using the Best Linear Approximation Dries Peumans Adam Cooman Gerd - - PowerPoint PPT Presentation

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using the best linear approximation
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using the Best Linear Approximation Dries Peumans Adam Cooman Gerd - - PowerPoint PPT Presentation

Dec 30, 2022 93 likes β€’304 views

Analysis of Phase-Locked Loops using the Best Linear Approximation Dries Peumans Adam Cooman Gerd Vandersteen Nonlinear behaviour degrades the envisioned performance Ideal Unwanted Nonlinear behaviour 2 Analysis of Phase-Locked Loops

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SLIDE 1

Analysis of Phase-Locked Loops using the Best Linear Approximation

Dries Peumans Adam Cooman Gerd Vandersteen

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SLIDE 2

Nonlinear behaviour degrades the envisioned performance

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Unwanted Ideal Nonlinear behaviour

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SLIDE 3

Analysis of Phase-Locked Loops using 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

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SLIDE 4

The PLL uses feedback to lock the phase of its oscillator to the reference

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CP PFD LF VCO DIV UP DOWN

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SLIDE 5

Can we come up with an ideal model?

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CP PFD LF VCO DIV UP DOWN

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SLIDE 6

PLL is best studied in the phase domain

1 Voltage and current domain Strongly nonlinear 2 Phase domain Linear

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𝑀 𝑒 = 𝐡 cos(πœ•π‘‘π‘’ + πœ’ 𝑒 ) Voltage 𝑀 𝑒 Phase noise πœ’ 𝑒

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SLIDE 7

You can linearize the behaviour in the phase domain

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PFD + CP LF VCO DIV

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SLIDE 8

The BLA combines concepts from both the linear and Volterra theory

1 Linear model + Easy to use / widespread βˆ’ Neglects nonlinearities 2 Volterra theory + Models nonlinearities βˆ’ Difficult βˆ’ Weak nonlinearities

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Best Linear Approximation + Linear + Strong nonlinearities

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SLIDE 9

The BLA extracts a linear model from nonlinear systems

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Linear Distortions

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Multisines make odd and even NLs distinguishable

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Multisines give more control

  • ver the excited frequencies

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Noise Multisine Wanted profile

Frequency Frequency

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Applying multisines as time jitter allows to characterise the distortions

1 Non-ideal oscillator 2 Digital reference clock Time jitter

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Phase domain multisine

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Phase domain multisines need to be quantised

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Phase domain multisines are 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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𝑍

𝑄𝐺𝐸

Even 𝑍

𝑇

Odd 𝑍

𝑇

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SLIDE 17

Introduce nonlinear behaviour in the CP

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1 Asymmetric delay πœπ‘‰π‘„ β‰  πœπΈπ‘‚ 2 Mismatch in current sources 𝐽𝑉𝑄 β‰  𝐽𝐸𝑂

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SLIDE 18

Effects of non-idealities in CP are significant

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Asymmetry of 1‰ Mismatch of 1%

𝑍

𝐷𝑄

𝑍

𝐷𝑄

Even 𝑍

𝑇

Even 𝑍

𝑇

Odd 𝑍

𝑇

Odd 𝑍

𝑇

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SLIDE 19

Analysis of Phase-Locked Loops using 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