Quartz Crystal Filters

This was one of the important reasons limiting the use of carrier telephone systems to the band just mentioned. Crystal filters⁷, together with other important developments, have extended the upper limit to millions of cycles.

The use of quartz crystals was suggested⁹ by Espenschied and has been made practicable by the work¹⁰ of Mason and others. As is well known, crystals of quartz vibrate at certain frequencies but not at others. They are electrically equivalent to tuned circuits. The Q of a quartz crystal is as high as 20000 or more.¹¹

Figure 47. A quartz crystal acts, when associated with a suitable electric circuit, as the network shown above. The reactance characteristics of this circuit are shown below. The resistance component is low at the resonant frequency fR and high at the antiresonant frequency fA. (Reference 11.)

The equivalent electrical network and the reactance characteristics of a quartz crystal are shown in Fig. 47. The inductance L represents the mass reaction of the crystal against motion (inertia effect); the resistance R represents the energy dissipation within the crystal; the condenser C₁ represents the compliance¹ of the crystal; and C₀ is the capacitance of the circuit with the crystal not in motion. As indicated, there is one series resonant frequency f_R and one parallel or antiresonant frequency f_A of the crystal. For a given crystal, these have a ratio such that f_A is 0.4 per cent higher than f_R.¹¹ This ratio can be reduced and controlled by adding a capacitor in parallel with the crystal,¹¹ and if the capacitor has low losses, the circuit will retain a high ratio of reactance to resistance or Q. In Fig. 48 are shown a crystal filter of the ladder type, the corresponding reactance curves, and the resulting filter characteristics.

Assume that the elements of Fig. 48 have the characteristics plotted in Fig. 47. For a single pass band, the series elements are resonant when the shunt unit is antiresonant. With this combination, maximum attenuation occurs when the shunt crystal is in resonance and when the series crystals are in antireso-nance because of the minimum shunt impedance and the maximum series impedances at this frequency. When the crystals pass through the antiresonant frequency f_A, the resistance component of the impedance rises to a high value as in the usual parallel circuit.

As was previously explained, the point of anti-resonance f_A is 0.4 per cent above the frequency of resonance f_R, Thus, the band passed is very narrow. For a 60,000-cycle carrier, the band would be only 240 cycles above and below the carrier, giving a total width of 480 cycles, a band too narrow for most purposes.⁹ Thus, with the ladder-type crystal filter, the band of frequencies passed is always less than 0.8 per cent of the midfrequency value.

Figure 48. Ladder-type filter network employing only crystals and capacitors, above; reactance characteristics, center (solid curve is series branch and dotted curve is shunt branch), attenuation characteristics, below. (Reference 11.)

The filter of Fig. 48 is of an elementary type. Much progress has been made in the design of crystal filters.^12,13,14 They are often made in the form of lattice structures giving improved characteristics. Sometimes the crystals are provided with divided electrodes^12,13 that pass energy from one set of electrodes to the other only at frequencies at which the crystal vibrates. Natural quartz was used in crystal filters until about 1947, and since then synthetic crystals¹⁵ have been used extensively.