L Pad - Radio-frequency (RF) Operation

Radio-frequency (RF) Operation

In RF (radio frequency) applications, the L network is the basis of many common impedance matching circuits, such as the pi network employed in amplifiers and the T network that is common in transmatches.

The L network relies on a procedure known as series-parallel transformation. For every series combination of resistance, R_S, and reactance, X_S, there exists a parallel combination of R_P and X_P that acts identically to the voltage applied across the series combination. In other words, the series components and the parallel components provide the same impedance at their terminals. The transformation ratio is the ratio of the input and output impedances of the impedance matching network.

The series-parallel transformation allows the input impedance to be dropped down to lower impedances while sustaining a voltage across the circuit. This system works in reverse as well. The equations needed for this transformation are as follows:

Q = X_S/R_S= R_P/X_P = ^0.5

R_P = R_S (Q2 + 1) and R_S = R_P / (Q2 + 1)

X_S = QR_S and X_P = R_P / Q

For the resistance R_s and reactance X_s in series, R_p and X_p exist as a parallel combination. One simply needs to know the input impedance R_p and to choose the output impedance R_s. Or conversely know R_s and choose R_p. Keep in mind that R_p must be larger than R_s. Because reactance is frequency dependent the L network will only transform the impedances at one frequency.

Inclusion of two L networks back to back creates what is known as a T-network. T-networks work well for matching an even greater range of impedances.