# Crystal Pullability: Series Vs Parallel Resonant Crystals

The image below is a common diagram implementing a crystal.  An even more common question is what is the purpose or function of the capacitors tied onto either terminal of the crystal?  The answer is that the capacitors (referred to together as “load capacitance”) affect the crystals pullability. Pullability refers to the change in frequency of a crystal unit, either from the natural resonant frequency (Fr) to a load resonant frequency (Fl), or from one load resonant frequency to another.  In essence, crystals can be ‘pulled’ by adding reactance (capacitance) to the terminations of the crystal.  Wide-tuning-range VCXOs use fundamental mode crystal units of large C1. Voltage control can be used for a variety of purposes: to frequency or phase lock two oscillators, for controlled frequency modulation, for direct compensation (TCXO), and for calibration (i.e., for adjusting the frequency to compensate for aging).  Now, for someone using a variable-load capacitor, the benefits are obvious, but there are many designs that call for a crystal with capacitors that have a constant value, so where is the benefit there?

The figure below is referred to as an impedance/reactance curve, and it represents the change in frequency of a crystal in relation to external components.  Notice as the frequency is increased, the curve reaches a point where the crystal appears purely resistive, with minimum impedance and the current flow is maximal. This point is known as the series resonant frequency (fs).  At this point the crystal is resonating at zero phase, and does not require a capacitive load in the feedback loop. By continuing to increase the frequency, another point of zero phase, known as the anti-resonant point, is reached (fa). At the anti-resonant point the resistance of the crystal unit is maximal and the current flow is minimal.  This frequency is inherently unstable, and should never be selected as the frequency of operation. The area between fs and fa is identified as the “area of usual parallel resonance” and a frequency within this area is considered a parallel resonant frequency.  So is this the benefit then, that we can reach higher frequencies with parallel resonant crystals?

In our previous post, we discussed how the motional capacitance (C1) represents the elasticity, or stiffness, of the crystal.  For maximum frequency stability with respect to reactance/phase perturbations in the oscillator circuit, the reactance/phase slope must be maximum. This requires that the C1 be minimum.  For crystals with very low C1, the available frequency bandwidth is only around 1000PPM (0.1 %).  As stated before, for applications where the capacitive load can be varied, this seems very helpful.   We still haven’t figured out why we would use parallel resonant crystals with a constant capacitive load!

Something that is overlooked by some designers (and only lightly touched on so far) is the effect of external components to a crystal’s phase.  Digital circuits that include their own reactive components (capacitors) will induce a phase shift on the crystal’s output that can cause significant stability problems.  It is therefore necessary for capacitors CL1 and CL2 to provide additional noise for starting oscillations with an initial phase shift in order to negate these effects and reach a state of zero phase, pulling the frequency to the desired value.  In older IC designs, this could be upwards of 32pF, but most current designs are 16pF and below.  For applications using ICs (wireless devices, bridge chips and other types of microcontrollers), parallel-resonant crystals are the obvious choice.