The electrically pumped terahertz quantum cascade laser is characterized by high output power, low threshold, high quality far-field beam, etc., which is one of the most efficient terahertz radiation sources in the frequency range between 1 THz and 5 THz. Due to its outstanding performances, the terahertz quantum cascade laser is an ideal semiconductor platform for the terahertz frequency comb generation. Different approaches, e.g., group velocity dispersion engineering, active microwave injection locking, passive stabilization, etc., have been employed to obtain broadband frequency combs based on terahertz quantum cascade lasers. Regardless of the stabilization technique employed, the radio frequency transmission in the terahertz quantum cascade laser cavity is a key point for the comb characterization, because the repetition frequency of the laser comb determined by the laser cavity length normally lies in the microwave frequency range. Previous studies mainly focus on the optimizations of laser structures to improve frequency stability. The design and optimization of broadband impedance matching unit are less investigated. In this article, a tapered microstrip line structure is designed to solve the impedance mismatching problem in the extraction and transmission of the radio frequency signal of the terahertz quantum cascade laser frequency comb. The input and output impedances of the tapered microstrip line structure are designed to be 20 Ω and 50 Ω, respectively. The simulation of the tapered microstrip line is carried out by employing a finite element method. The structure and parameter optimization of the tapered microstrip line is systematically studied. The calculated S₂₁ and S₁₁ are -0.1209 dB and -17.5133 dB, respectively, at the central frequency of 6.2 GHz. Then the electric field distribution of the tapered structure is simulated and the skin effect of the calculated electric field distribution of the tapered microstrip line is consistent with that of the traditional microstrip line. Furthermore, a corresponding equivalent circuit model is established to analyze its physical characteristics. In the experiment, the tapered microstrip line structure is applied to the extraction and characterization of the radio frequency signal of a terahertz quantum cascade laser frequency comb to verify the transmission effect of the tapered microstrip line. We first evaluate the basic performance of the terahertz quantum cascade laser. The maximum power is 0.75 mW at an operation temperature of 20 K. And the repetition frequency of the terahertz quantum cascade laser is successfully measured. The radio frequency linewidth and the signal to noise ratio are measured to be 3.7 kHz and 60 dB, respectively. And the repetition frequency shows a stable single-line signal in the injection current range of 700~900 mA. The stability of the repetition frequency is further verified under the condition of resolution bandwidth 500 Hz, video bandwidth 50 Hz, a driving current of 790 mA, and an operation temperature of 20 K. The frequency fluctuation range of the repetition frequency is measured to be 110 kHz in 30 s and 480 kHz in 2 min. And the amplitude Allen variance value of different tine intervals is basically between 10^-1 and 10^-2. The measured max-hold and amplitude Allan variance results also show a high-level stability of the repetition frequency. The experiments show that the designed tapered microstrip line is able to achieve the impedance matching between the laser chip and the external radio frequency transmission cable, which can significantly improve the signal-to-noise ratio of the comb repetition frequency by at least 10 dB and shorten its linewidth from 394 kHz to 3.7 kHz. The designed tapered impedance microstrip line can effectively transmit the repetition frequency and reflect the comb structure of a terahertz quantum cascade laser optical comb. This work provides a simulation and experimental basis for the radio frequency transmission study and mode-locking of optical frequency combs and dual-comb sources in the terahertz frequency range.