1. Frequency Stability FCC standards for FM Broadcast (p 337) Allocation:88.0 – 108.0 Mhz Channel Spacing/Width:200 khz Carrier Stabilility:+ 2 khz = 20 ppm

2. Temperature Stability Example: Nominal frequency is 21.400 Mhz at 25 o C. Measured frequency at 45 o C is 21.407 Mhz.  f = 7 khz,  T = 20 o C. Estimate the frequency at -15 o C f(T) = f nom +TCf nom (T-T nom ) = 21.4 +  f = 21.4 + (16.35 x 10 -6 )(21.4)(-15 - 25) = 21.386 Mhz

3. Improving Temperature Stability 1.Control Temp coefficient of components. 2.Neutralize or swamp out device variations. 3.Low Power Operation (benign environment) 4.Active TC compensation/tracking 5.Control/reduce circuit noise 6.Buffer output to isolate load variations 7.Thermal isolation/oven. 8.Use a crystal

4. Undeformed lattice X + + + + + + + + + + + + + + + + + + + + + _ _ _ _ _ __ _ _ _ _ __ _ _ _ _ _ _ _ Strained lattice + + + + + + + + + + + + + + + + + + + + + __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ X - + Y Y _ _ Quartz Crystal Structure Quartz Crystal

5. Piezoelectric Effect External Field Internal Field

6. Crystal Equivalent Circuit C x ~ 10 -15 f L x 1 – 10 h R x 50 – 200  C 0 2 – 10 pf Neutralization of Case Capacitance for Series Operation L n

7. Crystal Resonances X  Series Resonance -X C Parallel Resonance with case capacitance Reactance of Crystal Blank

8. Crystal Resonances X  Parallel Resonance with case capacitance Series Resonance Overtone Operation Tank Circuit is tuned to be resonant at desired overtone. Reactance of Crystal Blank with Package Capacitance Very small frequency difference. Very steep slope (large dynamic inductance)

9. Application to Oscillators (series mode) Hartley E C C E RxRx Colpitts