Passive Matching Networks

Controlling impedances in RF circuits are essential to maximize power transfer between blocks and to reduce reflections caused by impedance discontinuities along a signal path. In this module, we will define the quality factor, Q, for a device or a circuit, and use this Q to build circuits that modify the impedance seen across a port.

Device Quality Factor

The quality factor, Q, is a measure of how good a device is at storing energy. Thus, the lower the losses, the higher the Q. In general, if we can express the impedance or admittance of a device as ${\tfrac {1}{A+jB}}$, the quality factor can then be expressed as $Q={\tfrac {B}{A}}$. The imaginary component, $B$ represents the energy storage element, and the real component, $A$, represents the loss (resistive) component.

For a series RC circuit, $Y={\tfrac {1}{R_{S}+j{\tfrac {1}{\omega C}}}}$, we get

$Q={\frac {\frac {1}{\omega C}}{R_{S}}}={\frac {1}{\omega R_{S}C}}$

(1)