Inductance and capacitance measurement circuit

Since we made an inductance and capacitance measurement PCB in the previous post, lets talk a little more about it in this post.
The question I want to answer in this post is: “How does it work?”
Short Answer: It measures capacitance through RC charge time, and inductance through LC oscillation frequency.

Long Answer: First, it requires an input square wave. This square wave is generated by a Schmitt trigger circuit via an astable process. The duty cycle of the square wave depends on the resistor and capacitor values, which determines the charge and discharge rate, hence the on and off time of the square wave. Second, a RC charging circuit is used to determine the unknown capacitance value. A capacitor will require a certain time delay to elapse before it is fully charged. This time delay is known as τ, and for a RC charging circuit τ=RC. The capacitor will charge up to 63 % of the input voltage when τ has elapsed, and charge up to 100% of the input voltage when 5τ has elapsed. Therefore, based on τ=RC and on when the capacitor has charged up to 63% of the input voltage, the unknown capacitance value can then be deduced. Finally, a LC tank circuit is used to determine the unknown inductance value. Because the reactance of a capacitor decreases with frequency while the reactance of an inductor increases with frequency, there exists 1 frequency where the 2 reactances are equal. This is the oscillation frequency fr = 1/(2π(LC)½). Therefore, based on the oscillation frequency, the unknown inductance value can then be deduced. Testing: The RC charging circuit is used to determine the unknown capacitance value based on the time delay τ. The LC tank circuit is used to determine the unknown inductance value based on the oscillation frequency. 