Maximally Flat (Butterworth) High-Pass Filter Calculator
A maximally flat (Butterworth) high-pass filter has no passband ripple. Use it to reject interference below the operating band and to block DC. Enter the order, cutoff frequency and impedance to get the series-capacitor / shunt-inductor ladder values for two topologies and see the frequency response.
How to use
- Enter the order n (number of elements, 1–10). Raise the order for a steeper cutoff.
- Enter the cutoff frequency fc (MHz, −3 dB point) and the system impedance Zo (usually 50 Ω).
- Click Calculate. The table lists capacitors (pF) and inductors (nH) for both Type 1 and Type 2 circuits.
- Choose a topology from the circuit diagram: capacitors go in the series positions and inductors to ground. Select the nearest standard values and tune by measurement.
Theory and formulas
First compute the Butterworth low-pass prototype values (they depend only on the order):
The low-pass to high-pass transformation then turns each series inductor into a series capacitor and each shunt capacitor into a shunt inductor, with reciprocal values:
C = 1 / (gk · Zo · ωc) L = Zo / (gk · ωc)
Type 1 or Type 2?
Type 1 starts with a series capacitor, so the input is DC-blocked, which suits a preceding stage that carries bias. Type 2 starts with a shunt inductor, giving the input a DC path to ground that can drain static charge. Both have the same frequency response.
Design tips
- Use C0G/NP0 series capacitors and high-Q shunt inductors whose self-resonant frequency is well above the highest passband frequency; otherwise notches appear at the top of the band.
- Keep the ground connection of each shunt inductor short and direct (several ground vias); ground inductance reduces stopband rejection.
- fc is usually set to about 0.7–0.8 times the lowest frequency you need to pass, leaving margin at the lower band edge.
- If you need a steeper cutoff and can accept passband ripple, use the Chebyshev high-pass instead.
FAQ
- Are maximally flat and Butterworth the same thing?
- Yes. The maximally flat response is the Butterworth response: the derivatives of the passband response are zero at the centre, so it is as flat as possible with no ripple.
- How are high-pass values related to low-pass values?
- Both use the same prototype values gk. Low-pass: C = g/(Zo·ωc), L = g·Zo/ωc. High-pass swaps the positions and takes reciprocals: C = 1/(g·Zo·ωc), L = Zo/(g·ωc).
- The calculated values are not standard values. What should I do?
- Use the nearest E24 standard value, combine two parts in series or parallel if necessary, and fine-tune while measuring S21 with a network analyzer.
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