Crystal Electrical Equivalent Circuit

The circuit is the electrical model of a quartz crystal, which is used in oscillators, excited by a current source. The graph of the impedance of the crystal as a function of frequency will be obtained. The values of the electrical equivalent circuit is the motional arm parameters of a representative 4 MHz crystal. With a test current source of 100 mA, the magnitude of voltage across the crystal is 1/10 that of the crystal impedance. L = 0.06332573977646110715242466450608 H A crystal has a high equivalent inductance relative to its small size. fs = 3,999,991.7814544981367339837620941 Hz fp = 4,007,676.6910972157129698532915266 Hz Sweep configuration: Start frequency: 500 kHz Stop frequency: 10 MHz Linear Points per decade: 500 to 1000 Vertical scale: Linear/Logarithmic The impedance of a crystal is very very high at low frequencies (at DC the circuit is open), decreases as frequency increases, and falls to the parallel connection of Cp and R at series resonance. The impedance rises to very high value at parallel resonance (when L resonates with the series combination of Cs and Cp) then decreases as frequency is further increased. The impedance will completely fall to zero only at infinite frequency (Cp shorts out the RLCs branch). In order to focus on the details of the graph near the frequencies of resonance, the frequency sweep starts at a relatively high value of 500 kHz and ends at a relatively low value of 10 MHz.