This thesis discusses the theory, circuit design, software design and measurements of an atto-Farad resolution closed-loop impedance measurement bridge circuit for capacitive sensors implemented using commercial off the shelf components. A lock-in amplifier (LIA) method is used here. The capacitive sensor embedded in an impedance bridge is driven at 10MHz or higher by two inverting excitation sources (AD9959) that can adjust frequency, phase and amplitude with a certain resolution (32 bits, 14 bits and 10bits respectively). These parameters can be set through a graphical user interface (GUI). When the output signal is nulled by changing the amplitude of the excitation signal, the unknown capacitor value can be calculated. A simple test impedance bridge has been fabricated to measure a fixed impedance value of the capacitor sensor using the LIA measurement approach. The obtained results (capacitance and resistance values) are in good agreement with what we obtained using an alternative approach (AH2700A, is an ultra-precision capacitance bridge with 0.16ppm resolution at 1000Hz). The circuit has a 24.1ppm resolution at 10Hz bandwidth when the input frequency is 10MHz.