The Impedance Transforming Property of the LMatch Network
Key Takeaways

Impedance transforming networks convert the load impedance into smaller values to make the circuit powerefficient.

There are various types of impedance transforming networks, including the Lmatch network.

The Lmatch circuit cancels the imaginary part of the source and load impedance and converts the real part to a lower value so that maximum power is transferred to the load.
The characteristic impedance of most RF circuits is 50 Ω
Characteristic impedances in RF and microwave systems most often take the fixed value of 50 Ω. Power amplifiers and antennas in RF systems have both an input and output impedance equal to 50 Ω. To achieve higher output power in RF systems with various load impedances, the insertion of an extra network made of inductors and capacitors is required. The intention behind this insertion is for the extra network to possess impedance transforming properties and convert the 50Ω into a smaller value at specific frequencies. If the impedance transforming network is lossless, the power delivered to it reaches the load impedance directly, and higher power is achieved.
Networks with impedance transforming properties often get confused with impedance matching networks. Impedance transforming networks convert the load impedance into smaller values to make the circuit powerefficient. There are various types of impedance transforming networks—in this article, we will focus on the Lmatch network, its impedance transforming properties, and its use in electronics circuitry.
The LMatch Network
The Lmatch network reduces load impedance
Lmatch circuits usually consist of an inductor and/or capacitor placed in the shape of the letter ‘L’. However, this placement can be changed according to the given input. There are several configurations of Lmatch circuits (shown above). The insertion of the Lmatch network between the source and load impedance converts the 50 Ω load resistance to a lower value. The Lmatch network then cancels the reactive part of the load impedance and reduces the value of the real part. This adjustment helps to deliver full power to the real part of the load impedance.
In summary, the Lmatch circuit cancels the imaginary part of the source and load impedance and converts the real part to a lower value so that maximum power is transferred to the load.
Equations Governing the LMatch Network
The Lmatch network in a power amplifier (PA) circuit
The Lmatch circuit inserted between the input and output in the figure above converts the load resistance R_{L} of 50 Ω to a lower value, R_{in}.
Let’s analyze how R_{L} transforms into R_{in} with the Lmatch network. The equivalent circuit reduction principles are the basic equations governing the Lmatch circuit impedance transformation.
The steps involved in transforming R_{L} into R_{in} are:

Convert C_{m} and R_{L} into series equivalent C_{S} and R_{m}, where Q_{C} is the quality factor of C_{m} and R_{L}.

Let the operating frequency of the power amplifier (PA) circuit. To make the circuit resistive (real part only), the inductor L_{m} is made to resonate with the capacitor C_{s}. The equation can be given by:

At resonance, the resistive input impedance R_{in} of the Lmatch network equals R_{m.}

The impedance transformation ratio of the Lmatch circuit is given by:

The quality factor Qm of the transformation network is given by:

The Lm and Cm values can be obtained from the quality factor Qm as follows:

The output power is enhanced with the incorporation of the Lmatch network. The power enhancement ratio is as follows:
The steps above can be pictorially represented below:
Lmatch network transformation
In power amplifiers, antennas, and antenna filters used in RF and microwave circuits, Lmatch circuits with impedance transforming properties can be inserted to ensure maximum power transfer to the load. The Lmatch network is one example of an impedance transforming network, however, there are a variety of such networks available to transform load impedance to smaller values. When working on RF and microwave systems, make sure that an impedance transformation network is incorporated to achieve powerefficient circuit operation.