Voltage controlled oscillator using 555

A voltage controlled oscillator (VCO) gives an output frequency that depends on an applied control voltage. In the 555 timer, the control voltage is applied at pin 5 (CONTROL), which sets the comparator thresholds.

Circuit

              +VCC
         +------+------+
         |      |      |
       [RA]    (8)(4)  |
         |             |
         +----(7)      |
         |
       [RB]       (3) -----> output
         |
         +----(6)
         +----(2)
         |
       [C]
         |
        GND

  Vc o----(5)   control voltage input (e.g. from a pot or source)

Same as an astable multivibrator, but pin 5 is driven by an external voltage Vc (instead of the 0.01 µF capacitor to ground).

Derivation

With control voltage Vc at pin 5: the upper threshold = Vc and the lower threshold = Vc/2 (the internal divider of equal resistors).

Charging (HIGH): The capacitor charges toward VCC through (RA + RB) from Vc/2 to Vc:

Vc = VCC − (VCC − Vc/2) e^(−tH/(RA+RB)C)

tH = (RA + RB) C ln[(VCC − Vc/2)/(VCC − Vc)]

Discharging (LOW): The capacitor discharges through RB from Vc to Vc/2:

Vc/2 = Vc e^(−tL/(RB C))

tL = RB C ln 2 = 0.693 RB C

Frequency:

f = 1/(tH + tL) = 1 / { (RA + RB) C ln[(VCC − Vc/2)/(VCC − Vc)] + 0.693 RB C }

When Vc = 2VCC/3 (pin 5 unconnected): (VCC − VCC/3)/(VCC − 2VCC/3) = 2, so tH = 0.693 (RA + RB) C and f = 1.44/((RA + 2RB)C), the normal astable result.

Behaviour: Increasing Vc raises both thresholds, so charging takes longer and the frequency decreases. Reducing Vc raises the frequency. The frequency is therefore controlled by Vc, which makes a VCO. Applications: FM generation, tone generators, FSK, PLLs.