Issue 91, February 1998
Choosing the Right Crystal For Your Oscillator

Start •Why Quartz Crystals • Timing Budget & Accuracy • Frequency Tolerance • Frequency Stability • Aging • Load Capacitance • Series and Parallel Resonance • Frequency Tolerance and Load Capacitance • AT vs. BT Cut • Mode of Operation • Package Considerations • Crystal Placement • Crystal Clear • References

SERIES AND PARALLEL RESONANCE

The question of parallel and series resonant crystals often comes up and is occasionally a source of confusion. Let me clarify the situation.

There is no such thing as a series or parallel resonant crystal. Instead, crystals have different parallel and series resonant frequencies.

When a crystal is calibrated at the factory, it is trimmed to hit a particular frequency while operating in the series or parallel resonant mode. The parallel resonant frequency is greater than the series resonant frequency.

Most oscillators operate in the parallel resonant mode (i.e., they see a parallel load capacitance). Some examples of parallel resonant oscillators are the Pierce-, Colpitts-, and Clapp-style oscillators. Series-resonant oscillators, on the other hand, are uncommon.

Transforming mechanical parameters into electrical parameters is known as creating the electrical dual. The equivalent electrical circuit for a crystal is shown in Figure 2. Components C1, L1, and R1 make up the crystal’s motional arm.

Figure 2—The mechanical properties of mass, friction, and stiffness are mapped to inductance, resistance, and capacitance, respectively.

Co is the shunt capacitance. It is composed of packaging and lead effects, and is on the order of a few picofarads. Co is also known as the crystal’s static capacitance.

L1 is the crystal’s motional inductance. This value is determined by the crystal’s motional mass during oscillation, and is on the order of thousands of henries.

C1 is the crystal’s motional capacitance. It is determined by the crystal’s stiffness, and is on the order of a few femtofarads.

R1 is the crystal’s ESR when oscillating, and it is related to mechanical loss during oscillation. ESRs range from a few ohms to tens of thousands of ohms.

If the ESR is small, the crystal loses little energy while vibrating. A small ESR helps with startup and continued oscillation.

The series equivalent circuit for a crystal omits the shunt capacitor, Co. The crystal series resonant frequency is:

When crystals are connected to PC boards, they see a circuit that looks like Figure 3.

Figure 3—When the external load capacitance CL is taken into account, it appears as a capacitor in parallel with Co.

Here, CL is equal to the series combination of CL1 and CL2, and is attributed to board parasitics and/or load caps added to the oscillator. The resonant frequency changes from equation 2 to:

In most cases, Fp, the parallel load resonant frequency, is specified in the crystal datasheets. C1 and Co are part of the crystal, but the load capacitance, CL, is not.

At the factory, the crystal is calibrated (frequency-tolerance spec) with a particular load capacitance. This number appears in the datasheet as the load capacitance.

If your load capacitance doesn’t exactly match the load capacitance in the datasheet, your oscillator won’t run at the spec Fp frequency. (I look at the effects of mismatched load capacitance in the next section.) Note that the parallel resonant frequency is greater than the series resonant frequency.