Memristive elements, known as memristors, memcapacitors and meminductors, have become an important topic of research in the electronics world in recent years. As there is still no efficient way to manufacture two-terminal memristive elements, many researchers have focused their efforts on designing emulator circuits that mimic these devices. In this study, a memcapacitor emulator circuit using Current Derivative Buffered Amplifier (CDBA) is proposed, which has significant advantages such as wide dynamic range, differential structure at the input port, high sloping rate and wide bandwidth. The main advantages of the emulator are that it is floating without grounding constraint, it is electronically adjustable, it has charge-controlled incremental and decremental modes and it has a simpler circuit structure since it does not contain a memristor. To ensure the integrity of the circuit theory, the results of the mathematical model and the simulation of the memcapacitor are given together. In addition, the characteristics of the experimentally investigated memcapacitor emulator are in good agreement with the simulation results. To provide an illustration of the performance of the proposed emulator, firstly the second-order active low-pass filter circuit and subsequently the amoeba learning circuit are selected as the working environment. The results show that the filtering performance of the proposed emulator at a value after the cut-off frequency in the filter circuit is $25\%$ more efficient than a standard capacitor and in terms of power consumption, it consumes $27.93\%$ less power than a standard capacitor. Moreover, the emulator successfully accomplishes the learning and data storage tasks in the amoeba learning circuit.