Direct synthesis of transmission line low-/high-pass filters with series stubs

A direct synthesis procedure is presented for the design of transmission line low-/high-pass filters with series stubs. The proposed prototype consists of a cascade of series stubs of electrical length thetas_c alternating with uniform transmission lines of electrical length 2thetas_c. An exact network synthesis technique is applied on the fully frequency-distributed transmission line filter structures. By short-circuiting these series stubs, a low-pass prototype can be established to synthesise the filters with both predictable in-band and out-of-band behaviours. Instead, if the series stubs are open-circuited, a quasi-high-pass or wide band-pass filter can be designed with specified frequency bandwidth and centre frequency. Based on the formulation of a transfer function, a set of closed-form design formula is derived so that the synthesis design can be carried out for the proposed filters with Chebyshev equal-ripple frequency responses in the concerned low- and high-pass bands. As design examples, two five-pole planar filters based on the low- and high-pass topologies are implemented by using hybrid slotline and coplanar-waveguide structures. After final optimisation is executed via full-wave electromagnetic software to take all the discontinuities into accounts, two designed filters are fabricated and measured to verify the proposed synthesis approach and confirm the theoretical predictions.