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BELL SYSTEM TECHNICAL JOURNAL 



one of the wires is not located exactly on a node of the plate, the plate will 

 set the wire into vibration. For certain critical lengths of the wire, it will 

 offer considerable resistance to this motion and there will be a rapid increase 

 in effective resistance and some change in resonant frequency of the crystal 

 plate. 



The effect of wire \abration can be described in terms of its electrical 

 analogy. The vibrating wire, clamped at its far end, may be considered a 

 rather special electrical transmission line open-circuited at its far end. 

 WTien viewed from the crystal plate the impedance changes rapidly with 



X 



OR 

 R 



/ZJ315V 



Zc=Ri+jXi Zw=R2+iX2 



IMPEDANCE IMPEDANCE 



OF CRYSTAL OF WIRE 



PLATE RESONANCE RESONANCE 



Fig. 14.10. — Effect of wire resonance on the resonant frequency of a crystal unit. 



frequency in a succession of pronounced resonances and anti-resonances. 

 In the vicinity of an anti-resonance the electrical equivalent of the vibrating 

 wire may be approximated by a coil and condenser in parallel as shown by 

 L2 and C2 of Fig. 14.10. This acts in series with the mechanical resonance 

 of the quartz plate, represented by Zi and Ci. The impedance curves illus- 

 trate the effect of the wire resonance on the crystal impedance. R\, the 

 equivalent resistance of the crystal plate, is constant for frequencies in the 

 vicinity of resonance. Xi, the equivalent reactance of the crystal plate, 

 increases rapidly as the frequency departs frcm resonance. R2 and X2, the 

 equivalent resistance and reactance of the wire resonance, are typical of an 



