Pi-Match Impedance Matching Calculator

Overview

The Pi match impedance matching circuit is used to match the impedance between two points, usually a source and a load. The circuit got its name because the inductor and the capacitor form a Pi symbol (see schematic below).

This calculator will help you determine the correct values for the inductor and capacitor in a Pi match impedance matching circuit. The required parameters are the signal (or source) frequency, the impedance of the source and the impedance of the load. You can also specify if the circuit will pass or block the direct current (DC). The inductor quality factor is also computed.

Equations

For Pass DC Current:

$$Z_{input}=\left \{ \left [ \left ( R_{L}+jX_{L} \right )//\left ( \frac{1}{j\omega\cdot C_{L}} \right ) \right ]+j\omega\cdot L \right \}//\left ( \frac{1}{j\cdot \omega\cdot C_{s}} \right )$$

For Block DC Current:

$$Z_{input}=\left \{ \left [ \left ( R_{L}+jX_{L} \right )//\left ( j\omega\cdot L_{L} \right ) \right ]+\frac{1}{j\omega\cdot C} \right \}//\left ( j\omega\cdot L_{s} \right )$$

Applications

阻抗匹配在电气工程中很重要，因为它允许在两个点之间进行最大的功率传递。例如，在电话系统中，使用匹配阻抗可以最大程度地减少长距离线路的回声。电话混合动力线圈，在其中将两根电线转换为四根电线也可以通过匹配来实现。

In audio amplifiers, impedances are not matched as it is typical for amplifiers to have output impedances that is lower than the load impedance for better speaker damping. But for higher-power amplifiers, such as those that use vacuum tubes, impedance-changing circuits are used to get a low output impedance in order to better match the amplifier's performance to the load impedance.

Further Reading

• 教科书- Maximum Power Transfer
• 教科书- Impedance Transformation
• 工作表 - 阻抗匹配