XTAL model

Here is the Mercury parameter file for a variety of crystals. We will solve the equations for a 1MHz crystal.

; Typical Crystal Values:
; Freq      Mode     L1            C1        R1        C0        Q
; 32768   fund   4448 H       5.3e-15    11200      1.84pf    81780
;  1 MHz  fund    3.5 H       0.007 pf     340      3 pf      64679
; 10 MHz  fund    9.8 mH      0.026 pf       7      6.3 pf    87964
; 30 Mhz  3rd    14.9 mH      0.0018 pf     27      6.2 pf   104021
;100 MHz  5th     4.28 mH     0.0006 pf     45      7   pf    59760
;150 MHz  5th     1.9 mH      0.0006 pf     65      4.2 pf    27000
;; Variables:
; C0 = Crystal Shunt Capacitance
; C1 = Crystal Motional Capacitance
; CL = Crystal Load Capacitance
; FP = Parallel Resonant Frequency
; FS = Series Resonant Frequency
; L1 = Crystal Motional Inductance
;  Q = Crystal Q factor
; R1 = Crystal Series Resistance

; Equations:
  C1 = 1 / (Q * W0 * R1)        ; motional capacitance
  FP = FS * (1 + (C1 / (2 * (C0 + CL)))); parallel resonant frequency
  L1 = (Q * R1) / (W0)            ; motional inductance
  pf = C1 * 1e12            ; C1 in pf for easy SPICE entry
  W0 = 2 * pi * FS            ; series resonant frequency

; Solve for these parameters:
  C0 = 3e-12        ; crystal shunt capacitance
  CL = 27e-12        ; crystal load capacitance
  FP = 1e6        ; parallel resonant frequency
  Q  = 64679        ; crystal 'Q' factor
  R1 = 340        ; series resistance

The solution is

  C0 = 3.000000000000000E-12
  C1 = 7.2381954594622169E-15
  CL = 2.700000000000000E-11
  FP = 1000000.0000000000
  FS = 999879.377960441
  L1 = 3.5003762943696892
  pf = 0.0072381954594622176
  Q  = 64679.000000000000
  R1 = 340.00000000000000
  W0 = 6282427.4165529059