This paper presents a capacitance-to-digital converter (CDC) that employs a novel approach to perform accurate measurement of capacitance of a leaky capacitive sensor. This CDC employs a sinusoidal source for excitation, which is advantageous for various sensing applications including ice detection, liquid level measurement, humidity measurement, proximity sensing, etc. Recently, an Impedance-to-digital converter (IDC) based on the dual-slope conversion technique has been reported. It can measure the value of capacitance even when a parallel resistance is present, but requires a large number of sinusoidal excitation cycles to complete a conversion, leading to poor update rate. The CDC proposed in this paper gives much higher (about 125 times) update rate compared to the IDC as it requires only a few excitation cycles for the conversion, but still gives an accurate output due to the use of a specially designed clock which helps to count the number of charge packets received by the integrator capacitor during the de-integration. Other than the operation of the CDC, the paper also describes outcome of a thorough analysis conducted to quantify the effect of various circuit parameters on the output of the new CDC. A prototype of the improved CDC has been developed and its performance parameters such as accuracy (± 0.27%), conversion time (24 ms), effect of parallel resistance, etc. have been tested and the results are reported in the paper.