## 1 Introduction  
With the recent advance in the operating speeds of solid-state devices, high-frequency transistors based on SiGe BiCMOStechnology have been developed with \(f_{max}\) up to 500 GHz [1]. This has allowed the development of various solid-state systems above 100 GHz. These systems have been successfully demonstrated for numerous applications including radar, sensing, radiometric imaging, high-speed wireless communication, and spectroscopy [2; 3; 4; 5; 6; 7; 8; 9]. Generally, the basic circuit blocks used in these systems are designed to have fully-differential configurations, which have the advantage of high CMR (common-mode rejection ratio) for common-mode noise cancellation. Baluns are essential in constructing differential circuits as they transform single-ended (unbalanced) input signals to differential (balanced) output signals or vice versa [10; 11]. They are required in the design and characterization of differential circuits such as voltage-controlled oscillators (VCO), mixers, push-pull amplifiers, and frequency multipliers. Furthermore, single-ended antennas can be connected to differential circuits via a balun. The parameters that assess the performance of a balun are its input/output reflection coefficient, bandwidth, insertion loss, and phase and amplitude imbalance. Depending on the application, any deviation in the balun's performance from the ideal case can affect the inherent benefits of differential circuits. For instance, in characterizing broadband differential circuits, such as distributed amplifiers or frequency multipliers, the bandwidth of the balun itself must be larger than the circuits. In the case of mixers, the bandwidth, insertions loss, and phase and amplitude imbalance of the balun can directly influence its conversion gain. Baluns can be broadly divided into active and passive baluns [10; 11; 12; 13; 14; 15; 16; 17]. Active baluns have the advantage of a finite gain and occupy a very small area. However, they face linearity issues, which can limit the dynamic range of solid-state circuits. Unlike active baluns, passive baluns do not experiences noise and linearity issues. They can be further classified into lumped element and distributed baluns [14]. The Marchand balun is a type of distributed balun, which exhibits wideband characteristics. Several modifications of the conventional Marchand balun exist in the literature [14; 15; 16; 17; 18; 19; 20]. These modifications have been performed using different technologies (SiGe BiCMOS, CMOS) to improve bandwidth, return loss, reduce the size, and decrease the phase and amplitude imbalance. However, there are still some disadvantages associated with them in terms of limited operational bandwidth, higher losses, or large amplitude and phase imbalances. Furthermore, some of them occupy a larger chip area. Owing to the prominent applications above 100 GHz and the salient features of differential circuits, a broadband balun with minimal losses and amplitude and phase imbalances is highly desired. Electromagnetic field theory plays a vital role in understanding the behavior of various systems in designing engineered materials and devices for different applications. Recently, electromagnetic field manipulation has been used to design various devices based on metasurfaces, metamaterials, graphene, and plasmonics [21; 22; 23; 24; 25; 26]. In the field of THz electronics, the electromagnetic field analysis can assist in designing various passive structures such as baluns and power combiners and splitters. In this work, we report the design of an edged coupled balun based on three asymmetric coupled lines. First, we presented different capacitances associated with coupled lines that control the phase velocities in the even/odd mode. Then, a balun based on three asymmetric coupled lines is designed with IHP's 130-nm SiGe BiCMOS back-end process to cover the frequency band of 110-220 GHz. The three asymmetric coupled transmission lines increase odd mode capacitances, which improves the balun's performance parameters.