How does the formula for calculating Low and High Frequency in a Band-pass Filter occur?
How do these formulas come to be?


Start with a generalized picture of your circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

From the usual equations for an op-amp in negative feedback you can find,

$$ v_o = -Z_1\frac{v_i}{Z_2} $$

Now substitute in the impedances for the elements in your design and you will eventually be able to get the high and low frequency cut-offs in terms of those element values.

If you know these frequencies are well-separated, it may help to assume that \$Z_1\$ is in the low-frequency limit when calculating the low-frequency cut-off and \$Z_2\$ is in the high-frequency limit when calculating the high-frequency cut-off.