Study Unit 6: Filter Design - (Part 1) First Order Filters

Flashcards on Filter Design (Part 1) focusing on first-order filters.

Ideal Low-Pass Filter

Passes frequencies below ω and rejects frequencies above ω.

Ideal High-Pass Filter

Passes frequencies above ω and rejects frequencies below ω.

Ideal Band-Pass Filter

Passes frequencies between ωL and ωH, rejects frequencies below ωL, and rejects frequencies above ωH.

Ideal Notch Filter

Rejects frequencies between ωL and ωH, passes frequencies below ωL, and passes frequencies above ωH.

Transfer Function

The ratio of the output to the input, represented as H(s) = Xo/Xi = Vo/Vi.

Differentiator

A circuit whose transfer function is H(s) = -RCs.

Integrator

A circuit whose transfer function is H(s) = -1/(RCs).

Low-Pass Filter with Gain

Has a transfer function H(jω) = H0 / (1 + j(ω/ω0)), where H0 is the gain and ω0 is the cutoff frequency.

High-Pass Filter with Gain

Has a transfer function H(jω) = H0 * j(ω/ω0) / (1 + j(ω/ω0)), where H0 is the gain and ω0 is the cutoff frequency.

Band-Pass Filter with Gain

Has a transfer function H(jω) = H0 * j(ω/ωL) / (1 + j(ω/ωL)) * 1 / (1 + j(ω/ωH)), where H0 is the gain, ωL is the lower cutoff frequency, and ωH is the higher cutoff frequency.

Phase Shifter

A circuit with a transfer function H(jω) = (1 - jωRC) / (1 + jωRC), used to shift the phase of a signal.