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An Oscillator Scheme for Quartz Crystal Hayward, 15 Nov07 The familiar quartz crystal is modeled with the circuit shown below containing a seriesinductor LM, capacitor CM, and equivalent series resistor ESR, all paralleled by acapacitor subscript M used with L and C signify that these is a two terminal device, something that has but a single element can becharacterized by studying it with a network analyzer where it is placed between agenerator and a load. The scattering parameters are then measured. Detailed analysis isthen used to extract the four , this is not possible for those of uswithout a basement network analyzer and it is not very can do a simplified analysis with a stable oscillator (usually a VXO) operating as asignal generator with a very low source impedance and a very low load resistance. Thisis shown low source impedance has traditionally been generated with a transformer droppingfrom 50 Ohms down to a source impedance from 3 to 12 are inserted tofurther establish the the impedance is very low, the parallelcapacitance has little impact upon the voltage across the load and can be ignored, at leastfor this simple analysis, leaving nothing but a series tuned generator istuned to series resonanceto produce a maximum thisagainst a pieceof wire (a through connection to the network analyzer folks) allows the ESR to beinferred from the insertion the generator is then tuned to one side and then tothe other to the 3 dB points.

An Oscillator Scheme for Quartz Crystal Characterization. Wes Hayward, 15Nov07 The familiar quartz crystal is modeled with the circuit shown below containing a series

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