Crystals v Parallel LC Tuned Circuits for Frequency Selection
Although we generally think of a quartz crystal as affording higher selectivity than a standard inductorcapacitor (LC) tuned circuit, a crystal is not always the best choice when protection against far outofband signals is required. We'll explore why with the help of a software circuit simulator, Ansoft Serenade 8.5 SV.
Figure 1 shows crystalequivalent and LC tuned circuits set up for simulation in Serenade 8.5 SV. At its fundamental (lowestfrequency) resonance, a crystal can be modeled as a seriesconnected small resistance (generally ohms to hundreds of ohms), large inductance (commonly on the order of millihenrys for highfrequency crystals), and very small capacitance (on the order of femtofarads to tens of femtofarads) connected in parallel with a small capacitance (on the order of a few picofarads). The seriesconnected elements simulate the crystal itself; the parallel capacitance simulates the capacitance formed by the crystal electrodes (one on each side of the crystal plate) with the crystal acting as a dielectric. In practice, such a network has two main resonances: a series (lowimpedance) resonance formed by the crystal's seriesed equivalent resistance, inductance, and capacitance, and the parallel (highimpedance) resonance formed by the crystal electrode capacitance and the crystal (which at frequencies above its series resonance acts like an inductor, and below its series resonance point acts like a capacitor). A crystal's parallel resonance is always slightly higher in frequency than its series resonance, giving rise to a sharpdipandsharppeak impedance characteristic with rising frequency.

Figure 1—Schematic diagram of the equivalent electrical circuit of the fundamental (lowestfrequency) resonance of a quartz crystal (Crystal) and of a parallelresonant LC tuned circuit (Tuned_Circuit) as entered for simulation in Ansoft Serenade 8.5 SV. Both circuits are dimensioned to resonate (series resonance for the crystal, parallel resonance for the LC circuit) at 10 MHz. The LC tuned circuit inductor has a Q (quality factor) of 200 at 10 MHz; its capacitor is lossless. Although all of the simulated crystal's reactive (inductive and capacitive) subelements are lossless, the presence of a nonzero series resistance (7 ohms) indirectly sets a realistic Q for the crystal.


Figure 2—Predicted magnitude (absolute value) of impedance versus frequency for the crystal and parallel LC circuits. The very low impedance of the parallel LC circuit above and below resonance equates to significant rejection of offresonance signals when such a tuned circuit is used as a signal selector.


Figure 3—How low is low? This graph shows the predicted magnitude (absolute value) of impedance versus frequency for the crystal and parallel LC circuits with the impedance axis scaled to 1 kilohm. Only in a very narrow region around its series resonance (blue downward spike) does the crystal's impedance equal the generally low offresonance impedance exhibited by the parallel LC circuit.


Figure 4—Predicted magnitude of impedance versus frequency for an ideal 6.3pF capacitor, plotted on the impedance scale used in Figure 2. That this curve duplicates the offresonance behavior of the simulated crystal indicates that the crystal's relatively high offresonance impedance is almost entirely attributable to its small parallel (interelectrode) capacitance.
