L Network Impedance Matching With Two Components

Key Takeaways

• L network impedance matching is a simple filter that uses two reactive components.

• An L filter has a broad bandwidth yet weak response at its carrier frequency.

• Designers can combine multiple L filters to create a more robust response with a sharper Q-factor.

L network impedance matching requires only two reactive components.

Impedance matching is a fundamental topic in circuit power (delivery and losses), making it an excellent method to tighten up overall performance. Circuit stability also benefits from impedance matching by removing the reactive component of a line’s impedance that otherwise would contribute to standing waves, which can damage devices due to energy reflections. Finding the best solution for impedance matching is not a cut-and-dry solution, as designers will have to weigh the range of responsiveness against the pass/reject dB level. L network impedance matching is an excellent start when beginning with filter design or as a low-cost, broad bandwidth filter response.

How To Build an L Network Filter

The L network is a two-component filter network used independently and in cascading arrangements to build more complex filter networks. These can include the three-component networks (i.e., T and pi) or more intricate four-component networks. There’s an important distinction to be made between the pseudo-four-component networks (in actuality, functioning as a three-component network by combining the middle two components in parallel or series) resulting from two mirrored L networks and genuine four-component networks that use cascading L filters in a way that the middle components cannot as easily simplify. In any case, the L network is the essential building block for these filter networks. 

The L network gets its name from the simple arrangement: one component in series with a signal trace and one component in parallel, forming a right angle and rudimentary “L” shape. The most immediate advantage of the L network is the reduced component cost, making it the most readily realizable impedance-matching filter available (excluding a quarter-wavelength filter, which can only become efficient at high frequencies due to its shrinking length.) There are two dimensions to understanding the L network filter: orientation and component reactance. The filter network can use a parallel-series arrangement (i.e., the parallel component is closest to the source/furthest from the load) or vice versa, and the “first” component in the arrangement (again, depending on the source/load perspective) can either be an inductor or capacitor. Note that the L network uses an inductor and capacitor to build its response, so designating the reactance of one of the components fixes the other (similar to the orientation).

L/C L Filter Configurations

These two possible arrangements react differently to source current: a series-cap L filter will block low frequencies (i.e., DC) by shunting the current to ground through the parallel inductor; in other words, it functions as a highpass. Conversely, a parallel capacitor will short to ground at high frequencies, acting as a lowpass filter. However, the parallel and series orientation affect the overall impedance profile of the filter, too, with the parallel component responsible for the real resistance and the series component responsible for the series reactance. In this sense, it can be easier to consider impedance matching as the individual balancing of the resistance and reactance. Determining the relative arrangement of the parallel component to the series (since it essentially acts as a voltage divider) will depend on the greater resistance between the source and load for matching purposes.

L Network Impedance Matching Constraints

Any filter design will have to balance response bandwidth against the sharpness of the response; the behavior is the Q-factor of the system. In general, L network filters are considered low-Q — they operate well in a relatively large bandwidth around a carrier frequency but are significantly overdamped. In energy terms, the ratio of energy stored to the energy dissipated per oscillation cycle is low, making them liable to experience significant losses, which can also negatively impact the reliability of nearby components and board materials due to thermal wear. An L network simply cannot offer the sharp response of the higher-Q three- and four-component filters.

The nature of the design arbitrarily fixes the Q-factor of an L filter: between the source/load resistances, there are simply not enough variables to go around in the system. Therefore, the Q-factor is an unaddressable constraint in L filter networks, making the bandwidth/circuit response unsuitable for particular applications. Designers will want to ensure that the limited scope of the L filter can reasonably address the circuit’s performance needs. It’s also worth noting the method by which the filter removes excess energy can differ, and specific approaches are more beneficial depending on the topology:

• Absorption - The filter matches the system design to sink any stray reactance that could otherwise propagate through the system. This method implements a highpass filter design.
• Resonance - The filter generates an equal magnitude oppositely signed reactance to cancel the load/source reactance. This method implements a lowpass filter design.

With the noted restrictions of the Q-factor, L filters – unlike T/pi filters – do not have any inherent limitation on frequency. Depending on the topology, both lowpass and highpass networks are achievable.

Cadence’s Software Allows for Rapid Filter Design

L Network impedance matching is a simple filter matching method that lacks specificity but has a broad bandwidth application around the tuned frequency. While an L filter is competitive regarding component cost and board space, constraints on the Q-factor can limit its general applicability compared to more extensive and robust filter networks. Careful calibration of the system response is necessary for proper signal integrity; Cadence’s PCB Design and Analysis Software suite gives production teams a wide range of ECAD features. Incorporating impedance matching is a cinch with OrCAD PCB Designer, and comprehensive design rules through the Constraint Manager support customizable DFM productions.

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