What is the filter cutoff frequency?

The filter cutoff frequency (also called the -3 dB frequency, half-power frequency, or corner frequency) is where the magnitude response drops to 1/sqrt(2) of the passband value, corresponding to -3.01 dB or half the power. For a lowpass filter: f_c = 1/(2*pi*RC) for a simple RC circuit. For an Nth-order Butterworth: the cutoff is defined as the frequency where |H(jw)|^2 = 1/2. For Chebyshev filters: the cutoff is the frequency at the edge of the equiripple band, which corresponds to -ripple dB (not -3 dB). This distinction matters when comparing filter specifications across types.

What is waveguide cutoff frequency?

For rectangular waveguide, the cutoff frequency of the TE_mn or TM_mn mode is: f_c = (c/2) * sqrt((m/a)^2 + (n/b)^2), where a is the broad wall dimension and b is the narrow wall dimension. The dominant mode TE10 has: f_c = c/(2a). For WR-90 waveguide (a = 22.86 mm): f_c(TE10) = 6.56 GHz. The usable bandwidth is from 1.25*f_c to 1.89*f_c (approximately 8.2-12.4 GHz for WR-90), limited at the low end by high dispersion and at the high end by the onset of the TE20 mode.

What happens below cutoff in a waveguide?

Below the cutoff frequency, the propagation constant becomes imaginary, meaning the wave does not propagate but instead decays exponentially: E = E_0 * exp(-alpha*z), where alpha = (2*pi/lambda) * sqrt(1 - (f/f_c)^2). The attenuation is approximately 54.6 dB per cutoff wavelength. This evanescent behavior is useful in two ways: (1) Waveguide below cutoff acts as a high-pass filter, providing enormous attenuation (used in EMI shielding and ventilation panels). (2) Evanescent-mode waveguide filters use the reactive coupling of evanescent modes between resonant cavities to create very compact, high-performance bandpass filters.

Fundamental Concepts

Cutoff Frequency

/kut-off free-kwen-see/ (f_c)

Cutoff Frequency has two meanings in RF: (1) Filter: the -3 dB (half-power) point defining the passband edge. (2) Waveguide: the minimum frequency for mode propagation; below cutoff, waves are evanescent and decay at ~54.6 dB per cutoff wavelength. For rectangular waveguide TE₁₀: f_c = c/(2a), where a is the broad wall dimension.

Category: Fundamental Concepts

Filter: -3 dB point

Waveguide: f_c = c/(2a)

Understanding Cutoff Frequency

Cutoff frequency is one of the most fundamental parameters in RF. For filters, it tells you where the passband ends and the stopband begins. For waveguides, it tells you the lowest frequency the guide can carry. Both definitions share a common physics: below the cutoff, energy cannot propagate efficiently. In filters, the signal is attenuated. In waveguides, the wave becomes evanescent. Understanding cutoff is essential for selecting waveguide sizes, designing filters, and specifying the bandwidth of any RF component.

Cutoff Frequency Formulas

Waveguide cutoff:
f_c = c/(2a) (TE₁₀, rectangular)
f_c = 1.841c/(2πa) (TE₁₁, circular)

RC filter cutoff:
f_c = 1/(2πRC)

LC filter cutoff:
f_c = 1/(2π√(LC))

Transistor f_T:
f_T = g_m/(2πC_total)

Standard Waveguide Cutoff Frequencies

Waveguide	Band	a (mm)	f_c TE₁₀	Usable Range
WR-284	S-band	72.14	2.08 GHz	2.60-3.95 GHz
WR-137	C-band	34.85	4.30 GHz	5.85-8.20 GHz
WR-90	X-band	22.86	6.56 GHz	8.20-12.4 GHz
WR-42	K-band	10.67	14.1 GHz	18.0-26.5 GHz
WR-10	W-band	2.54	59.0 GHz	75-110 GHz

Key Equations

Decibel conversion:
Power: dB = 10log(P₂/P₁)
Voltage: dB = 20log(V₂/V₁)

dBm to watts:
P(W) = 10^{(dBm−30)/10}
0 dBm = 1 mW, +30 dBm = 1 W

Wavelength:
λ = c/f = 300/f(MHz) meters

Comparison

Context	Formula	Example	Application	Notes
WR-90 (TE10)	c/(2a)	6.56 GHz	X-band WG	a=22.86mm
RC LP filter	1/(2πRC)	1.59 MHz (R=100,C=1nF)	EMI filter	Simple
LC LP filter	1/(2π√LC)	7.1 MHz (L=1μH,C=0.5nF)	RF filter	Resonant
CMOS 65nm f_T	g_m/2πC	~150 GHz	Transistor	Technology limit
SiGe HBT f_T	g_m/2πC	~300 GHz	mmW design	Highest Si-based

Common Questions

Frequently Asked Questions

Filter cutoff?

-3 dB (half power) point. Simple RC: fc = 1/(2piRC). Butterworth: |H|^2 = 1/2 at fc. Chebyshev: edge of equiripple band (not -3 dB). The definition varies by filter type.

Waveguide cutoff?

TE10: fc = c/(2a). WR-90: fc = 6.56 GHz, usable 8.2-12.4 GHz. Below cutoff: evanescent mode, ~54.6 dB/wavelength decay. Upper limit set by next mode (TE20).

Below cutoff?

Wave decays exponentially. Used in EMI shielding (ventilation panels = waveguide below cutoff). Evanescent-mode filters exploit reactive coupling between cavities for compact, high-performance BPFs.

Related Terms

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