Tools & Calculators › Filters › Crystal Ladder Filter
Crystal Ladder Filter
Cohn, Butterworth and Chebyshev crystal ladder filters from your measured crystals: coupling caps, matching to any source and load, and the response.
Measure one crystal
G3UUR method: measure the crystal's frequency in a test oscillator, then again with a series capacitor Cs added. The shift gives the motional Lm and Cm.
Type them instead (Lm, Rs and C0 from a data sheet or a crystal analyzer).
Crystal bench log
Enter every crystal's frequency (same oscillator, no Cs). The tool picks the closest-matched set.
Lm and Cm fill in from the two frequencies (G3UUR). A row with no "f with Cs" uses the Beginner Measure crystal. Rs sets the unloaded Q (Qu = ωLm/Rs).
Filter
Terminations
Each end is matched to RE with a low-pass L-network (series L, shunt C). No termination resistor is fitted.
Response
S21 solid; S11 dashed, shown in the passband only. The dotted line marks −3 dB. Hover or tap the plot to read f, S21 and S11.
Schematic
Parts
Exact values from the design equations; E12 is the nearest standard value. An end with a direct connection has no parts rows. Insertion loss is simulated with each crystal's own Lm, Cm, C0 and Rs; the estimate is EMRFD's loss formula.
Sources & verification
Design equations are from Hayward, Campbell & Larkin, Experimental Methods in RF Design (EMRFD), ARRL, 1st ed. (2003), chapter 3: G3UUR motional parameters (p. 3.19, Fig 3.35, with the EMRFD errata correction that adds C0 to Cs), coupling capacitors (Eq 3.11), end resistance including crystal loss (Eq 3.12), raising the end resistance (Eqs 3.13, 3.14), mesh tuning (Eq 3.15), the Cohn equal-capacitor design (Eqs 3.16, 3.17, p. 3.22) and the low-pass L-network (Fig 3.65, Eqs 3.30–3.32, p. 3.30). Butterworth and 0.1 dB Chebyshev k and q values come from Zverev, Handbook of Filter Synthesis (Wiley, 1967), sec. 6.10; the minimum q0 check follows Hayward, "Refinements in Crystal Ladder Filter Design", QEX, June 1995, p. 17. The center frequency and the loss estimate are derived from these. The response is a nodal analysis of every crystal (Lm, Cm, Rs, C0) and every capacitor, so crystal spread and holder capacitance show up as skew. Holder C0 compensation follows QEX June 1995 pp. 18–20: Leff predistortion (Eqs 12, 13, evaluated at the top of the passband and iterated; valid only while Leff < 2Lm), or an inductor L = 1/(ω²C0) across each crystal (Fig 8; EMRFD p. 3.21), the default. The calculator uses the ideal L; QEX Fig 8 uses a slightly smaller L plus a trimmer (about 9.1 pF for its 3.58 MHz, 4 pF, 151 µH example). After Leff predistortion the simulated −3 dB BW is checked against the target and flagged past 5%. Default holder C0 is 3 pF (EMRFD p. 3.19). Automated tests check the engine against the spec's worked examples and against ngspice. The 5% bandwidth flag, the 2% direct-connection band, the 30:1 warning and the 300:1 and 1 Ω–100 kΩ limits are QRPedia design choices, not from the sources. Engine: .