosen as the nonlinear element, due to its high sensitivity and low-cost packaging. The diode barrier voltage is \(15\,\mathrm{mV}\), and the typical voltage and power sensitivities are at \(2.45\,\mathrm{GHz}\)\(30\,\mathrm{mV}/\mathrm{\SIUnitSymbolMicro W}\) and \(-56\,\mathrm{dBm}\), respectively.