#### The L-shaped Matching Network

Following the previous educational content on the “Basics of the Smith chart”, this document presents one of the four different types of matching networks: L, Pi, T, and series L-shaped networks. All of these networks can be used to match the load and source impedances, and their selection is determined by your requirements and applications.

###### L-shaped Matching Network

Two elements L-shaped matching networks are the simplest method to adjust for the imaginary components of the load and source impedances and provide the equal resistance to the source. In this manner, the circuit is matched, and the source will deliver the greatest amount of power to the load. For instance, in the figure below, the impedance that must be observed from the source is 6+6j. As a result, the imaginary part of the source will be compensated, and the real component will be the same for delivering maximum power to the load [1].

Presented below are four different L-shaped matching networks. For the low pass matching network, a parallel capacitor is required, whereas for the high pass, a series capacitor is required to block DC voltage [1].

In case of RL(load resistor) > RS(source resistor) a shunt element must be connected to the load, while for RL< RS the series element must be added to the load.

Importantly, the Q (quality factor) of the L-shaped matching network is dependent on the RS and RL. Due to the fact that these two impedances were assigned specified values during the circuit’s design, the Q will also have specific values based on these two resistors. It is a disadvantage that can be addressed in other matching networks such as Pi or T, by taking a virtual resistor into account, to achieve our desired Q. The Q of the L-shaped network has the smallest value compared to the other mentioned networks and can be achieved as [1]:

Where QS and QP are the Q of the series and shunt legs, respectively. Rp is Shunt resistor and RS is Series resistor.

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