Pspice simulation quartz crystal oscillation circuit

1、 Quartz crystal equivalent model

1.1、 Frequency calculation

From the equivalent circuit , Quartz crystal has two resonant frequencies , namely

（1） When R、L、C When series resonance occurs in the branch , Its Series resonance The frequency is

because C0 Very small , Its capacitive reactance ratio R Much more , therefore , The equivalent impedance of series resonance is approximately R, It is purely resistive , And its resistance value is very small .

（2） When the frequency is higher than fs when ,r、l、c The branches are perceptual , When and C0 happen Parallel resonance when , Its oscillation frequency is

because C<<C0, therefore fs And fp Very close to .

Usually, the nominal frequency given by quartz crystal products is neither fs Neither fp, Instead, a small capacitor is connected outside Cs Time corrected oscillation frequency ,Cs It is connected in series with quartz crystal as shown in the figure below .

utilize Cs The resonant frequency of quartz crystal can be adjusted in a small range .Cs The value of should be selected to be higher than C Big . Can calculate access Cs After the new series resonance frequency

 

Expand the above formula into a power series , And notice C<<C0+Cs, Thus omitting the higher-order items , It can be approximated

When Cs -> 0 when ,f's be equal to fp, And when Cs -> ∞ when ,f's be equal to fs. When practical ,Cs It is a fine-tuning capacitor , send f's stay fs And fp Between a narrow range of changes .

 1.2、 Summary of model parameters

Crystal	source	R（Ω）	C（fF）	L（H）	C0（pF）	Fs（Hz）	Fp（Hz）	Conclusion
32KHz	Fairchild AN340	200k	3	7000	1.7	34.730K	34.782K	Why? Fs Greater than 32KHz？
200KHz	Fairchild AN340	2k	24	27	9	197.711K	197.975K	Why? Fp Less than 200KHz？
2MHz	Fairchild AN340	100	12	0.529	4	1.9976M	2.001M	reasonable
30MHz	Fairchild AN340	20	2.6	0.011	6	29.760M	29.767M	Why? Fp Less than 30MHz？
10M	Abracon ABM8W	53.82	1.56	0.16202	0.88	10.011M	10.020M	Why? Fs Greater than 10MHz？
27M	Abracon ABM8W	11.83	3.80	0.00916	1.16	26.976M	27.020M	reasonable
50M	Abracon ABM8W	7.61	4.14	0.00245	1.16	49.973M	50.062M	reasonable
25M	Yingdali	8.8	3.66	11.07	1.01	25.004M	25.049M	Why? Fs Greater than 25MHz？

Reference resources

[1] Chen Tuo ,《PSPICE Simulate quartz crystal oscillation circuit 》,2011

[2] Electromechanical home ,《 Basic characteristics and equivalent circuit of quartz crystal 》