### Oscillator Circuits

```Oscillator Circuits
Outline
• Oscillators
– Inverter-Based Oscillator
– Introduction of Phase Noise Simulation
– LC-Tank Based Oscillator
• Laplace Analysis
• Circuit Implementation
• Quality Factor Analysis
Inverter-Based Oscillator
Delay Per Stage of the Inverter
(273 pS)
(395 ps)
Period: 395-273=122 pS, Delay per stage (TD): 234-214=20 pS. Period is 2NTD
Oscillation Frequency
Calculation
• fosc=2.14 GHz
• Tosc=467 pS=2NTD
– TD=20 pS
– N=Tosc/(2TD)=467 pS/(2 20)=11.68
– N must be odd.
– Choose N as 11.
11 Stage Oscillator
11 Stage Oscillator
Period: 1.501 nS-1.052 nS=0.449 nS, Freq=2.227 GHz
Phase Noise
Harmonics
Pnoise
Phase Noise of a Ring Oscillator
LC Tank Oscillator
Laplace Transform Analysis
LC Tank Oscillator
• Resonant Frequency: 2.14 GHz
• L=1 nH
LC Tank Oscillator
Transient Simulation
Frequency: 1.941GHz
Reduce the Value of Capacitor
(2.16 GHz)
PSS and Pnoise Setting
Phase Noise
Quality Factor of 10 for the
inductor
Oscillation dies out since gtank is greater than gm of the transistor.
Rind=100 mΩ
This is the maximum parasitic resistance we can have without destroying the oscillation.
Transient Simulation
Phase Noise with Rind=100 mΩ
Even a little series resistance at unreasonably high Q (130) can degrade phase noise quickly.
```