# ## Power supply noise optimization for best phase noise

Having a low-noise power supply is critical for frequency synthesizers as the power supply noise modulates oscillators, creating phase noise. This additive phase noise needs to sufficiently below the phase noise specification (of the full synthesizer). Therefore, there needs to be a procedure to calculate maximum allowable power supply noise, given particular oscillator parameters. Power supply noise specification is also depended on filter bandwidth of power supply filter, which is between power supply and oscillator. Commonly, this filter is a simple RC decoupling filter, with R pretty small (<10 ohm), considering typical VCO supply current (not to create a huge drop on oscillator supply voltage) and C typically less than 100uF, the cutoff frequency would be >100Hz. If phase noise specification is important for around 100 KHz or less; then, typically, simple RC filter would not be sufficient to ignore power supply noise. Of course, the RC filtering have to be included into calculation of the required power supply noise, and this is assumed to performed in advance to come up with a modified phase noise mask (synthesizer specification low-pass filtered by RC filter). There might be a few iterations if initial filter choice leads to a difficult Power Supply design.

The Leeson equation, describes how the phase noise of a VCO is affected by various VCO parameters: Where, R is equivalent noise resistance of the tuning diode and all extra resistance on tuning port, K0 is the tuning sensitivity, fm is offset frequency, fc is the center frequency, and the last statement is the contribution due to power supply or tuning diode noise.

The following will show why we can lump power supply noise with tuning diode noise.

Assuming:

VCO has no power supply filtering inside (if it does it should be combined with RC filter mask, as discussed above)

- Pushing sensitivity can be used, outside of it's typical DC-measurement, for sub-MHz transfer function from power supply to frequency (phase) noise. This might not be true for all VCOs, in which case another transfer function needs to be derived and be lumped together with the RC filter outside of VCO.

Considering the fact that, pushing and tuning sensitivity numbers are both in Hz/V, and, technically, both convert voltage noise into phase noise with the last statement in the Leeson equation, we can add extra term which looks exacltly like the one for tuning diode: Finally, the phase noise degradation (ΔL [rad]) due to power supply noise density (vn) at offset (fm) with pushing sensitivity (K0) is: [rad/Hz]

Where we replaced R with noise voltage spectral density: [V/√Hz]

Considering that we allow certain degradation from the phase noise mask, in dB, call it dLdB, we can write an expression for required power supply noise spectral density (before taking into account all RC filtering at power supply): [V/√Hz]

Where L(fm) is a single-side-band (SSB) phase noise of the VCO [rad/Hz] at offset fm [Hz] and K0 is pushing sensitivity [Hz/V] of VCO. This equation is verified with references , and in practice. In most cases phase noise is specified in dBc/Hz, which case we need to convert from dB scale to linear scale. Linear (SSB) phase noise in terms of SSB phase noise on dB scale is: As we can see the power supply noise spectral density is a high pass function over offset frequency. This means that power supply spectral density requirements get tougher for lower offsets. Typical linear regulators have higher noise at lower offsets with typical plateau around 1KHz - 10 KHz. This presents a design problem for low frequency offset noise (10 Hz - 1 KHz). One way to reduce noise at lower offsets is to use common-base cleaning circuit after, but only if current is known or other method of load regulation is available.