What are Reflectionless Filters?

Reflectionless filters (also known as Absorptive Filters) are specialized electronic filters that are designed to minimize or eliminate the signal reflection at their input and output ports across their entire bandwidth of operation. Unlike standard filters, which reflect the unwanted stopband signals back to the source, reflectionless filters provide seamless impedance across both the stop band and pass band, which improves the performance of the overall RF signal chain. These filters have S11 and S22 as close to 0 as possible.

Whenever there’s an impedance mismatch in a conventional filter, part of the signal is reflected back to the source and can cause some sort of interference, as that signal is then re-reflected and can then impact the integrity of the overall signal. 

Due to this characteristic, reflectionless filters are useful in applications where signal integrity is crucial, such as high-frequency communication systems, signal processing, and measurement systems.

Theory and Design Principle of Reflectionless Filters

The reflectionless filters are designed as symmetric networks, meaning that the left and right halves of the filter are mirror images of each other. This structure enables the use of an even-odd mode analysis technique. In even mode, the two ports are stimulated by signals of equal amplitude and phase, meaning there is no current passing across the symmetry plane. In the odd mode, the signals stimulated at the ports are equal in amplitude but opposite in phase (180 degrees out of phase). 

Using symmetry, the network can be divided in half. In the case of even mode, the nodes on the symmetrical plane are assigned as open-circuit, and in the case of odd mode, the nodes on the symmetrical plane are assigned as short-circuit. The overall reflection at the input is the sum (or superposition) of the reflections that occur in both the even mode and the odd mode. Thus, the reflection coefficient (S11) of the full two-port can be determined by considering the contributions from both the even and odd mode equivalent circuits. 

Mathematically, 

S11 = Reflection from even mode + Reflection from odd mode 

A low-pass, high-pass, band-pass, and band-stop filters can be created by choosing a filter topology whose reflection characteristic matches with the desired transfer characteristic (even-mode circuit), then creating the dual of the chosen filter topology (odd-mode circuit), then performing some topological modifications that result in the symmetry between the even/odd mode circuits without affecting the circuit behavior, and finally combing the two circuit-halves to form the final two-port filter network. For a filter to be reflectionless, the reflection coefficient (S11) should be zero, which implies that the even and odd mode reflection coefficients are equal in magnitude but opposite in phase.

Example of Reflectionless Filter Topology 

Consider a terminated high-pass filter as the even mode equivalent circuit and its dual as the odd mode equivalent circuit. The dual circuit can be constructed by exchanging the inductors with capacitors, series elements with shunt elements, etc. This ensures that the even and odd modes will have equal amplitude reflection coefficients with the opposite sign.

High Pass Filter and  the Dual CircuitThe first step is to exchange the positions of the series resistor and capacitor in the even mode equivalent circuit and change the grounding of some elements in the odd mode circuit from absolute to virtual. In the second step, open-circuited elements are added to the even-mode side (symmetry for even mode), and the capacitor is shorted at both ends on the odd-mode side (symmetry for odd mode).

The final reflectionless filter topology is given in the diagram given below, along with the simulated transmission coefficient of the reflectionless filter. All inductors L = Z0/ωz, capacitors C= Y0/ωz, and resistors R=Z0, where ωz is the frequency of the attenuation zero.

Final reflectionless topology  

Reflectionless filters absorb unwanted signals falling in the filter’s stopband, preventing reflections back to the source, and thus preserving the integrity of the signal. This reduces the generation of additional unwanted signals thereby improving the dynamic range of the system, without the use of additional components which also saves board space. These filters are ideal for applications where suppression of strong spurious signals and intermodulation products is needed.

As the reflectionless filters maintain good impedance in the stopband; they can be integrated with high-gain, wideband amplifiers without the risk of creating instabilities. They can be cascaded in multiple sections to provide a sharper and higher attenuation, while also preventing any standing waves that could affect the pass band. They have high power handling capability which extends the usability of these filters to the transmit path for inter-stage filtering.

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