Is it possible to get an exponential capacitance curve from coded dip switch

Question

I have a capacitor that controls frequency for a specialty IC with the relationship

\$F \propto 1/C\$

I want to be able to get a number of frequencies in evenly spaced intervals. Currently I have a string of series capacitors some of which I short out with regular dip switches in a binary code to give 16 steps.

^{simulate this circuit – Schematic created using CircuitLab}

This works as adding capacitors in series follows the relationship below giving linear steps.

\$ F \propto \frac{1}{C} = \frac{1}{C} + \frac{1}{2C} + \frac{1}{4C} +\frac{1}{8C} \$

To make it more intuitive to set the frequency for people who are not used to binary code I would like to use a coded rotary dip switch such as this

This means the switches are not all separate and have a common pin.

^{simulate this circuit}

Because of this the relationship is exponential and it is not possible to get even steps based on this circuit

\$ F \propto \frac{1}{C} = \frac{1}{C + 2C + 3C+ 4C}\$

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TLDR

Is there a simple way to get evenly spaced frequency steps using a coded rotary dip switch, without needing too many more components.

Answer 1

Edited:

The 4 relay idea from Tom C is one option.

Other then that, if using a group of relays is not practical, then an old fashion 16 position rotary switch could do the trick too.

You could create a similar capacitor string as in your first diagram using 16 equal value capacitors, (much easier then finding several specific values) then use the 16 position switch to connect to each of the 16 intersections within the string. That would give you the "division" format you seem to need.

Low cost 12 position switches can be had from surplus dealers.