Our 6-Decade Resistance Substitution Box described in April 2012 lets you easily find the right value for a resistor in your circuit. Sometimes though, you also need to vary a capacitance. For example, you may have an RC oscillator where the resistor is integrated in an IC so you can’t change it.

For whatever reason, when you need to tune the value of a capacitor, this new 6-Decade Capacitance Substitution Box is ideal. It gives you hundreds of thousands of different capacitance values to play with, from about 30pF to 6µF. It can be used to tune oscillators, filters, time delays, compensation networks, rise and fall times, AC-coupling stages, rail-splitters, feedback loops and so on.

Even in situations where you can calculate the required value of a capacitor, you may still need to tweak it to work in a real circuit.

### Design

A capacitance substitution box is slightly trickier to design than a resistance substitution box. Because resistor values sum when connected in series, a rotary switch can be connected to a resistor string giving you a variable “tap” point. For example, with 10 x 100Ω resistors and an 11-position rotary switch, you can select a resistance in the range of 0-1000Ω in 100Ω steps.

But connecting capacitors in series gives a different result: two 100pF capacitors in series gives 50pF, three gives 33pF, four 25pF and so on. The resulting values aren’t multiples of 10 and even if the values were convenient, there’s the additional problem that the more capacitors you put in series, the larger they need to be for the whole string to have even a modest capacitance.

So we need to connect capacitors in parallel to make a substitution box. In practice, this means we need 10 sets of capacitors per decade, with values of (for example) 100pF, 200pF, 300pF, etc. Each switch selects one set for that decade and the decades are wired in parallel so that the capacitances combine. For example if you select 300pF with one switch and 2nF with another, that will give you 300pF || 2nF =

2.3nF.

Because capacitor values are assigned logarithmically, to get decimal values, we need one, two or three capacitors in parallel. For example, 300pF can be made using two 150pF capacitors while 400pF can be made with 220pF and 180pF capacitors. We have used values from the E6 series where possible as these are the most common ones. A few values from the E12 series have also been used, where necessary.