As operating frequency is raised and as more integration with active and passive elements is required, it becomes difficult to fabricate more than 120 ${Omega}$ characteristic impedance of a mierostrip line. To solve this problem, an equivalent high impedance transmission-line section is suggested, which consists mainly of a pair of coupled-line sections with two shorts. However, it becomes a transmission-line section only when its electrical length is fixed and its coupling power is more than half. To have transmission-line characteristics(perfect matching), independently of coupling power and electrical length, two identical open stubs are added and conventional design equations of evenand odd-mode impedances are modified, based on the fact that the modified design equations have the linear combinations of conventional ones. The high impedance transmission-line section is a passive component and therefore should be perfectly matched, at least at a design center frequency. For this, two different solutions are derived for the added open stub and two types of high impedance transmission-line sections with 160 ${Omega}$ characteristic impedance are simulated as the electrical lengths of the coupled-line sections are varied. The simulation results show that the determination of the available bandwidth location depends on which solution is chosen. As an application, branch-line hybrids with very weak coupling power are investigated, depending on where an isolated port is located, and two types of branch-line hybrids are derived for each case. To verify the derived branch-line hybrids, a microstrip branch-line hybrid with -15 dB coupling power, composed of two 90$^{circ}$ and two 270$^{circ}$ transmission-line sections, is fabricated on a substrate of ${varepsilon}_r$= 3.4 and h=0.76 mm and measured. In this case, 276.7 ${Omega}$ characteristic impedance is fabricated using the suggested high impedance transmission-line sections. The measured coupling power is -14.5 dB, isolation and matching is almost perfect at a design center frequency of 2 GHz, showing good agreement with the prediction.