Reflectionless RF Filter: Theory and Topologies

Key Takeaways

• Reflections greatly disturb signal propagation pathways, up to irreversible damage from the reflected energy.

• Reflectionless RF filters use symmetric filter networks to absorb, rather than reflect, frequency energy outside the pass-band.

• Traditional filters have limits to cascading due to reflections, opening up new network topologies.

Reflectionless RF filters ensure signal propagation without any distorting effects.

Filters are a fundamental part of circuit design, targeting desirable signals for propagation while restricting those that are unnecessary or disruptive. While necessary in nearly every circuit application, traditional models do not account for the energy propagation that does not pass through the filter. Some of this will return to its source in a process known as reflection, which can undermine performance and potentially damage the circuit. A reflectionless RF filter protects systems and enhances communications by severely curbing these effects while enabling additional filter topologies.

Applications Where Reflectionless RF Filters Improve Circuit Characteristics

How Reflections Degrade Signal Quality

Filtering is an effective tool to remove unwanted component frequencies from signals outside the pass-band of the network, allowing the desired bandwidth to pass through unabated. Rejection of these signal components occurs due to impedance mismatches at the receiver end that block components outside the pass-band. At the same time, some of this energy dissipates as heat due to resistive loss; a considerable amount returns to the source through reflection. The reflected energy can wreak havoc on a transmission line, forming a standing wave if reflected a second time at the source, leading to multiple detrimental effects:

• Gain compression - When an amplifier leaves the linear region of its transfer function, the signal output is no longer linearly proportional to signal input, creating a distortion effect that reshapes the entire waveform.
• Parasitic oscillations - A coupling between the output and input energy of an amplifier stage can produce significant EMI via radiation or by inductively coupling to another nearby line. The generated power can also overload connected circuitry if it grows beyond maximum ratings.
• Resonance - Reflection at the resonant frequency can produce significantly higher voltages and currents as the energy oscillates between electrical and magnetic field maximums. Even if this disturbance doesn’t damage the network, it can cause noise and distortion.
• Stability loss - Excessive reflections can push a circuit’s response away from its center of stability and out of its stability region, leading to borderline or full-blown oscillation behavior at the output.
• Dynamic range loss - Intermodulation products from mixers can reflect from adjacent filters in the RF chain that can recombine with the fundamental signal of the mixer and produce a range of undesirable frequencies that limit the dynamic range before reflection.

Traditional assembly options to combat reflections are limited in scope, and their size may preclude them from dense assemblies or small form factors. While the best solution (often, as is the case) is removing the reflection energy at the source, another possibility is a filter design that absorbs rather than reflects the energy outside the pass-band. In this design, the filter and surrounding area may need to be more thermally robust to avoid damage or poor performance owing to the additional dissipated heat. 

The Requirements and Improvements of Reflectionless RF Filters

The most basic form of the reflectionless RF filter begins with an even/odd mode analysis, where a two-port network has the same amplitude excitations at both ends, either in-phase (even) or out-of-phase (odd). This amplitude symmetry is significant as it allows the network analysis to reduce the network nodes to open or ground for even and odd modes, respectively. These conditions are crucial because of two S-parameter equations:

Similar to the odd-mode excitations, the reflection coefficients (gamma) must also be equal in amplitude and opposite in sign to fulfill the criteria S₁₁ = 0 and S₂₁ =  Γ_even = Γ_odd. Maintaining these two conditions in an idealized filter network means that all reactive components (i.e., inductors and capacitors) are equal, and all resistors must be equivalent. In actuality, real-world effects like parasitics and performance drift in components of a genuinely equivalent lumped-element model are unrealizable. Fortunately, designers can still reap the benefits of a nearly reflectionless RF filter.

The simplified reflectionless filter model does not account for more complex transmission implementations:

• Transmission lines - At high enough frequencies, the limitations of a lumped-element model become more apparent as parasitic losses cause efficiency to plummet. Instead of discrete components, designers will use quarter-wavelength stubs as capacitive or inductive contributors to build a symmetric filter with a balanced impedance throughout (hence the quarter-wavelength stubs).

• Diplexing - The lumped-element reflectionless filter is a four-port design that inherently “isolates” between its branches, i.e., absorbed energy outside of the pass-band on either input dissipates at the resistive load on the same side of the filter. Practically, some of the energy on one input makes it to the other leg of the filter before dissipating across the series inductance branch at the output. However, a coupling path within the filter can improve the attenuation of the stop-band response.

Designers shouldn’t expect to build a reflectionless circuit every time a circuit calls for it, as many manufacturers provide various filter topologies and technology for simple integration. Advantageously, reflectionless RF filters support a high level of cascadeability: regular filters suffer from rippling and instability when chained together, but reflectionless filters allow designers to enhance the signal response of a single filter while only having to account for the additional insertion loss of each filter stage. Not only will circuit designers see a better response in a pass/stop-band filter built of complementary filters, but the building-block high- or low-pass filter can add to itself meaningfully.

Cadence Solutions for Signal Integrity

Reflectionless RF filters offer numerous improvements over traditional filters by accounting for the reflected energy that degrades signal response and reduces service life via dissipation. Eliminating reflections adds another wrinkle to filter design and, by extension, simulation. For the cases where a custom reflectionless filter is beneficial, designers rely on the extensive modeling capabilities of the Cadence PCB Design and Analysis Software suite for unparalleled circuit analysis capabilities–coupled with the powerful yet easy-to-use OrCAD PCB Designer, board design has never been faster. 

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