Reference Oscillator Tuning Using LASERtrim® Chip Caps
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Scope:This discussion will focus primarily on the oscillator frequency tuning of a simple crystal oscillator. A basic LC oscillator and crystal specifications are discussed in sufficient detail to determine the required trim capacitor range for given crystal. Example calculations using an off-the-shelf reference oscillator are included.
LC Oscillator:Figure 1 shows a generic single inductor, dual capacitor oscillator circuit from which many of the classic configurations can be derived. The main difference between the implementation of these configurations is the terminal of the gain block which is chosen to be the AC ground reference. For example, if the non-inverting input of this circuit were the ground reference it would be a classic Pierce configuration. If the output of the gain block were the ground reference it would be a Colpitts configuration. There are advantages and disadvantages for each configuration, but that discussion is beyond the scope of this paper.
Figure 1: Generic LC OScillator
The oscillator frequency can be calculated using the following relationship.
For this discussion we will ignore the loading effects and stray capacitance of the gain block. In practice the capacitor values of the circuit would be adjusted to compensate. One way to make a reference oscillator based on the architecture of Figure 1 is to replace the inductor with a quartz crystal.
Quartz Crystal Model:A quartz crystal is a piezoelectric transducer that couples signals from one terminal to the other. Signal frequencies that excite a mechanical vibration mode of the quartz will pass through with minimal loss. Other frequencies are coupled through the stray capacitance created by the coupling structure to the quartz. The equivalent circuit of a quartz crystal is shown in Figure 2.
Figure 2: Crystal Equivalent Oscillator
Rm represents the signal loss due to heating during the quartz vibration. For our discussion on tuning, Rm will be ignored. Co represents the stray capacitance of the coupling structure. Co is usually on the order of a few picofarads. Lm and Cm are referred to as the motional inductance and motional capacitance respectively. Lm is analogous to the mass of a mechanical system and is on the order of a few millihenrys. Cm is analogous to the elastic restoring force of the system and is on the order of a few femtofarads.
The crystal will present an inductive impedance only in the very narrow range of frequencies bounded by the series resonance of Lm with Cm and the parallel resonance of Co with Lm and Cm. This parallel resonance is often referred to as anti-resonance. The frequency span between series resonance and anti-resonance is on the order of several parts per million. Across that frequency span the effective inductance of the crystal varies from 0 to infinity. Crystal oscillators that operate in this inductive range are commonly described as using the crystal in parallel mode.
Since the oscillator frequency is a function of both the effective inductance of the LO crystal and the capacitors C1 and C2, electrical parameters of the crystal are specified for a specific capacitive load. The values of C1 and C2 are chosen such that their series equivalent capacitance is equal to that load.
Crystal Tolerances:In order to get LO crystals in large quantities at the lowest possible price the allowable tolerances of the crystal must be wide enough to maximize the component yield of the crystal supplier. As a result the oscillator will require tuning to compensate for the tolerances if frequency accuracy is critical. This can be accomplished by adjusting the value of C1 or C2.
The tolerances of Cm and Lm are necessary to calculate the tolerance of the effective inductance of the crystal from which the required capacitor trim range can be determined. However, Cm and Lm are generally not specified explicitly. There are five critical parameters of the crystal from which Cm and Lm can be determined. They are nominal frequency, make tolerance, load capacitance (Cload), Co, and pullability (denoted as Df/f). These parameters are an indirect means of specifying the range of Cm and Lm in terms of parameters that can be measured accurately and easily.
Nominal Frequency: Specified operating frequency of the crystal at the reference temperature (usually 25 Celsius) with the specified load. Note this is not necessarily the crystal resonant frequency. It is often the series resonant frequency of the circuit comprised of the crystal and its capacitor load.
Make tolerance: Allowable deviation from the nominal frequency at the reference temperature.
Co: Static capacitance across the crystal resonator. Except for frequencies in the range of crystal resonance, the crystal equivalent circuit is simply Co.
Df/f: Pullability is an indicator of the sensitivity of the resonant frequency of the capacitively loaded crystal circuit to a change in the load capacitance. It is the ratio of the difference between the resonant frequencies of the loaded crystal circuit (fl) and unloaded crystal (fs) to the resonant frequency of the unloaded crystal.
Df/f is generally on the order of several ppm.
The value of Cm can be calculated from Co, Cload, and Df/f.
Lm can be calculated two ways. The method of calculation depends upon whether the crystal series resonant frequency (fs) or the loaded resonant frequency (fl) is specified.
If fs is specified, then
If fl is specified, then
Sample Calculation:Now that it has been shown how to calculate the reactances of the crystal equivalent circuit let’s demonstrate the calculation using a standard production crystal. The table below shows the frequency specifications for a Motorola KXN6316AA reference oscillator crystal.
The tolerance situation that will require the widest capacitor trim range is the case which results in the smallest value for Cm. From Eq. 3 it can be seen that Cm is smallest when Co and Df/f are at the lower limits of their specified ranges.
The values of Lm at the extremes of the make tolerance range can be calculated using Eq. 5 and using 12.8 *(1 +/- 15E-6) MHz for fl.
Using the minimum values of Cm and Co together with the two values calculated for Lm using Eq. 5, the maximum range of effective inductance presented by the crystal at the desired frequency of operation (Fo) can be calculated using Eq. 6.
The required capacitance range of the effective value of our oscillator capacitors C1 and C2 is calculated from the two values calculated for Leq and Fo
A summary of these calculations for the Motorola crystal is shown in Table 2. The values in the second row of the table are used to calculate the values in the last six rows.
A trimmer capacitor can be used in parallel with C1 to achieve a Ceq range of 30-34pF. This configuration is shown in Figure 2. Thus with C1=56pF and C2=62pF, a 2- 20pF trimmer capacitor will cover the range with some margin left over on each end of the trim range.
To tune this oscillator when the crystal make tolerance is +15ppm, Ctrim would be 18.7 pF. For a crystal make tolerance of -15ppm, Ctrim would be 3.2pF. Specifications for KXN6316AA crystal Frequency Make Load Æf/f Co (loaded) Tolerance Cap (ppm) 12.8 MHz ± 15ppm 32 pF 330 ±33 3.5-6.5 pF (series)
Figure 3: Crystal LO with trimmer capacitor
Manual vs. Lasertrim® Capacitor:If a manual trimmer capacitor, with 180 degree full range rotation, were used to tune this oscillator the technician performing the tuning operation would have to be extremely precise. The operator would require the ability to spin the trim tool consistently to an accuracy of about 2 to 2.5 angular degrees in order to achieve a frequency tuning accuracy 0.5 ppm. This would be a difficult, time consuming operation. In addition, the mechanical relaxation of a manual trimmer after the trimming operation would likely introduce frequency drift in an oscillator this sensitive to the trimmer value.
Incorporating Johanson Technology’s LASERtrim® tuning capacitors in the design offers several advantages. Laser trimming offers superior precision for fine tuning and is ideal for automated tuning operations. In addition LASERtrim® caps do not suffer from mechanical relaxation (or operator relaxation), so there is virtually no capacitance drift over time. Since nothing except the laser beam comes in contact with the circuit there is no stray capacitance introduced during tuning as would be the case with a mechanical trimmer trim tool. Johanson LASERtrim® capacitors are Hi-Q, low profile surface mount devices and are available in sizes as small as 80x50 mils and often at a lower cost then many manual trimmers.
Retuning in the Field:In some cases the ageing characteristics of the crystal are such that the oscillator may need to be retuned after it has been in the field for a year or more. Laser trimming for re-alignment is not necessary nor recommended. In this case a relatively narrow range manual trim cap in parallel with the laser trim cap can be used to adjust the frequency. Since the manual trimmer only needs to be able to adjust the frequency a small fraction of the total tolerance range, the sensitivity issues discussed earlier are much less of a problem. For example given earlier a manual trimmer with a 0.5-2.5pF range would give roughly a +/- 2ppm adjustment range. This is equivalent to about 22 degrees of rotation for 0.5 ppm frequency adjustment.
Summary:A simple LC oscillator circuit was presented which is the basic building block for most communications oscillator circuits. A special case of this oscillator circuit was shown which incorporates a quartz crystal for precise frequency control. The equivalent circuit of a quartz crystal was presented along with parameters used to specify its frequency and tuning characteristics. An example calculation of the equivalent circuit along with its worst case tolerances was presented for a standard industry crystal. An application circuit capable of operation with this crystal over all frequency tolerances was presented. Finally it was demonstrated why tuning this circuit with a laser trim capacitor has numerous performance, manufacturing, and cost advantages over tuning with manual trim capacitors.
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