In technical literature and product applications, there are three different definitions and characteristics of resonance frequencies for quartz crystal resonators

1. Series resonant frequency and parallel resonant frequency (fs, fp)
2. Resonant frequency and anti resonant frequency (fr, fa)
3. Maximum and minimum conductivity frequencies (fm, fn)
The admittance diagrams of these three frequencies can be clearly seen from the complex coordinates in the figure below

Complex Admittance of Resonators

The series coupling frequency and parallel coupling frequency, fs and fp, are the frequencies at which the conductance (real part of the admittance) and impedance (real part of the electric input impedance) are maximized, respectively
The resonant frequency and anti resonant frequency, fr and fa, are the two frequencies at which the conductivity is equal to zero (pure resistance characteristic) At this time, the impedance of fr is 1/Rr and the impedance of fa is 1/Ra
When evaluating the equivalent circuit during resonance, the series resonance frequency and parallel resonance frequency, fs and fp, are the two most important frequency parameters We can express the relationship between the series resonant frequency and the parallel resonant frequency (fs and fp) using the following formula:

C1 and L1 in the formula are respectively the dynamic capacitance and dynamic inductance in the above figure; Co is a static capacitance