Equivalent circuit diagram of an oscillating quartz crystal

The equivalent circuit diagram of a quartz crystal describes the electrical behavior of a quartz crystal in the range of its resonant frequencies. It consists of the motional elements L1, C1 and R1 as well as the parallel capacitance C0. This makes it possible to understand how the quartz crystal converts mechanical oscillation into an electrical equivalent model. This model is particularly important in order to better understand resonance, losses and parasitic capacitance. For developers, the equivalent model is a central basis for the design of precise frequency circuits.

R1 stands for the resonance resistance and models the losses in the crystal, for example due to mechanical damping and conduction losses. L1 represents the mass inertia of the oscillation and thus electrically simulates the mechanical inertia of the crystal. C1 is referred to as motional capacitance and corresponds to the elastic restoring force in the crystal. C0 describes the parallel capacitance between the connections of the quartz, for example through the electrodes. Only the interaction of these four variables enables a realistic description of the resonance behavior of a quartz crystal.

The values in the equivalent circuit diagram depend on the design, frequency range and crystal type. R1 is typically in the range of a few ohms to several hundred ohms for MHz quartz crystals, and also in the kOhm range for kHz oscillating quartz crystals. C1 usually ranges from a few fF to the pF range and is therefore very small. L1 is typically a few mH and represents the mechanical inertia of the crystal. Depending on the crystal, C0 is usually between 1 and 7 pF and has a significant influence on the behavior between the connections.

Theoretically, you could also generate a frequency with a circuit consisting of L1, C1, R1 and a parallel capacitance C0. In practice, however, this frequency would be significantly less accurate than with a real oscillating quartz crystal. In addition, such a discrete circuit is complex to set up and costs more to assemble. In contrast, oscillating crystals offer very high accuracy, a long service life and an economical solution for stable frequencies. This is why they are the preferred choice for precise clock generation in many industrial applications.

C0 is the so-called shunt capacitance and describes the electrical capacitance between the connections of the quartz crystal. This capacitance is created by the electrodes and the physical structure of the component, among other things. Although C0 is comparatively small, it has a significant influence on the overall electrical behavior of the quartz crystal. It is an important component of the equivalent model, especially when considering resonance. Typical values are between 1 and 7 pF, depending on the quartz crystal.

PETERMANN-TECHNIK is a specialized partner for quartz crystals and frequency-generating components in the industrial environment. The company combines technical expertise with practical advice when it comes to understanding and selecting suitable quartz solutions. Instead of complicated and inaccurate discrete equivalent circuits, customers receive precise, durable and cost-efficient quartz crystals. The frequency experts at PETERMANN-TECHNIK provide fast and direct support by phone or e-mail. This makes PETERMANN-TECHNIK a strong choice for companies that rely on quality, accuracy and reliable support when it comes to frequency technology.