The charge carrier mobility is a crucial parameter determining the device performance for numerous different semiconductor applications. Consequently, an accurate measurement of this quantity is crucial. For this purpose, the transient space charge limited current (SCLC) method is commonly applied and is preferable over, for example, Hall or field effect measurements, as the analyzed current direction is in line with typical device architectures. For the transient SCLC method, a voltage step is applied and the transit time of injected charge carriers is determined using displacement currents. Consequently, the difficulty of this method is the use of an adequate RC time constant for the sample charging, as it needs to be much shorter than the transit time. This parameter generally limits the application of transient SCLC strongly, in terms of obtainable charge carrier mobility or minimum required film thickness. Here, we demonstrate a measurement circuit with a low RC time constant, which works in a wide current range (1 A–0.5 A) and thus allows for significant flexibility in terms of minimum film thickness or detectable charge carrier mobility. The circuit is fast enough to measure, for example, charge carrier mobilities of up to for a 76 nm thick 4,4’,4”-Tris[phenyl(m-tolyl)amino]triphenylamine (MTDATA) layer, without using limited bridge circuitry. For this purpose, a capacitor coupled fast transistor switch generates a voltage step to avoid voltage oscillations and a fast operational amplifier is used for amplification of the voltage over a variable measurement resistor. We demonstrate the circuit working principle by measuring benchmarked MTDATA diodes and discuss its range of application.