Corner Cutoff Frequency
RC Low-Pass Filter (LPF):
\(f_H = \frac{1}{2\pi RC}\)
RC High-Pass Filter (HPF):
\(f_L = \frac{1}{2\pi RC}\)
RL Low-Pass Filter (LPF):
\(f_H = \frac{R}{2\pi L}\)
RL High-Pass Filter (HPF):
\(f_L = \frac{R}{2\pi L}\)
Note:
The cutoff frequency is the point where the filter response magnitude
falls to \(1/\sqrt{2}\) (approx. 0.707) of its peak passband value,
corresponding to −3 dB.
Filter Bandwidth (Bandpass contains both fH and fL)
Bandwidth represents the frequency range over which a filter permits signals to pass with minimal attenuation.
Typically, bandwidth is measured between the lower cutoff frequency (\(f_L\)) and upper cutoff frequency (\(f_H\)), where the signal response drops −3 dB from its maximum level.
Bandwidth (BW) = \(f_H - f_L\)
Corner Cutoff Frequency
RC Low-Pass Filter (LPF):
\(f_H = \frac{1}{2\pi RC}\)
RC High-Pass Filter (HPF):
\(f_L = \frac{1}{2\pi RC}\)
RL Low-Pass Filter (LPF):
\(f_H = \frac{R}{2\pi L}\)
RL High-Pass Filter (HPF):
\(f_L = \frac{R}{2\pi L}\)
Bandwidth Calculation
Bandwidth (BW):
\(BW = f_H - f_L\)
Lower Cutoff (\(f_L\)):
\(f_0 - \frac{BW}{2}\)
Upper Cutoff (\(f_H\)):
\(f_0 + \frac{BW}{2}\)
Note:
Bandwidth is the range of frequencies between the −3 dB points.
In symmetric filters, these points are located at \(f_0 \pm \frac{BW}{2}\),
where \(f_0\) is the center frequency.
RLC Filter Characteristics
Resonant Frequency:
\(f_0 = \frac{1}{2\pi\sqrt{LC}}\)
Bandwidth (Series RLC):
\(BW = \frac{R}{2\pi L}\)
Bandwidth (Parallel RLC):
\(BW = \frac{1}{2\pi RC}\)
Approx. Cutoff Frequencies:
\(f_L \approx f_0 - \frac{BW}{2}\) | \(f_H \approx f_0 + \frac{BW}{2}\)
Note:
The \(f_0 \pm \frac{BW}{2}\) formulas are approximations. They are only
accurate for High-Q circuits (Q ≥ 10). For low-Q
circuits, the relationship \(f_0 = \sqrt{f_L \cdot f_H}\) should be used.