Analysis of Phase-Locked Loops using the Best Linear...
Transcript of Analysis of Phase-Locked Loops using the Best Linear...
Analysis of Phase-Locked Loops
using the Best Linear Approximation
Dries Peumans
Adam Cooman
Gerd Vandersteen
Nonlinear behaviour degrades the envisioned performance
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UnwantedIdeal
Nonlinear behaviour
Analysis of Phase-Locked Loopsusing the Best Linear Approximation
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1 How to describe the PLL?
Architecture and linear models
2 How to characterise the nonlinearities?
Best Linear Approximation (BLA) and multisines
3 How to combine both?
Pitfalls and results
The PLL uses feedback to lock the phase of its oscillator to the reference
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CPPFD LF
VCO
DIV
UP
DOWN
Can we come up with an ideal model?
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CPPFD LF
VCO
DIV
UP
DOWN
PLL is best studied in the phase domain
1 Voltage and current domain
Strongly nonlinear
2 Phase domain
Linear
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𝑣 𝑡 = 𝐴 cos(𝜔𝑐𝑡 + 𝜑 𝑡 )
Voltage 𝑣 𝑡
Phase noise 𝜑 𝑡
You can linearize the behaviourin the phase domain
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PFD + CP LF VCO
DIV
The BLA combines concepts from both the linear and Volterra theory
1 Linear model
+ Easy to use / widespread
− Neglects nonlinearities
2 Volterra theory
+ Models nonlinearities
− Difficult− Weak nonlinearities
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Best Linear Approximation+ Linear+ Strong nonlinearities
The BLA extracts a linear modelfrom nonlinear systems
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Linear Distortions
Multisines make odd and even NLs distinguishable
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Multisines give more controlover the excited frequencies
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Noise Multisine
Wanted profile
Frequency Frequency
Applying multisines as time jitterallows to characterise the distortions
1 Non-ideal oscillator
2 Digital reference clock
Time jitter
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Phase domain multisine
Phase domain multisinesneed to be quantised
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Phase domain multisinesare applied as the reference signal
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A 4th-order type-II PLL is analysed using the BLA
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PFD behaves linearly in phase domain
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𝑌𝑃𝐹𝐷
Even 𝑌𝑆
Odd 𝑌𝑆
Introduce nonlinear behaviour in the CP
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1 Asymmetric delay
𝜏𝑈𝑃 ≠ 𝜏𝐷𝑁
2 Mismatch in current sources
𝐼𝑈𝑃 ≠ 𝐼𝐷𝑁
Effects of non-idealities in CP are significant
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Asymmetry of 1‰ Mismatch of 1%
𝑌𝐶𝑃 𝑌𝐶𝑃
Even 𝑌𝑆
Even 𝑌𝑆
Odd 𝑌𝑆 Odd 𝑌𝑆
Analysis of Phase-Locked Loopsusing the Best Linear Approximation
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1 How to describe the PLL?
Architecture and linear models
2 How to characterise the nonlinearities?
Best Linear Approximation (BLA) and multisines
3 How to combine both?
Pitfalls and results