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Filtering High S/N Digitally Tuned Oscillator




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High S/N Digitally Tuned Oscillator

MINI-POLE® and MAXI-POLE® filters make excellent resonators for use in digitally tuned, low noise oscillators.  The output signal to noise (S/N) ratio of an oscillator may be expressed as:

   dBc/Hz

where:

P0 = Oscillator output power
Q = Resonator loaded Q
K = Boltzmann’s constant
T = Temperature (° Kelvin)
ω0 = RF oscillator frequency
ωm = Frequency removed from ω0
F = Amplifier noise figure
G = Amplifier gain

For small ωm (close-in), For large ωm (ultimate),
dBc/Hz dBc/Hz

Assuming the use of a low noise amplifier, the design problem reduces to operating power and tuned circuit Q (or, more accurately, the rate of change of phase vs. frequency at ω0).  Power and Q both control the resultant S/N ratio close-in; in essence, as a squared function of Q and as a linear function of power.  Thus, for example, raising the power level of an oscillator by 30 dB increases the close-in S/N ratio just as much as increasing the Q by a factor of 32!  Note Q has no effect on ultimate S/N.  Often in the quest for higher S/N ratio, only the Q of the oscillator is ignored.

In the simple example shown below, the oscillator is allowed to operate near the 1 Watt power level, producing an ultimate S/N ratio approaching 200 dBc/Hz.  Not only is the ultimate S/N ratio very good, but it is achieved relatively close-in.  In the example shown, the ultimate S/N would be reached at less than 2% removed from f0.












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