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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
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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. |