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The bulk electronic properties of compensated topological insulators are strongly affected by the self-organized formation of charge puddles at low temperature, but their response in the microwave frequency range is little studied. We employed broadband impedance spectroscopy up to 5 GHz to address the ac transport properties of well-compensated BiSbTeSe2, where charge puddles are known to form as metallic entities embedded in an insulating host. It turns out that the average puddle size sets the characteristic frequency νc in the GHz range, across which the insulating dc behavior is separated from a metal-like high-frequency response of delocalized carriers within the puddles. This νc is found to be controlled by a magnetic field, giving rise to a large positive magneto-conductivity observable only in the GHz range. This curious phenomenon is driven by the Zeeman energy which affects the local band filling in the disordered potential landscape to enhance the puddle size.One of the most prominent features of topological insulators is the spin-momentum locking in the surface states [1], which is particularly useful for spintronic applications [2]. To efficiently utilize the spin-momentum-locked surface states in applications, one should get rid of the residual bulk conduction, and this has been achieved by carefully compensating residual donors by residual acceptors through composition tuning in the Bi x Sb 2−x Te y Se 3−y compound [1,3,4]. Although such compensated topological insulators show reasonably high bulk insulation in dc, it has been elucidated that their transport properties are not only determined by the topologically protected surface states but also by the presence of charge puddles in the bulk [5], particularly at finite frequencies up to the infrared range [6]. This is because the Coulomb disorder of the randomly distributed charged donors and acceptors gives rise to potential fluctuations which grow as √ R in a volume of size R 3 [5, 7]; this inevitably leads to the self-organized formation of charge puddles on a mesoscopic length scale L at low temperatures. On this length scale, portions of a sample contain delocalized charge carriers which give rise to a Drude-like contribution to the optical conductivity σ (ν) above the Thouless cut-off frequency 2πν c = D/L 2 [6]. This cut-off is given by the time scale needed to diffuse through a puddle with the diffusion constant D. Using a simple scaling argument [5,7], L ≈ 100 − 500 nm is expected on the basis of infrared data [6]. This corresponds to ν c in the GHz range.Since the current-day information technology operates in the GHz range, understanding the microwave response of topological-insulator materials would be of crucial importance for their future applications in spintronics; nevertheless, the role of puddles in the transport properties in the GHz range has not yet been studied. This work is conceived to address this lack of understanding. At low temperature, the Drude-like puddle contribution to σ (ν) and its discrepancy with the dc conducti...