Print Close Window

Equivalent Series Resistance/ Mode Of Oscillation
Mode Of Oscillation:

A quartz crystal is designed to vibrate on its fundamental frequency or one of its overtones. Generally, fundamental frequencies up to 30 Mhz are attainable using standard crystal designs and processes. For frequencies above 30 Mhz, overtone modes are recommended. Fundamental mode crystals, at these frequencies, become more expensive because the quartz blank is extremely thin and subject to a higher rate of breakage during production. The ability to use the overtone crystal, instead of the fundamental, produces significant cost savings. As the frequency range is extended, the oscillation mode of the crystal changes to other overtones. Normal overtone modes are 3rd, 5th, 7th, and 9th and can be referred to as "multiples" of the fundamental frequency. As an example, a 60 Mhz 3rd overtone crystal would look like a 20 MHz crystal at it's fundamental. A 20 Mhz crystal can be made to oscillate at 3, 5, 7, etc times the fundamental frequency. A frequency of 60 Mhz is achieved by optimizing certain electrical parameters in an overtone oscillator circuit derived from a 20 Mhz crystal. Crystals in the range of 60-110MHz are generally 5th overtones, while crystals in the range of 110-175MHz generally are 7th overtones. Never attempt to use a fundamental mode crystal unit operating at an overtone frequency.

Equivalent Series Resistance (ESR):

The equivalent series resistance is the resistive element (R1) of the quartz crystal equivalent circuit. (see Equivalent Circuit below) This resistance represents the equivalent impedance of the crystal at natural resonant frequency (series resonance) ESR is measured by a Crystal Impedance (CI) meter.

ESR values are generally stated as maximum values expressed in ohms. The ESR values vary with frequency, mode of operation, holder type, crystal plate size, electrode size, and mounting structure.

It is worth noting that the ESR value at a given frequency for an AT- strip crystal design is generally higher than that of the standard (round blank) design. This becomes more significant at lower frequencies. When transitioning from a series resonant through-hole HC-49/U type crystal to a smaller surface mount type utilizing an AT-strip crystal, some consideration may be given to the difference in the ESR values produced by different cuts.

The ESR becomes critical when resistance values reach a point were the oscillator circuit cannot adequately drive the crystal. Sluggish start-up or unwanted modes of operation may result.

Equivalent Circuit:

The equivalent circuit (shown in Figure A) depicts electrical activity of a quartz crystal unit operating at its natural resonant frequency. The shunt capacitance (Co), represents the capacitance of the crystal electrodes plus the capacitance of the holder and leads. R1, C1, and L1 compose the "motional arm" of the crystal, and are referred to as the motional parameters. The motional inductance (L1) represents the vibrating mass of the crystal unit. The motional capacitance (C1) represents the elasticity of the quartz, and the resistance (R1), represents bulk losses occurring within the quartz.

Useful Equations:

Equations Definitions
fS = (Series) frequency = C0 = Static Capacitance in farads
CL = Load capacitance = C1 = Motional capacitance in farads
Co = Shunt capacitance = CL = Load capacitance in farads
C1 = Motional capacitance = f = Nominal frequency in Hz
L1 = Motional inductance = fL = Anti-resonant frequency in Hz
R1 = Series resistance = fS = Series resonant frequency in Hz
Q = Quality factor = L = Inductance into Henrys
fL - fS = f = PL = Pullability (ppm/pF)
PL = Pullability = Q = Quality factor
R1 = Series resistance in ohms | Site Map