A CMOS Schmitt trigger CD4093 IC allows to create a simplest oscillator circuit that includes a resistor, capacitor and one NAND gate. If add several components, the oscillator circuit turns into voltage controlled oscillator circuit (see the Figure 1). The circuit includes voltage to current converter, it is based on the operational amplifier DA1, transistor Q1 and resistor R1.
How it works. If output of the gate DD1.1 is high, the capacitor C1 is charges through the diode D1 and resistor R2. When the voltage across C1 gets high enough to switch the gate DD1.1, the gate changes output to low logic level. Now the network D1R2 doesn't conduct the current. The capacitor C2 discharges through the transistor Q1 and the resistor R1, these components are the part of the voltage to current converter circuit. The operational amplifier DA1 controls the current through the resistor R1. When the voltage across C1 lowers below the threshold voltage of the gate DD1.1, it changes its output logic level to the opposite state, and the process repeats over and over again. The gate DD1.2 is used as a buffer.
The Figure 2 shows typical characteristics of the voltage controlled oscillator circuit. These response curves are obtained at different power supply voltage values (5, 10, 15 Volts). As it seen from the response curves, the linear span is in the range of 0.5..1.5 Volts for the power supply voltage of 5 Volts, and it extends form 0.5 to 3.5...4 Volts for power supply voltage of 10..15 Volts.
Note, all input pins of unused gates of DD1 should be connected to the ground wire.
The LTSpice simulation of the circuit is here: voltage_controlled_oscillator_with_a_cmos_schmitt_trigger.asc, it requires the CD4000 library for the simulation that can be downloaded here: CD4000.