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

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

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

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

Piezoelectric Effect External Field Internal Field

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

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

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)

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