This sheet is a general purpose design sheet for LC VCOs and PLLs.
Start by entering the VCO components assuming a Colpitts topology.
Then, calculate the effective VCO Q
Then, calculate the VCO phase noise profile,
Then, the loop bandwidth and the integrated phase noise.
I will try to put some simulation results in soon, but at the moment this looks ok to me.
VCO Noise floor
VCO Details, QC is Q for the Capacitor which is assumed to be high compared to the L, The VCO is assumed to be Colpitts.
First calculate the noise factor (F) of the VCO transistor as defined by Rogers & Plett, Radio Freq Integrated Circuit Design (page 286), where
The noise equations are from Gray & Meyer page 752 and 759
and the higher this is, the higher the VCO
This plot on the right shows the effective noise
figure of the VCO under different QL, and
inductor values.
bias resistance and the transistor gm, but NOT the transistor noise.
Noise Floor in dBm
Now that we have the noisefloor, the phase noise can be found from Rogers & Plett, Radio Freq Integrated Circuit Design (page 286), equation 8.90 and adding the affect for noise floor but ignoring flicker noise.
Qt = Q of Oscillator tank
Vtank = peak voltage swing in LC
Ps = power in loop (assumed to be output power)
PN is relative phase noise in dB
The VCO output power is
This calculates the phase noise accoding to the Leeson's equation assuming the phase-noise is dominated by the Q, i.e the noise slope is 20dB/decade.
This plot will have the same wideband noise floor as specified above (in dBm)
The phase noise is in dBc
dBc
These plots show how the phase noise changes.
There are only two ways to improve the phase noise, increase Q and increase current.
The phase noise calculation inside a synth loop is found from the Deans Book from Nat Semi
The Phase detector phase noise (PDPN) is guessed at and is in dBm/Hz, The limit is typically -207
prf is the phase-reference-freq
This part calculates the PLL in-band phase-noise in -dBc/Hz.
First we need to calculate the in-loop phase noise from
Noise from the phase detector dominates the in-band noise floor, given here.
Then calculate Fc.....
dBc/Hz
The integrated RMS phase noise in degrees is a very useful single-figure measure of performance and can be calculated using equations from page 50 of Deans book assuming a certain amount of peaking given in dB.
These results are interesting as they show that the total integrated-phase-noise, in a properly designed synth varies with CURRENT, Q, and N but not much with INDUCTANCE.
High Current, High Q, Low N