Column: Design with frequency components
Quartz crystal characteristics In a crystal oscillator, mechanical pressure causes the materials to generate an alternating electrical field at a frequency. Its equivalent circuit is shown in Figure 1, where R1
is the series
resistance of the quartz crystal (usually specified as upper limit), C0
is its static
capacitance (usually specified as upper limit), C1
is the dynamic (motional)
capacitance of the quartz crystal (rarely specified), L1
(rarely specified), and then there are parameters (not shown in Figure 1) like fL
frequency and CL
as the quartz crystal’s nominal as its nominal load
capacitance. All these values are usually specified in the datasheet by the quartz crystal manufacturer. Exact values can be found by analyzing the quartz crystals with a network analyzer.
The topology of a Pierce oscillator The Pierce oscillator, named after its inventor George W. Pierce, is the most common circuit used as a clock generator in microprocessors – it contains an inverter and a feedback network. The inverter provides the necessary amplification and a -180o phase shift, and the feedback network, typically composed of capacitors and sometimes a resistor, ensures that the signal is fed back to the inverter with the correct phase and magnitude to sustain oscillations. The crystal itself acts as a highly selective filter within the feedback network. The output resistance of the inverter, and the PI
together with the resistor Rv
element Cb/quartz/Ca, forms a narrow bandpass filter with a frequency- dependent phase shift. According to the oscillation condition, the total phase must be 360°, thus enabling the circuit to oscillate at the frequency of the quartz crystal. Te inverter usually provides
slightly over 180°, due to additional, semiconductor-related propagation delays. Te external phase shiſt, due to the bandpass, can therefore be slightly under 180°.
is the dynamic inductance
Table 2: Important parameters of quartz crystal and oscillators
Figure 2: Pierce oscillator
Design parameters Selecting the right component for the application is not necessarily a simple task: It depends on the technical requirements of the application, the target cost of the system and, ultimately, on the business case.
Focusing on the technical aspect, Table
2 shows the most important parameters, along with the function of crystals and oscillators.
Tis series continues in the next edition of Electronics World
www.electronicsworld.co.uk September 2025 13
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