Pi / T Network Impedance Matcher
Pi and T networks add a degree of freedom over the L-network: Q can be chosen independently of the impedance ratio. Higher Q gives better harmonic rejection but narrower bandwidth. Pi networks are preferred when both ports are high impedance; T networks when both ports are low impedance.
Equations & Parameters ▸
Pi LP: \(C_1=\dfrac{Q}{\omega R_1},\ L=\dfrac{R_v(Q+Q_2)}{\omega},\ C_2=\dfrac{Q_2}{\omega R_2},\ R_v=\dfrac{R_1}{Q^2+1}\)
| f | Matching frequency. |
| R₁, R₂ | Source and load impedances (Ω). Works for any ratio. |
| Q | Loaded Q of the network. Must satisfy Q > √(R_max/R_min − 1). Higher Q → sharper response. |
| Pi (low-pass) | Two shunt capacitors + one series inductor. Good for harmonic suppression. |
| Pi (high-pass) | Two shunt inductors + one series capacitor. |
| T (low-pass) | Two series inductors + one shunt capacitor. |
| T (high-pass) | Two series capacitors + one shunt inductor. |
Physical constants used
| c | Speed of light = 2.998×10⁸ m/s |
| µ₀ | Permeability of free space = 4π×10⁻⁷ H/m ≈ 1.2566×10⁻⁶ H/m |
| ε₀ | Permittivity of free space = 8.854×10⁻¹² F/m |
Inputs
Ω
Ω
must exceed √(R_max/R_min − 1)
Results
Network Elements
Element 1 (shunt/series)—
Element 2 (series/shunt)—
Element 3 (shunt/series)—
Performance
Q_low (verified)—
Bandwidth (−3 dB)—
Virtual impedance R_v—
Diagram