Passive and Active Filters

Evaluate a passive circuit transfer function H(jω) at a specified angular frequency.

Calculate the magnitude of a transfer function and express the gain in decibels.

Calculate the phase angle of a transfer function at a specified frequency.

Derive the transfer function of a series RC low-pass filter using impedance division.

Calculate the magnitude and phase responses of a series RC low-pass filter.

Determine the cutoff frequency of an RC low-pass filter from its component values.

Derive the transfer function of a series RL low-pass filter using impedance division.

Calculate the magnitude and phase responses of a series RL low-pass filter.

Determine the cutoff frequency of an RL low-pass filter from its component values.

Sketch the asymptotic magnitude response of a first-order low-pass filter.

Design a series RC low-pass filter for a 3 kHz cutoff frequency.

Derive the transfer function of a series RC high-pass filter using impedance division.

Calculate the magnitude and phase responses of a series RC high-pass filter.

Determine the cutoff frequency of an RC high-pass filter from its component values.

Derive the transfer function of a series RL high-pass filter using impedance division.

Calculate the magnitude and phase responses of a series RL high-pass filter.

Determine the cutoff frequency of an RL high-pass filter from its component values.

Sketch the asymptotic magnitude response of a first-order high-pass filter.

Design a series RL high-pass filter for a 15 kHz cutoff frequency.

Derive the transfer function of a series RLC bandpass filter with the output taken across the resistor.

Determine the center frequency of a series RLC bandpass filter from L and C.

Calculate the lower and upper half-power cutoff frequencies of a series RLC bandpass filter.

Calculate bandwidth from the two cutoff frequencies.

Calculate the quality factor from center frequency and bandwidth.

Use ω₀=√(ωc1ωc2) to relate center frequency to the cutoff frequencies.

Relate R, L, and C to bandwidth and quality factor in a series RLC bandpass filter.

Select series RLC component values to meet specified center-frequency and quality-factor requirements.

Derive the transfer function of a series RLC bandreject filter with the output taken across the combined inductor and capacitor.

Explain how series resonance produces attenuation at the center frequency of an RLC bandreject filter.

Calculate the center frequency of a series RLC bandreject filter from L and C.

Calculate the cutoff frequencies, bandwidth, and quality factor of a series RLC bandreject filter.

Sketch the magnitude response of a bandreject filter from its center frequency and cutoff frequencies.

Determine resistor and inductor values for a bandreject filter with a 4 kHz center frequency and quality factor of 5 when the remaining design value is specified.

Verify a passive-filter design by checking its limiting behavior, cutoff conditions, bandwidth, and component units.

Select an appropriate passive-filter topology for a stated frequency-selection requirement.