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Pi-network calculator

Why three elements here

Unlike an L-network, a pi-network lets you choose the Q — and it is the Q that governs the trade-off. A lower Q gives a wider bandwidth and lower coil losses, a higher one better harmonic suppression. That is precisely why the output tank of a valve amplifier is a pi-network.

Rin 2000 ΩLC1C2Rout 50 Ω
The classic output tank: Q sets both the bandwidth and the harmonic suppression
Frequency (MHz)
Input impedance, valve side (Ω)
Output impedance, into the load (Ω)
Loaded Q
Power (W)
Values
C1 — valve side
L — coil
C2 — load side
Check
Virtual impedance
Lowest achievable Q
Tank bandwidth
Estimated second-harmonic suppression
Voltage amplitude across C1 / C2

📐 The formulas​

R_virt = R_in / (Q² + 1)             ← the virtual intermediate impedance
X_C1   = R_in / Q
Q2     = √( R_out / R_virt − 1 )
X_C2   = R_out / Q2
X_L    = R_virt × (Q + Q2)

C1 = 1/(2πf·X_C1)    C2 = 1/(2πf·X_C2)    L = X_L/(2πf)

Condition for a solution:

Q > √( R_in/R_out − 1 )

Estimated second-harmonic suppression:

A ≈ 20·log10(Q) + 6    [dB]

Symbols:​

  • R_in — the impedance on the valve side (typically 1500…5000 Ω)
  • R_out — the load impedance (usually 50 Ω)
Where this calculator stops:
  • Harmonic suppression is an estimate, not an exact filter calculation
  • The valve's output capacitance, which forms part of C1, is not accounted for: on the higher bands it can exceed the calculated value
  • Coil losses are not accounted for; at Q > 15 they become noticeable
  • Only the RF component of the voltage across C1 is shown — a real capacitor also has to stand the anode DC

🎯 In practice​

  • The output tank of a valve amplifier — the main use.
  • Matching a high-impedance source to a 50 Ω load.
  • Checking an existing design: is the Q enough to meet the harmonic limits.
Practical advice:
  1. Q = 12 is the classic default on HF.
  2. The valve's output capacitance is already part of C1 — subtract it from the calculated value.
  3. Give the coil headroom in current: at Q = 12 it carries twelve times the load current.
  4. If you need better harmonic suppression without raising the Q, fit a separate low-pass filter after the tank.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Pi-network calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/others/pi_network (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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