How the pi network works
A valve amplifier's plate needs a load of a few thousand ohms, but the antenna is 50 Ω. The pi network, a capacitor to ground, a series inductor and another capacitor to ground, transforms the impedance and also filters out harmonics. The loaded Q sets the balance: higher Q gives better harmonic suppression but more circulating current and loss in the coil, while lower Q makes tuning broad but filters less. A Q of 10 to 15 is the usual choice.
The formulas
The plate load is roughly the plate voltage divided by a factor times the plate current, with the factor depending on the class of operation, about 1.8 for class AB2 or B. The calculator then uses the standard ARRL Handbook formulas: XC1 = R1 ÷ Q, XC2 = R2 × √((R1 ÷ R2) ÷ (Q² + 1 − R1 ÷ R2)), and XL = (Q × R1 + R1 × R2 ÷ XC2) ÷ (Q² + 1). On the low bands, C2 can become very large, which is why many amplifiers switch in extra capacitance there.
Safety
Valve amplifiers use lethal voltages, and the tune capacitor sees the full plate voltage plus RF. Choose capacitor spacing for at least twice the plate voltage, use a plate choke and blocking capacitor, and always fit and test bleeder resistors and interlocks. For transistor amplifiers, matching is usually done with transformers: see the transformer calculator.
Questions
What Q should a pi network have?
10 to 15 for most HF amplifiers. 12 is a common design value.
How do I find the plate load resistance?
Divide the plate voltage by about 1.8 times the plate current for class AB2 or B, 1.5 for AB1 and 2 for class C.
Why is C2 so large on 160m?
The load capacitor's reactance has to be low at low frequencies, which needs a lot of capacitance. Amplifiers often switch in fixed capacitors on 160m and 80m.
Does a pi network filter harmonics?
Yes. It's a low-pass network, typically reducing the 2nd harmonic by about 30 to 40 dB at a Q of 12.