How do you design a bandstop filter from a bandpass prototype?

A bandstop filter is designed by applying a frequency transformation to a lowpass prototype. The transformation maps the lowpass stopband (DC to cutoff) to the bandstop rejection band and maps the lowpass passband to both passbands of the bandstop response. In circuit implementation, every series inductor in the lowpass prototype becomes a parallel LC resonant circuit (series arm), and every shunt capacitor becomes a series LC resonant circuit (shunt arm). The LC values are calculated from the lowpass prototype element values, the desired center frequency f_0, and the fractional bandwidth. This approach works for Butterworth, Chebyshev, and elliptic response types. For microstrip implementation, coupled-line sections or open-circuit stubs replace the LC elements.

When should you use a bandstop filter versus a bandpass filter?

Use a bandstop filter when you need to remove a specific narrow interference from a wideband signal while preserving all other frequency content. Common scenarios include: rejecting a strong nearby transmitter leaking into a wideband receiver, removing LO feedthrough or mixer spurious products, suppressing a harmonic of a local oscillator, and filtering specific EMI frequencies from a measurement setup. Use a bandpass filter when you want to select a specific signal band and reject everything else. The choice depends on whether the wanted signal occupies a wider bandwidth than the interference (use bandstop) or a narrower bandwidth (use bandpass). In many receiver architectures, both are used: a bandpass preselector selects the operating band, and a notch filter removes a known in-band interferer.

Passive Components

Bandstop Filter

/band-stop fil-ter/

A filter that attenuates signals within a specific frequency band (the stopband) while passing all frequencies above and below with minimal insertion loss. Also called a band-reject or notch filter, a bandstop filter is the frequency-domain complement of a bandpass filter. It is used to remove specific interfering signals, such as a nearby transmitter's carrier, LO feedthrough, mixer spurious products, or EMI sources, from a wideband RF signal path without disturbing the desired frequency content.

Category: Passive Components

Notch Depth: 20 to 80 dB typical

Also Called: Band-reject, notch filter

Understanding Bandstop Filters

A bandstop filter creates a frequency "hole" in an otherwise flat passband. The rejection band is defined by its center frequency (f₀), 3 dB rejection bandwidth (BW_3dB), and maximum attenuation depth. The fractional bandwidth (BW_3dB/f₀) can range from less than 0.1% for a crystal notch filter to 50% or more for a wideband coupled-line design. The filter's quality factor Q = f₀/BW_3dB determines how narrow the rejection band is; higher Q means a sharper, more selective notch.

Bandstop filters are implemented in two fundamentally different ways. A series-connected parallel LC resonator blocks signals at resonance (presents high impedance) while passing all other frequencies. A shunt-connected series LC resonator shorts signals at resonance (presents low impedance) to ground while appearing as an open circuit at other frequencies. Multi-section bandstop filters cascade these elements to achieve steeper rejection slopes and deeper notch depths, following the same Butterworth, Chebyshev, or elliptic approximation theory used for other filter types.

Bandstop Filter Parameters

Center Frequency:
f₀ = 1 / (2π√(LC))

Quality Factor:
Q = f₀ / BW_3dB

Fractional Bandwidth:
FBW = BW_3dB / f₀ = 1/Q

Lowpass-to-Bandstop Transformation:
ω → FBW / (ω/ω₀ - ω₀/ω)
Series L → Parallel LC (series arm)
Shunt C → Series LC (shunt arm)

Stub Notch Filter (quarter-wave):
Rejection at f₀ = ∞ (ideal open stub), > 30 dB practical
Stub length = λ/4 at f₀

Bandstop Filter Topologies

Topology	Notch Depth	Fractional BW	Frequency Range	Application
Lumped LC	20-40 dB	5-50%	DC to 3 GHz	General purpose, EMI suppression
Crystal Notch	40-60 dB	0.01-0.1%	1-200 MHz	IF interference, oscillator spurious
Cavity Notch	40-80 dB	0.1-2%	100 MHz to 18 GHz	Transmitter harmonic, co-site
Microstrip Stub	20-35 dB	5-30%	500 MHz to 40 GHz	PCB-level interference rejection
Active (feedback)	30-60 dB	0.1-5%	DC to 500 MHz	Tunable, adaptive cancellation

Common Questions

Frequently Asked Questions

What is the difference between a bandstop filter and a notch filter?

A notch filter is a bandstop filter with a very narrow stopband, typically less than 1% fractional bandwidth. Notch filters target a single frequency (carrier leak, LO feedthrough, specific EMI) while passing everything else. A bandstop with 10% fractional bandwidth would not typically be called a notch. Notch filters use high-Q resonators (crystals, cavities, active circuits) for 40 to 80 dB depth in less than 1 MHz, while wider bandstop filters use coupled lines or lumped elements.

How do you design a bandstop filter from a lowpass prototype?

Apply the bandstop frequency transformation to a lowpass prototype: every series inductor becomes a parallel LC (series arm) and every shunt capacitor becomes a series LC (shunt arm). The LC values are calculated from the prototype element values, center frequency, and fractional bandwidth. This works for Butterworth, Chebyshev, and elliptic responses. For microstrip, coupled-line sections or open-circuit stubs replace the LC elements.

When should you use bandstop versus bandpass?

Use bandstop when removing a narrow interference from a wideband signal while preserving other content: nearby transmitter rejection, LO feedthrough, harmonic suppression, specific EMI. Use bandpass when selecting a specific band and rejecting everything else. The rule is: if wanted signal bandwidth is wider than interference bandwidth, use bandstop. If narrower, use bandpass. Many receivers use both: a bandpass preselector for the operating band plus a notch for known in-band interferers.

Related Terms

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