A filter's cutoff frequency is the point where its response drops 3 dB below the passband reference level. It is fixed by four inputs: the frequency range the application must pass, the passband and stopband edges the system can tolerate, the required 3 dB bandwidth, and the physical design — filter order, resonator type, dielectric material and component values.
Key takeaways
- The 3 dB point is a relative level: it is measured against the minimum insertion loss inside the passband, not against an ideal 0 dB.
- First-order RC circuits give fc = 1 / (2πRC); an LC resonant network gives fc = 1 / (2π√(LC)).
- For bandpass filters, BW = fH − fL and the centre frequency is the geometric mean f0 = √(fL × fH).
- Filter order and ripple shape the transition band; they do not change the meaning of the cutoff.
The Short Answer
Cutoff frequency is not an arbitrary number and it is not picked from a catalogue. It is the frequency boundary that makes the system work: the highest frequency a low-pass channel can still carry, the lowest frequency a high-pass stage must survive, or the two edges of a band that must pass with everything outside rejected.
In RF work the cutoff usually comes from a standard or a link budget rather than from a formula. A band is defined by the air interface, and the filter is specified to pass that band with a stated insertion loss and to reject everything outside it by a stated amount. The formulas in the next sections then translate those requirements into component values or resonator dimensions.
Key Factors That Set the Cutoff Frequency
Application frequency range
The operating band is defined by the application, not by the filter. A 2.4 GHz WLAN front end must pass 2.400–2.4835 GHz, so its passband edges are fixed before any component is chosen; the design work is deciding how much margin to add on each side.
Passband and stopband edges
The passband is where signals must survive, the stopband is where they must be attenuated, and the gap between them is the transition band. A narrow transition band forces a higher filter order, more resonators and more insertion loss; a wide transition band lets a simple second-order section do the job.
The 3 dB reference level
The cutoff is defined at −3 dB relative to the minimum insertion loss in the passband. A filter with 0.5 dB minimum loss therefore reaches its cutoff at −3.5 dB absolute. This is why two filters quoted at the same cutoff can behave differently in a receiver chain.
Filter order and response type
Order sets the steepness of the skirt, and the response family sets where the corner actually lands. A Butterworth design is −3 dB at the nominal cutoff whatever its order, while a Chebyshev design places the cutoff at the edge of its passband ripple. In the insertion loss design method, a low-pass prototype is normalised to 1 rad/s, then scaled to the real cutoff and system impedance through the g-values.
Component parasitics and system impedance
Calculated values assume ideal parts. In hardware, inductor self-capacitance, capacitor ESL, PCB trace inductance and a mismatched source or load all pull the corner, which is why a filter is tuned on a network analyser rather than trusted from a datasheet alone.
Cutoff Frequency Formulas by Filter Type
| Filter type | Cutoff or bandwidth formula | Response | Typical use |
|---|---|---|---|
| Low-pass |
fc = 1 / (2πRC) fc = 1 / (2π√(LC)) |
Passes below fc, rolls off above | Power rail filtering, harmonic rejection |
| High-pass | fc = 1 / (2πRC) | Passes above fc, blocks DC | DC blocking, image and LO leakage rejection |
| Bandpass |
BW = fH − fL f0 = √(fL × fH) |
Passes fL to fH, rejects both sides | Wi-Fi, cellular and base station front ends |
| Band-stop | BW = fH − fL | Rejects fL to fH, passes the rest | Notching a carrier, EMI suppression |
Where fc is the cutoff frequency, fL and fH are the lower and upper cutoff frequencies, f0 is the centre frequency and BW is the bandwidth. The RC equations describe a first-order circuit; for an ideal lossless LC filter the corner sits at the resonant frequency. Higher-order designs keep the same cutoff definition but add poles and zeros around it.
A band-stop section is specified the other way round: the notch width matters more than the cutoff, because the passband must stay untouched. That is why narrow, deep notches are usually built as cavity or cavity bandreject filters rather than as a wide low-pass.
A Worked Bandpass Filter Example
Take an RF bandpass filter specified at a centre frequency of 2.4 GHz with a 3 dB bandwidth of 100 MHz.
- Centre frequency f0: 2.4 GHz
- 3 dB bandwidth: 100 MHz
- Lower cutoff fL: 2.4 − 0.05 = 2.35 GHz
- Upper cutoff fH: 2.4 + 0.05 = 2.45 GHz
fL = f0 − BW / 2 fH = f0 + BW / 2
2.35 GHz to 2.45 GHz — the effective passband of this filter
Check the centre frequency against the geometric mean: √(2.35 × 2.45) = 2.3995 GHz, within 0.02% of the arithmetic value. For narrow-band filters the two definitions are interchangeable; for wideband designs the geometric mean is the correct one and the arithmetic mean drifts. Filters of this type are commonly realised as small size band pass cavity filters when the rejection requirement is tight.
Note what the number means in practice: inside 2.35–2.45 GHz the signal passes with insertion loss, and outside it the signal is attenuated progressively rather than cut off instantly. The 20 dB bandwidth of this filter will be noticeably wider than 100 MHz, and the ratio between the two is the shape factor you should specify alongside the bandwidth.
How to Shift the Cutoff Frequency in Practice
Lumped LC designs
Change L or C, or both. Lowering capacitance raises the corner; adding inductance lowers it. Keep an eye on component Q, because a low-Q inductor flattens the skirt instead of moving it cleanly. Compact small size LC filters are usually re-tuned at the prototype stage rather than in the field.
LTCC and ceramic parts
The cutoff is set inside the ceramic stack: electrode length and overlap define the effective inductance and capacitance, dielectric constant sets the scaling, and layer count sets the order. Once tooled, the response is stable but not adjustable, so LTCC filters are specified early and frozen with the PCB.
Cavity and dielectric resonator parts
In a cavity filter the cutoff follows the resonator length and the iris coupling, and tuning screws trim each resonator after assembly. Dielectric resonator designs behave the same way with the puck size and its mode; because Q is high, the transition band is narrow and the dielectric resonator filter family covers roughly 400 MHz to 7 GHz.
Frequently Asked Questions
Does a higher cutoff frequency mean better filter performance?
No. The cutoff only marks where the response crosses −3 dB; it says nothing about insertion loss, rejection or selectivity. A filter with a higher cutoff and a shallow skirt can be worse than a lower-cutoff design with a steep one.
What is the difference between cutoff frequency and centre frequency?
The centre frequency is the middle of a bandpass response; the cutoff frequencies are its two edges. For a narrowband filter the centre is close to the arithmetic mean of fL and fH; for a wideband filter the geometric mean √(fL × fH) is the definition that keeps the response symmetrical on a logarithmic frequency axis.
Can the cutoff frequency be changed after the filter is built?
Only within limits. Cavity and waveguide filters have tuning screws that move each resonator by a small percentage. SMD LC, LTCC and thin-film parts are fixed once assembled — changing the corner means changing the values or re-tooling the layout.
Why do the 3 dB and 20 dB bandwidths differ?
Because the skirt is not vertical. The 20 dB bandwidth is always wider than the 3 dB bandwidth, and the ratio between them — the shape factor — is the honest measure of selectivity. When the operating frequency moves into the microwave range, low-loss narrow skirts are easier to reach with distributed structures such as waveguide filters.
Designing the Cutoff Around Your System
Determining a cutoff frequency is a system decision before it is a formula. Start from the band the application must carry, add margin for temperature and tolerance, decide how steep the transition has to be, and only then choose a topology: lumped LC for compact low-cost designs, ceramic and LTCC for surface-mount radios, cavity and dielectric resonator parts for narrow bands with high rejection, waveguide for the upper microwave range.
Whichever route you take, specify the cutoff together with insertion loss, 3 dB and 20 dB bandwidths, rejection at defined offsets, power handling and package — a cutoff alone is not a specification. Cavity filters from Yun Micro, for example, cover 200 MHz to 40 GHz in band-pass, low-pass, high-pass and band-stop versions, which is usually the range where a single topology stops being enough.
Need the cutoff pinned down for your band?
Send the band edges, the rejection you need and the package limit. Yun Micro designs and manufactures RF and microwave passive components from 10 MHz to 40 GHz — LC, cavity, dielectric resonator, LTCC and waveguide filters — in an ISO 9001:2015 plant, with every unit tested before shipment.
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