|This is a Smith Chart of a 9 MHz quartz crystal, in 100 Hz steps
over a +/- 3 kHz range, nearly centered on the crystal's series
resonant frequency. This plot shows that the impedance of a crystal,
near series resonance, can be essentially modelled as a series RLC
circuit. This model loses accuracy as the parallel resonant frequency
is approached, which is dominated by a capacitance that shunts the
series RLC network.
Series resonance for this crystal is also seen to be approximately 320 Hz below 9 MHz and the series R is approximately 14 ohms. Additional analysis of this data and measurements can be used to fully characterize the equivalent circuit model for this crystal.
Please feel free to contact me with any comments or questions
Paul Kiciak, N2PK