Figure 1 shows a diagram of the generator. When power is first applied to the circuit, the capacitor C3 begins to charge through the resistor R1, while voltage across C3 increasing the logic elements go into an unstable state and oscillation begins. The frequency of oscillation is determined by the parameters of serial tanks C1L1 and C2L2.
Fig. 1. IC1 - CD4011
In the oscillating state, if C1 = C2 and L1 = L2 then voltage across C3 equal to half the supply voltage, and signals on outputs "A" and "B" of DD1.1 and DD1.2 gates has duty cycle 50%. If capacity or inductance of any tank (C1L1 or C2L2) will be changed then it would change the duty cycle of signal. Inputs DD1.1 and DD1.2 gates contains diodes that shunt LC circuit, so it's recommended to connect the inputs and DD1.1 DD1.2 with the LC circuit through resistors 10K...100K.
Fig. 2. Op-amp - 741
The duty cycle of signal can be converted into a voltage by adding to the circuit buffers DD1.3 and DD1.4 and two integrators R2C6 and R3C5 (Fig. 2). This scheme can be used for measure capacitance or inductance. Changing the voltage at the output of op-amp is proportional to the change of the parameters C1L1 or C2L2.
This multivibrator was used for measure of small movements, with C1 = C2 = 680 pF, the coils L1 and L2 were wound on a frame with a diameter 8 mm and with small ferrite rods inside, each coil contained 40 turns of copper enameled wire 0.3 mm in diameter (AWG 28), the one of ferrite rod is a sensor and it's moving freely in the frame (fig. 3), the operating frequency is about 1 MHz, supply voltage - 12V. If you will move both ferrite rods simultaneously, then you obtain a differential sensor.
The output of the operational amplifier can be connected to a varicap (Fig. 4), which is connected to the upper terminal of the coil L1 to create a negative feedback - this is the circuit with automatic adjustment, the error signal could be taken from the output of the op amp.