For the purposes of crystal selection and tuning, two sets of information are required. The crystal is a circuit element characterized by the first set, C0, C1, and CL and the load curve shown in Equation 1 (also refer to AN-831, The Crystal Load Curve). Also required are the values of the VCXO oscillator's voltage variable capacitors when the control voltage is set to the maximum and minimum values. These two capacities, ΔCVH and ΔCVL, define a capacitance range on the load curve for the untuned VCXO. Both sets of data allows the tuning capacitor and the tuning range to be calculated directly as will be shown. Note that the fractional frequency offsets have not been converted to ppm; ΔFL and FL are in Hz. CLn is the nominal parallel load capacity that tunes the crystal parallel resonance to the nominal frequency. The normalization of all capacities by Y=C0+CLn simplifies the tuning derivation that follows.
The polarity of the voltage transfer curve of the VCXO is not relevant to the tune procedure. It is immaterial whether the maximum and minimum control voltages correspond to the maximum and minimum VCXO frequencies or vice versa. Further, the varactor capacities being used are the equivalent parallel varactor capacities across the crystal terminals. The varactor capacitors are typically implemented as two shunt capacitors to ground, one on the VCXO oscillator input and on the oscillator output. If these capacitors are provided by the oscillator manufacturer ground referenced, simply divide the values by two to obtain the parallel values of ΔCVH and ΔCVL. First solve Equation 1 for the normalized parallel load capacity across the crystal for a given ΔFL/FL.
Equation 2 is used is used to determine the normalized values of ΔCVH and ΔCVL in terms of the fractional offset frequency errors measured when the control voltage is at the maximum and minimum value respectively in Equation 3 and Equation 4.