[time-nuts] equations for crystals, frequency vs temp vs angles

Jim Lux jimlux at earthlink.net
Fri Aug 28 09:29:33 EDT 2015

Someone was asking about changing cut angles and the effect.  You might 
find some useful stuff in Mark Haney's thesis "Design Technique for 
Analog Temperature Compensation of Crystal Oscillators"


Here's a matlab snippet:
% Method 1: Use AT coefficients given by Gerber & Ballato [p101]:
% ref: (Gerber & Ballato, "Precision Frequency Control, Vol. 2", 1985)
% Angle determines frequency tolerance.
Theta_0 = 35.25;     %ref angle that produces a zero TC slope at
                      %the ref temp
del_Theta = 1.7/60;  %# of minutes off ref angle to produce desired
A1 = -5.08e-6 * del_Theta;
A2 = -0.45e-9;
A3 = 108.6e-12
curve1 = A1*(T-T0)+A2*(T-T0).^2+A3*(T-T0).^3;

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