The 555 frequency can be varied via adjusting the voltage at pin 5. However, the range and linearity of frequency adjustment is very limited. This is a way to greatly improve performance using the inverted 555 timer circuit that was previously posted.
Q2 is connected in the common base configuration. In this mode of operation, the collector current is a function of emitter current regardless of the collector voltage. In this way, it can perform a linear charge function upon C1. The emitter must be driven from a negative supply voltage. Frequency is scaled to 10V = 10kHZ via R5. Frequency range in this set-up is 180 to 10kHZ.
Q3 is wired as a self-biasing transistor by connecting the base to the collector and feeding it a bias current via R4. Voltage drop is 0.6V. Originally, I had a 1N4148 diode and its voltage drop was 0.45V that added too much offset to the emitter of Q1. Ideally, the voltage drop across Q3 should equal Vbe of Q2. This is a compromise because they are matched only under the condition of Ie = (9V – 0.6V) /R4 = 84uA. The emitter current varies from about 3 to 303uA.
Lowest low end offset would occur with both transistors matched and R4 increased to 3M—in that case, the hFE @ 3uA must >100—this looks practical, but would require a different transistor selection—I did not experiment with this option.
Q1 is a 2N4401. It varies from the 2N3904 in that its current gain (hFE) is optimized at a higher current. The reset current must be high due to its low duty cycle.
Linearity is shown over two orders of magnitude. While not perfect, it shows how the circuit performs. The error on the low end is caused by input offset voltage that is not perfectly nulled via the voltage drop of Q3. On the high end, non-linearity is caused by the finite reset time of the 555 that runs about 6% @ 10kHZ.
Spread sheet data
There is some extra stuff here to generate a -10V reference from a single 19V supply.
Frequency is a function of Vcc—requires stable supply
High component count
Requires negative reference voltage—no issue if already using split supply
I do not generally recommend this circuit, but believe that it would make a great lab experiment for those who really want to learn more about VCO’s and the versatile 555.
For the future
XR4151 VCO circuit
Charge pump VCO circuit
Preferred components for the serious experimenter