Design of Cavity Bandstop Filters with Sharp Attenuation Skirts for Interference Mitigation

1. Introduction: Bandstop Filters in Interference Mitigation

1.1 Background

A bandstop filter passes most frequencies while strongly attenuating a specific band; it is the complement of the bandpass filter. When the stopband is narrow and the cavity Q high, it is generally called a notch filter. In RF and microwave systems it is used to suppress known narrowband interferers, adjacent-channel noise or self-oscillation without disturbing the rest of the spectrum. [1][2][3]

Typical scenarios include duplex interference suppression in base stations, image-noise removal in radar, adjacent-station protection in broadcasting, and spectrum cleanup in multi-band coexistence environments. In public-safety communications, a bidirectional amplifier (BDA) must pass the target public-safety band while suppressing adjacent commercial cellular bands — such as 800 SMR or LTE Band 14 — by more than 45 dB to prevent uplink/downlink cross-interference. Because a bandstop filter attenuates only a specific narrow band and barely affects passband insertion loss, it is a more precise and lower-loss solution than a broadband attenuator. [4][5][6]

The cavity structure uses air as its transmission medium and offers a rugged build, stable and reliable performance, high unloaded Q, good heat dissipation and distant higher-order spurious passbands. It is therefore particularly well suited to narrowband, deep-rejection bandstop responses and is one of the most common practical implementations. [5][6][25]

1.2 Motivation and Objectives

As spectrum grows scarcer, isolation requirements between adjacent systems keep rising while the available guard band keeps shrinking. This imposes two simultaneous and mutually constraining demands on the bandstop filter: rejection greater than 60 dB within the stopband, and recovery to below 2 dB of passband insertion loss over a very short frequency interval on either side. Classical Chebyshev and Butterworth prototypes place transmission zeros only at infinite frequency and cannot produce a sufficiently steep rise near the stopband edges.

The objectives of this study are:

• (1)to establish quantitative definitions of skirt, shape factor and selectivity as a common language for specification;
• (2)to review systematically the four principal techniques for introducing finite-frequency transmission zeros with a limited cavity count;
• (3)to analyse the composite attenuation and inter-stage matching issues arising when a cavity bandstop filter is cascaded with lowpass or highpass filters;
• (4)to map the findings onto TEMWELL's production specifications using public-safety interference mitigation as a case study; and
• (5)to clarify the instrument dynamic-range conditions required for deep-rejection measurement, so that specification verification is not distorted.

2. Defining the Attenuation Skirt: Shape Factor and Selectivity

2.1 Basic Response of a Cavity Bandstop Filter

A cavity bandstop filter can be viewed as one or more high-Q resonant cavities shunted across a transmission line. At the resonant (notch centre) frequency, energy entering the cavity is reflected back out of phase with the original signal, creating a virtual short of near-zero impedance across the line; most of the applied energy is reflected back toward the source by the resulting impedance mismatch, with only a small fraction absorbed and dissipated in the cavity. Away from the centre frequency the cavity presents a high impedance and provides almost no attenuation. [25]

Fig. 1 shows the typical S-parameter response of an f0 = 885 MHz cavity bandstop filter. Three essential characteristics are visible: S11 approaching 0 dB within the stopband (near-total reflection), passband insertion loss held below 2 dB, and the rapidly recovering skirts on either side of the stopband. This reflective — rather than absorptive — mechanism is a key premise for high-power system design.

2.2 Skirt, Shape Factor and Selectivity

The skirt describes how steeply the response transitions from the passband (low attenuation) to the stopband (high attenuation); the faster the transition, the better the selectivity. Selectivity reflects how much of the filter's total bandwidth is consumed by the transition band — the narrower that band, the more guard band is saved and the higher the spectral efficiency. [7][8]

The core metric for skirt steepness is the shape factor, defined as the ratio of bandwidths measured at two different attenuation levels:

For a bandpass filter, F2 and F3 are the passband (3 dB) edge frequencies and F1 and F4 the stopband (60 dB) edges. In a bandstop filter the roles are reversed: the 3 dB crossings lie outside and the 60 dB crossings inside, so the shape factor is computed as the 3 dB bandwidth divided by the 60 dB bandwidth. In either case, a value closer to unity indicates a steeper skirt and better selectivity. [9][10][7]

Fig. 2 marks the four key crossings for the design target of this paper. With a six-pole Chebyshev bandstop prototype (0.05 dB passband ripple, FBW = 0.393), BW3dB = 310 MHz and BW60dB = 128 MHz give a shape factor of 2.43. The resulting 60 dB rejection range matches the 820–950 MHz specification of the TEMWELL 885 MHz standard model, and the passband edges (745 / 1052 MHz) are close to the published 738 / 1042 MHz.

The influence of pole number N on the shape factor follows directly from the Chebyshev prototype. Table 1 lists the theoretical shape-factor limits and design implications for 0.05 dB passband ripple.

Table 1 shows that the shape factor improves rapidly with pole number but with diminishing returns, while every added pole raises passband insertion loss and tuning complexity. When a sharper skirt is required with a limited cavity count, introducing finite-frequency transmission zeros is therefore usually more efficient than simply adding poles — the subject of Section 3.

3. Design Techniques: Introducing Transmission Zeros

3.1 Operating Principle of Transmission Zeros

The core technique for achieving a sharp skirt is to introduce finite-frequency transmission zeros (TZs) into the transfer function, driving S21 toward zero (infinite attenuation) at chosen frequencies. Classical Chebyshev and Butterworth prototypes generate transmission zeros only at infinite frequency; adding cross-coupling or multiple coupling paths creates zeros at finite frequencies, markedly improving both skirt steepness and stopband depth. [11][12][13]

3.2 Cross-coupling Bridges

An additional coupling path between non-adjacent resonators creates two or more propagation routes through the filter. Where the two paths are of comparable magnitude and opposite phase, cancellation occurs and a transmission zero is formed at that frequency. This raises both notch depth and skirt slope without increasing the cavity count. [12]

Fig. 3(a) illustrates the common M14 cross-coupled topology using a four-pole structure; Fig. 3(b) compares a single-cavity notch with a cross-coupled multi-cavity design. The latter forms two additional transmission zeros within the stopband, expanding the region of ≥ 60 dB rejection from a few tens of megahertz into a flat, deep stopband while markedly steepening both skirts.

3.3 Multi-network Coupling

Mutual suppression between different coupling networks places one transmission zero either side of the stopband centre, producing a symmetric dual-zero notch response. This is particularly effective where a wide and deep stopband is required. A reported wideband bandstop filter with three transmission zeros measured deep rejection at 1.39 GHz (46 dB), 2.14 GHz (55 dB) and 2.89 GHz (53 dB), achieving 87.3% fractional bandwidth at the 20 dB rejection level — confirming that multi-zero techniques can deliver both deep rejection and a wide stopband. [14][15]

3.4 Narrowband High Unloaded-Q Cavity Design

Raising the unloaded Q of each cavity moves the transmission poles and zeros closer to the real axis, making the stopband attenuation curve both steeper and deeper. In practice, Q is raised principally by increasing the physical cavity size (mechanical Q). Larger cavities improve selectivity without significantly increasing insertion loss, but this is a design change rather than a field adjustment, and in most cases it does not alter the depth limit of the selectivity. [11][25]

3.5 Coupling-Matrix Synthesis

Suitable for narrowband designs with fractional bandwidth under 10%. Designing the coupling coefficients within the coupling matrix gives direct control over transmission-zero placement and stopband selectivity; physical dimensions are then extracted by eigenmode simulation. A published narrowband high-rejection cavity filter followed exactly this flow: coupling-matrix synthesis software fixed the order, zero configuration and topology, yielding the coupling bandwidth and quality factor, which were then verified by HFSS full-wave modelling. Measurements achieved 50 dB rejection at 2515 MHz, in-band insertion loss of about 5 dB and return loss better than 20 dB. [13][26]

4. Composite Attenuation: Cascading with Lowpass and Highpass Filters

An ideal bandstop filter can be regarded as a lowpass and a highpass filter combined in parallel: the lowpass section passes signals below the stopband centre, the highpass section passes those above it, and the intersection forms the stopband. In practical cavity designs, however, a single bandstop filter attenuates only near the notch centre and its selectivity vanishes rapidly further out, making it unsuitable on its own where both a notch and broadband suppression are required. [1][5][25]

The usual remedy is to cascade the cavity bandstop filter with a lowpass (LPF) or highpass (HPF) filter, adding attenuation in a chosen direction outside the stopband. Fig. 4 uses a cascaded 1.5 GHz lowpass as the example: the bandstop filter alone offers virtually no rejection at the third harmonic of the carrier (≈ 2655 MHz), whereas the composite response reaches about 60 dB there — while the depth and skirts of the 885 MHz notch remain entirely unaffected.

The TEMWELL Standard Cavity Bandstop Filter line illustrates this: its specifications define several passband intervals at once (for example DC to one frequency, plus a higher frequency up to several GHz) while delivering more than 60 dB of rejection in the central stopband. This wide-dual-passband, narrow-deep-stopband structure is precisely the embodiment of combined lowpass / bandstop / highpass design. Table 3 summarises the typical specifications, showing that passband range and rejection depth follow a consistent design principle as centre frequency rises. [16][5]

Note that the composite attenuation is not a simple linear sum: inter-stage impedance matching and return-loss interaction must be taken into account. Within its stopband the bandstop filter approximates a short circuit with a reflection coefficient near unity; if the input impedance of the following stage is not properly handled over that band, reflected energy oscillates between stages, degrading passband insertion loss or introducing unwanted ripple. The whole multi-stage structure should therefore be jointly optimised in electromagnetic simulation rather than designed stage by stage and simply cascaded. [17][18]

5. TEMWELL Case Study: Bandstop Design for Public-Safety Band Interference

Public-safety communication systems — the dedicated 800 MHz and 700 MHz police, fire and EMS networks — typically sit immediately adjacent to commercial cellular bands in urban areas, making them vulnerable to intermodulation interference and blocking from high-power neighbours. The standard remedy is a bandstop filter at the front end of the bidirectional amplifier (BDA), suppressing the adjacent interfering band (such as 800 SMR or LTE Band 14) by more than 45 dB while preserving low insertion loss within the public-safety band itself. [4]

Three specification characteristics define this scenario. First, the guard band is extremely narrow — interferer and protected band are often only a few megahertz apart, demanding a shape factor near or below 2. Second, rejection depth is high — 45 dB is the floor and practical specifications are usually written at 60 dB. Third, passband loss is critical — every additional decibel of insertion loss at the BDA front end directly erodes receive sensitivity. The simultaneous presence of all three is precisely why the high-Q cavity bandstop filter has no ready substitute.

The TEMWELL Standard Cavity Bandstop Filter series is designed for exactly this need, offering several narrowband high-rejection models across 700–1600 MHz with rejection generally exceeding 60 dB and passband insertion loss held within 2.0 dB — directly applicable to interference isolation at public-safety base-station front ends. Such designs typically combine a multi-cavity coupled structure with transmission-zero techniques, pulling deep rejection out rapidly at the stopband edges while maintaining low passband loss, meeting the demanding narrow-guard-band, high-rejection requirement of public-safety applications. [5][4]

A second, often overlooked application is transmitter sideband-noise reduction. Besides the carrier at its assigned frequency (typically 50 W / +47 dBm to 100 W / +50 dBm), a transmitter also radiates harmonics and broadband noise outside its allocated bandwidth; regulations require such emissions to be attenuated by 43 + 10 log(P) dB. The notch filter's advantage is that it can attenuate only a few hundred kilohertz from the carrier, whereas a bandpass filter often needs more than 1 MHz of guard band — sometimes several cascaded stages — for the same result. Its limitation is equally clear: the notch is effective over only a very narrow band, so it is unsuitable for sites with co-located transmitters or multiple same-band receivers. [25]

6. Measurement Considerations: Dynamic Range for Deep Rejection (> 60 dB)

Once stopband rejection reaches 60 dB or more, the dynamic range of the measurement system itself becomes the limiting factor on result credibility. A vector network analyser's dynamic range is the difference between the maximum measurable power and the minimum measurable power, the latter set by the receiver noise floor. If the filter's stopband attenuation approaches or exceeds that range, the measured trace reflects the instrument's own noise floor rather than the true stopband response. [19][20][21][22]

Fig. 5 quantifies the effect: the same filter, with a true rejection depth of about 95 dB, yields entirely different conclusions under three IF bandwidth settings. At 30 kHz IF bandwidth (dynamic range ≈ 55 dB) the stopband trace is completely masked by the noise floor and rejection is under-reported at about 55 dB — failing the 60 dB specification. At 1 kHz (≈ 72 dB) the part passes, though the reading still does not reflect the true depth. Only at 10 Hz with averaging enabled (≈ 92 dB) does the measurement approach the real response.

As a rule of thumb, the VNA dynamic range should exceed the maximum attenuation specification of the device under test by at least 3–6 dB. For a 60 dB rejection target, allowing for measurement tolerance, a dynamic range of roughly 100–120 dB is normally recommended. Most modern VNAs provide about 120 dB and can meet this requirement, but precision measurement still calls for attention to the settings listed in Table 4. [21][22]

Where dynamic range is inadequate, the result shows either an artificially low stopband rejection value or noise-floor ripple on the trace, both of which invite misjudgement of the filter's true performance. Verification of deep-rejection specifications must therefore begin by confirming adequate instrument margin, and the measurement report should record the IF bandwidth, averaging count and source power used. [19][22]

7. Conclusions: Selection and Customisation Guidelines

7.1 Findings

This study of cavity bandstop filters with sharp attenuation skirts reaches the following conclusions:

• (1)The shape factor is the common language of specification. For a bandstop filter it is computed as the 3 dB bandwidth divided by the 60 dB bandwidth — the inverse of the bandpass convention. The six-pole configuration here gives 2.43, a useful reference for most adjacent-band suppression scenarios.
• (2)Adding poles yields diminishing returns. Table 1 shows the shape factor improving sharply from 30.1 at N = 2 to 2.38 at N = 6, but only to 1.98 at N = 7 and 1.74 at N = 8, while passband insertion loss and tuning difficulty continue to rise.
• (3)Transmission zeros are the more efficient route. Where cavity count is constrained, cross-coupling or multi-network coupling delivers both a steeper skirt and a deeper, flatter stopband (Fig. 3).
• (4)Cascades require joint optimisation. With a stopband reflection coefficient near unity, a bandstop filter cascaded with an LPF or HPF must be optimised as a complete multi-stage structure to avoid inter-stage reflection degrading the passband.
• (5)Measurement dynamic range is a precondition of verification. Insufficient range systematically under-reports rejection depth (Fig. 5) and can cause conforming parts to be rejected.

7.2 Selection and Customisation Guidelines

When selecting or customising a cavity bandstop filter, the decision sequence in Table 5 is recommended.

Finally, customisation specifications should be derived backwards from the application. For public-safety interference mitigation, prioritise a narrowband high-rejection design (such as the TEMWELL series with rejection above 60 dB and insertion loss within 2.0 dB), and confirm that the passband range covers every adjacent signal interval requiring protection — only then will the deployed system deliver the expected isolation. [4][5]

7.3 TEMWELL's Production-Ready Capabilities

Drawing together the design, cascading and measurement themes above, Table 6 summarises five TEMWELL capabilities in cavity bandstop filters that are production-ready today and map directly onto customer value.

TEMWELL, headquartered in Taipei with more than 25 years of RF filter design and manufacturing experience and partners in over 20 countries, offers a complete portfolio of cavity, helical, SMD ceramic and SAW filters together with diplexers, duplexers and multiplexers. The bandstop design and measurement methods presented here map directly onto TEMWELL's current engineering and production capabilities, with customised delivery within a 7–10-day lead time.