A AT-cut crystal has motional parameters

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Circuit foundations and passive networks · Feedback, operational amplifiers and analogue signal processing

Inside the Instrument, Ch Filters, crystal oscillators and phase-locked loops

Problem

A 20 MHz20\,\mathrm{MHz} AT-cut crystal has motional parameters C1=15 fFC_1 = 15\,\mathrm{fF}, R1=25 ΩR_1 = 25\,\Omega and electrode capacitance C0=4 pFC_0 = 4\,\mathrm{pF}. Its series resonance is fser=20 MHzf_{\rm ser} = 20\,\mathrm{MHz}, and it is specified to run with a load capacitance CL=15 pFC_L = 15\,\mathrm{pF}, but the oscillator board actually presents CL=25 pFC_L = 25\,\mathrm{pF}. ((a)) Find the motional inductance L1L_1. ((b)) Find the crystal's QQ. ((c)) Using fL≈fser(1+C12(C0+CL))f_L \approx f_{\rm ser}\left(1 + \dfrac{C_1}{2(C_0+C_L)}\right), find the fractional pulling (in ppm) and the frequency shift (in Hz) between operation at CL=15 pFC_L = 15\,\mathrm{pF} and at CL=25 pFC_L = 25\,\mathrm{pF}.

Browse the problem library