# Objective

During IC design it is often required to choose appropriate resistor and capacitor sizes to implement a filter or design networks. Here we derive a formula to decide what resistor and capacitor values can be used for a given time constant so that the area is minimized.# Derivation

`$C_□$`

= capacitance per unit area for the process`$R_□$`

= resistance per square for the process`$τ$`

= Time constant of the circuit = `$RC$`

Here W = width of the resistor, this is chosen based on the accuracy needed for the resistor according to the process data

Differentiating with respect to C we have:

Equating that to 0 and calculating C we have:

Thus using this capacitance value and using

`$R=τ/C$`

would give the optimized area for the RC network