## 1 Introduction  
In recent years, the enormous demand for high-speed communication, high-resolution imaging, and high-precision measurements has promoted the development of terahertz devices [1; 2]. Among them, mixers play an important role and have become a research hotspot in many fields such as detection, fast imaging, planetary science, and remote sensing [3; 4; 5]. Over the past few decades, a series of mixers with different functions, structures, and materials have been proposed and fabricated. The mixer based on the GaAs Schottky diode is one of the most researched mixers due to its simple structure, high stability, low noise, and room temperature working conditions [6]. At present, the development of the terahertz sub-harmonic mixer is moving towards high frequency, high harmonic, and high integration [7; 8; 9]. For practical demands, two active circuit models have been widely used for the design of terahertz mixers. Among them, the mixer's active circuit model based on the SDM is the most common, which is characterized by its stable performance and simple design [10]. The performance of a mixer based on this model is hindered by its limited optimization variables and small optimization space. As Figure 1 shows, the structures and parameters of a mixer's RF transition model and LO-IF (local oscillator-intermediate frequency) diplexer model are fixed and nonadjustable in the optimization process. The impedance matching of this model only relies on the suspended microstrip on both sides of diode. As a result, the working bandwidth of a mixer based on this model is usually narrow and the return loss is not satisfactory in most situations. Moreover, if the conversion loss is not optimal, it is time-consuming to re-optimize passive functional units. In [11], a 205-230 GHz sub-harmonic mixer combining single-stage reduced technology with SDM was reported. The measured SSB conversion loss was 8-11 dB when IF frequency was fixed at 1 GHz. The mixer also showed a complicated structure and the circuit size (8.908 mm) was large. To increase optimization variables and optimization space, an active circuit model based on the GDM was proposed [12]. By utilizing basic transmission line units, passive functional models were broken down into individual units to simulate a mixer, as shown in Figure 2. Compared with the active circuit model based on the SDM, the lengths and impedance of the waveguide and suspended microstrips can be optimized in this model and the circuit structure can be more flexible and changeable. Usually, a mixer based on this model has the characteristics of a simple structure and larger working bandwidth. However, the active model based on the GDM also has disadvantages. As there are many optimization variables, the mixers' design process needs constant optimization and iterations, which is much more time-consuming. In addition, the lack of initial simulated parameters causes random optimization results, which are uncertain in most cases. Distinguished from the active circuit model based on the SDM, the RF transition model and LO-IF diplexer model are not simulated in this model. In actual applications, the active circuit model based on the GDM show poor stabilities. In [13], a 199-238 GHz sub-harmonic mixer based on the GDM was reported. The measured SSB conversion loss was just 9-12 dB and was not flat, which showed an obvious difference to simulated results. In the mixer optimization and reconstruction process, some problems such as poor conversion loss, long time consumption, and bad RF return loss cannot be solved well by these models. However, at this moment, the demand for high-performance mixers is huge. For example, in a terahertz communication system, the mixer performance has a close connection with the transmitter output power and the receiver noise figure, which are closely connected with the communication distance.