Editing Sallen–Key topology (section)

===Branch impedances===

By choosing different [[Passivity (engineering)|passive components]] (e.g., [[resistor]]s and [[capacitor]]s) for <math>Z_1</math>, <math>Z_2</math>, <math>Z_4</math>, and <math>Z_3</math>, the filter can be made with [[#Application:_low-pass_filter|low-pass]], [[#Application:_bandpass_filter|bandpass]], and [[#Application:_high-pass_filter|high-pass]] characteristics. In the examples below, recall that a resistor with [[electrical resistance|resistance]] <math>R</math> has [[electrical impedance|impedance]] <math>Z_R</math> of
:<math>Z_R = R,</math>
and a capacitor with [[capacitance]] <math>C</math> has impedance <math>Z_C</math> of
:<math>Z_C = \frac{1}{s C},</math>
where <math>s = j \omega = 2 \pi j f</math> (here <math>j</math> denotes the [[imaginary unit]]) is the [[complex number|complex]] [[angular frequency]], and <math>f</math> is the [[frequency]] of a pure [[sine-wave]] input. That is, a capacitor's impedance is frequency-dependent and a resistor's impedance is not.