The circuit, as shown in Fig.5 denotes the quantities L1,C1,R6 and C0 as the electrical equivalent the electromechanical and electrical properties of the quartz and holder assembly. L1 and C1 are referred to as the motional inductance and capacitance

Fig.5 Equivalent Circuit

respectively, and R1 is know as the effective series resistance (ESR).C0 is the static or shunt capacitance whose value is the sum of the capacitance between the electrodes and capacitances added by the leads and holder.

Equivalent Series Resistance (ESR)
The resistive element, measured in ohms, of a crystal device. At the frequency denoted by the following formula, the motional inductance (L1) and motional capacitance (C1)are of equal ohmic value are exactly opposite in phase, the net result is that they cancel one another and only a resistance remains in the series leg of the above equivalent ciruit(Fig.5).The ESR measurement is made only at the series resonant frequency (Fs),not at some predetermined parallel resonant frequency (FL). Crystal resistance measured at some parallel load resonant frequency is often called the effective resistance.

Overtone Crystals
Because of physical properties and geometry of an AT cut quartz blank, a crystal can vibrate at many frequencies. The lowest frequency is called the fundamental frequency and can be supplied up to about 45MHz. Higher frequencies (to over 200MHz) are achieved by operating the crystal oscillates at its designed overtone frequency (Fig.6).
Overtone crystals are specially processed for plane parallelism and surface finish in order to enhance their performance at the required overtone frequency. The overtone frequency is higher than the equivalent harmonic multiple of the fundamental by approximately 25MHz per overtone.

Fig.6 Overtone Response of a Quartz Crystal