PI Network Impedance Matching Calculator

π-Network Matching Component Calculator

Input Fields

Source Resistance

Rₛ

Ω

Resistance of the source (Ohms)

Load Resistance

Rₗ

Ω

Resistance of the load (Ohms)

Frequency

f

Hz

Operating frequency in Hertz

CalculateReset

Calculate automaticallyIf enabled, the result will update automatically when you change any value.

Your Results

Q Factor

Reactance of CapacitorXc

Reactance of InductorXl

CapacitanceC

InductanceL

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PI Matching Network Formulas

$$Q = \sqrt{ \frac{R_l}{R_s} – 1 }$$ $$X_C = \frac{R_l}{Q}, \quad X_L = R_s \cdot Q$$

Where:

• $$Q$$ = quality factor
• $$R_s$$ = source resistance (Ω)
• $$R_l$$ = load resistance (Ω)
• $$X_C$$ = capacitive reactance (Ω)
• $$X_L$$ = inductive reactance (Ω)

These formulas are used when the source resistance is less than the load resistance.

PCB Microstrip Crosstalk – Calculation Example

Given:

• $$R_s$$ = 25 Ω
• $$R_l$$ = 100 Ω

Calculation:

1. $$Q = \sqrt{ \frac{100}{25} – 1 } = \sqrt{4 – 1} = \sqrt{3} ≈ 1.732$$
2. $$X_C = \frac{100}{1.732} ≈ 57.74~Ω$$
3. $$X_L = 25 \cdot 1.732 ≈ 43.30~Ω$$

The π (pi) network is commonly used in RF design for impedance matching between a source and load, especially in power amplifiers and antenna circuits. It consists of two capacitors and one inductor. This calculator is tailored for the case where the load resistance is greater than the source resistance (Rs < Rl), ensuring maximum power transfer and minimal signal reflection. By adjusting Q, XC, and XL, the network achieves effective transformation and desired bandwidth.