Although not an active filter, crystal (Quartz) filters are very high \(-Q\) filters. Some can have \(Q\) 's approaching 100,000. High \(Q\) means high selectivity; hence, crystal filters are used extensively in communications where fine-tuning is essential. In its simplest form, a quartz crystal is a rectangular cut crystal with metal plates attached to its flattest sides-imagine a parallel-plate capacitor with the crystal as the dielectric. An electronic equivalent of a quartz filter is shown in Figure P14=57. \(C\) O is called the shunt capacitance, and \(C_{1}, L_{1}\), and \(R_{1}\) are the mechanical capacitance, inductance, and resistance of the crystal, respectively. A particular crystal has \(C_{\mathrm{O}}=1.2 \mathrm{pF}, C_{1}=\) \(2.3 \mathrm{fF}, L_{1}=6.2 \mathrm{mH}\), and \(R_{1}=32 \Omega\). Assume \(R_{\mathrm{L}}=10 \Omega\). Analyze this filter and determine its \(Q\) and \(\omega_{o}\). Use MATLAB or Multisim to examine this circuit and help calculate the requested parameters.

Transcribed Image Text:

otto Circuit symbol VI(1) Equivalent circuit Co 41000 M C L R RL v(1)