Linear Capacitance Meter

The reactance X of the unknown capacitor determines the amplifier gain when it is compared with a fixed resistor R2 with a value of 47kΩ. In other words, the amplifier gain is equal to R2/X. When these values are equal, the gain is unity, and the meter can be calibrated to read full-scale under these conditions. Since G is proportional to 1/X and X is proportional to 1/C (X = 1/(2πfC)), then G is directly proportional to C, and the scale is linear. RV1 is used to calibrate the meter range and can be adjusted to give full-scale with a known value of Cx = 10nF with an input of 1 V rms at a frequency of 338Hz. The range of capacitance stops at 100nF because a further decade up to 1µF would mean an input frequency of only 3.38Hz unless some other factor can be changed. This "other factor" is the amplitude of the input voltage. If this is reduced 10:1 to 100mV while the frequency is kept at 33.8Hz, a further range up to 1µF full-scale is created. The main difficulty of the design is the need for a variable input frequency.