PI-Match

PI Network Impedance Matching

Inputs

Frequency
F
Source Resistance
RS
Ohm
Source Reactance
XS
Ohm
RL
Ohm
XL
Ohm
Q Factor
Q
Ohm
Circuit DC Current

Outputs

L:

C:

Q:

Plots:

• Mag & Phase
• Real & Complex

Freq:

Mag:

Phase:

PI Match Impedance Calculator

The Pi match circuit gets its name because the circuit topology can look like a pi symbol. This tool will help you create a matching circuit so that optimal power transfer occurs between unmatched loads. This technique doesn’t work for wide band requirements, but is a simple way to achieve this at a specific frequency. This calculator will give you the circuit topology as well as the component values.

PI Match Circuit Description

There are some important items to understand when using this tool. The circuit topology can change depending on the inputs. For example in some topologies there may be 2 inductors and one capacitor and in a different configuration it may be 2 capacitors and one inductor. There is one menu item to select if there is to be any DC current or not, that also affects the topology. The inputs ask for source resistance and source reactance. If you are unsure what the reactance is set it to zero for a first pass approximation.

The outputs of this tool give you the component values as well as a graph of the impedance looking into the pi circuit from the source. This allows you to double check the calculator and make sure that it selected appropriate values, by making sure the impedance correctly matches the input impedance. Also remember that the circuit input reactance will be opposite in polarity with the source reactance when matching.

PI Match Circuit Formulas

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 )