Quartz Crystals

Quartz Crystal Units

Introduction:

Quartz crystals have very high Q and the AT cut crystals have excellent temperature Vs. Frequency stability. Quartz Crystals have very large applications from simple quartz clocks to sophisticated mobile communication equipment. The purpose of this document is to explain the characteristics of a quartz crystal to the designer of electronic circuits.

Equivalent Circuit of a Crystal


The Equivalent circuit of a quartz crystal is shown in Figure 1:-

The Series combination of the R1, the Equivalent Series resistance, C1 the motional capacitance and L1, the inductance along with C0 the shunt capacitance represents the quartz crystal. The C0 is the capacitance of the electrodes that are formed by thin metal film on the surface of the quartz crystal and the capacitance of the crystal cover. The R1 is a result of the mounting arrangement of the crystal blank on the crystal base and also the mounting stresses and the resultant loss in the quartz. The L1 results from the mass of the crystal blank and the C1 results from the stiffness of the quartz. All these parameters can be measured by using a Crystal Impedance meter.

The reactance characteristic of the quartz crystal is shown in Figure 2



The series resonant frequency of the crystal FS is:


Where FS, the series resonant frequency in hertz, the L1, the motional inductance is in Henries and C1 is in Farads.

Load capacitance

When a Capacitive load CL is used with the crystal, the effect is to change the Frequency of Oscillation FL The frequency of Oscillation FL is:


Where r is the capacitance ratio
r = C0 / C1

The change in the frequency of oscillation FL due to the Load capacitance CL is determined by:


For example, the Frequency of Oscillation of a 10 MHz fundamental crystal with a load capacitance of 30 pF, C0 of 6 pF and r of 230 will be about 3.6 kHz above the series resonant frequency. The rate of the frequency change due to the change in CL is high where the value of CL is small and also when the capacitance ratio r is small.

Load Capacitance can be measured by:
1) Measuring the FL and calculating CL  when motional parameter values are known; or
2) Measure the crystal in a Crystal Impedance meter and find the CL that gives the correct FL.

Pullability
Crystal pullability is the change in the crystal frequency due to the change of the CL. The Pullability is expressed in two ways:


As DL the actual frequency change from FS to FL

DL can also be expressed as:


Pullability is also expressed as trim or pulling sensitivity and is calculated as



Table 2 Typical Values of C1 and C0
Frequency Range Mode C1 in fF C0 in pF
1 to 2 MHz Fundamental 5 - 8 3
2 to 4 MHz Fundamental 6 - 12 4
4 to 8 MHz Fundamental 8 - 20 5
8 to 30 MHz Fundamental 16 - 26 6
20 to 85 MHz 3rd Overtone 1 - 2.5 6
60 to 120 MHz 5th Overtone <0.5 6

Frequency Vs Temperature Characteristics

The frequency Vs. Temperature characteristic of an AT cut crystal unit describes a cubic curve that has an inflection or inversion point at room temperature. Inversion points are the points of zero temperature coefficients and there are two inversion points: the lower and upper inversion point. Changing the crystal blank cutting angle q can change the slope of the curve and the points of inversion.


Figure shows how the frequency Vs temperature characteristic of an AT cut 10 MHz Series resonant mode crystal changes with the change of the crystal angle:

The Frequency Vs temperature characteristics of a fundamental mode crystal and an overtone mode crystal unit can have the same cubic curve but this is achieved by changing the angle of cut considerably. Crystals designed for Oven controlled circuits have an angle of cut so that the upper inversion point occurs at the oven temperature.

Crystal Packages

Crystals are available in two kinds of enclosures: Resistance weld enclosures and Cold weld enclosures. Resistance welding packages The resistance welding is done in an inert dry Nitrogen atmosphere offer the lowest cost and have typical ageing rates of about ± 5 ppm during the first year and ± 3 ppm per year thereafter.

Cold weld packages which are specially processed and welded in a high vacuum offer much better ageing rates and typically the ageing rates of cold weld crystal is less than ± 1 X 10-6 per year (± 1 ppm).

Resistance Weld Package Equivalent Cold Weld Package
HC 49/U HC 43/U
HC 50/U HC 42/U
HC 51/U HC 47/U
HC 48/U HC 36/U
UM-1 Nil