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The goal is to use a control voltage from 0-5V to generate a square wave signal from 1 (ideally, but around 10 would be acceptable) to 3000 Hz (linearly, although I could work around it not being linear).

I've been experimenting with a 555 (556 actually) and can easily achieve that by altering R1, R2 and C, but I need to keep those fixed, as the only variable input I'll have is the voltage.

Duty cycle is not particularly critical here although around 50:50 would be nice - it's to control a stepper motor driver which needs a minimum 1.5uS pulse, so only the most ridiculous duty cycle would not conform at those frequencies.

I've looked at the formula at What is the equation for the 555 timer control voltage? (the one at the top of tardate's answer; the one in the question appears to be wrong) and by applying it it appears clear that the range I want is not possible with just Vcontrol.

I'm open to using both timers in the 556 if that could work, but I haven't been able to figure out a solution.

If a 555 is just not appropriate for this, can someone suggest an alternative? I could always dust off the PIC programmer and get it to do this but I was hoping there was a simpler alternative.

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    \$\begingroup\$ Seems that your goal is to design a VCO (Voltage controlled oscillator). Google "555 vco" or go for 566 IC. \$\endgroup\$ – Rohat Kılıç Oct 18 '16 at 19:44
  • \$\begingroup\$ Please provide a circuit diagram with the tool \$\endgroup\$ – Voltage Spike Oct 18 '16 at 19:44
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    \$\begingroup\$ 3.5 magnitudes is an awful lot of frequency range for a 555... \$\endgroup\$ – Ignacio Vazquez-Abrams Oct 18 '16 at 19:51
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    \$\begingroup\$ Dust off the PIC. It is your "simpler alternative". \$\endgroup\$ – brhans Oct 18 '16 at 20:27
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    \$\begingroup\$ Honestly, if it's for controlling a stepper, I wouldn't go for a VCO. You'd rather use any decent MCU with a PWM output (and eventually an ADC, if you really want to keep the analog input control). Design will be much simpler, and you'll achieve a much wider frequency range. \$\endgroup\$ – dim lost faith in SE Oct 18 '16 at 20:38
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It feels a little wrong to answer my own question, but just to conclude this, I think it's fair to conclude that a 555 is not really suitable for this specific task. Thanks to those who commented.

I'm going to go the MCU route - it gives me more control and if I need to broaden the frequency range even further at some point it's then easy-enough to do.

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If you want the range from 1 to 3000 Hz it might be easier to use a counter as a frequency divider, for instance divide by 16 and let the 555 generate 16 to 48000 Hz. Dividing by a power of 2 provides a clean square wave with 50 % high and 50 % low.

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If you use the 555 as a comparator you can make a VCO that will handle that range by adding an op-amp and a transistor.

The op-amp acts as an integrator and the transistor, controlled by the 555 output, changes from positive to negative integration.

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