## 1 Introduction  
Recently, a variety of flexible and wearable electronic devices have appeared on the market. Particularly for the development of microwave technology, flexible radio frequency (RF) devices have attracted growing attention due to their flexibility, light weight, low power consumption and good biocompatibility, and have been applied in wireless communication [1, 2, 3, 4, 5, 6, 7], biomedicine [8, 9, 10, 11], sensing [12, 13] and military [14] fields. Flexible RF devices are obtained by improving the physical material or structure of traditional RF devices, so that they can possess the excellent electrical characteristics of traditional RF devices under deformation. Up to now, tremendous work has been performed on flexible materials to realize the flexibility of RF devices.  
There is a considerable amount of research focused on plastic substrates. In some research, flexible RF devices are prepared by fabricating a structure made of some metal materials on flexible substrate. For example, Au/Ti was deposited on polyether sulfone (PES) substrate to fabricate a coplanar waveguide for flexible monolithic microwave integrated circuit (MMIC) [1]. A method to prepare flexible frequency selective surface (FSS) polarizer is to glue copper tapes with a designed pattern to paper substrate [14]. Gold layers patterned on polyimide film and then coated with a thick polydimethylsiloxane (PDMS) layer have been used to obtain a flexible RF reasoner in medical research [11]. In addition, novel nanomaterials such as silver nanoparticle [4, 5, 12], silver nanowire [5] and silicon nanomembrane [2] are also reported to be used to manufacture flexible RF devices. Li et al. fabricated flexible antenna on textile by inkjet printing technology [4]. An RF switch was developed by flip-transferring single-crystal silicon nanomembranes on plastic substrates by Qin and partners [2]. Inui et al. prepared a flexible antenna on a nanopaper mixed with silver nanowire [5]. However, microcracks may appear when the flexible RF devices suffered from larger deformations.  
Microracks, which commonly appear when structural materials are bended, stretched or suffer from other deformations, are usually considered defects [15]. For flexible electronics, microcracks may result in the degeneration of the device's performance [16]. The negative influences are more pronounced when the flexible electronics are required to be more flexible and stretchable for some applications such as electronic skin [17], flexible display [18] and implantable devices [19]. Therefore, in terms of stretchable RF devices, the influence of microcracks on RF characteristics has to be addressed.  
Herein, this paper aims to reveal the influence of microcracks on RF performance in flexible microstrip transmission lines. The microstrip, which consists of stretchable Polydimethylsiloxane (PDMS) substrate and an Ag microparticles/PDMS (AgMP/PDMS) composite strip conductor, was fabricated and stretched to form microcracks in the strip conductor. The RF characteristics of the microstrip were monitored with a variety of tensile displacements. Both the transmission and reflection characteristics can be tuned via strain. An equivalent circuit model of microstrip with microcracks was proposed to reveal the mechanisms. The calculation results show a good match with the experimental results. It was found that both the effective resistance, which contributes form resistivity change of the material and change of the conductive pathways, effective inductance and effective capacitance, which result from the microcracks, can lead to the change in RF characteristics. Additionally, further investigations were conducted to confirm this mechanism. The morphology of the microcracks was characterized by SEM and the direct-current (DC) resistance of the strip conductor was monitored under strain. This study will be helpful in the future design of flexible RF devices.