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

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 using the Best Linear Approximation 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 3

The PLL uses feedback to lock the phase of its oscillator to the reference UP PFD CP LF DOWN VCO DIV 4

Can we come up with an ideal model? UP PFD CP LF DOWN VCO DIV 5

PLL is best studied in the phase domain 1 Voltage and current domain Strongly nonlinear Voltage 𝑤 𝑢 𝑤 𝑢 = 𝐵 cos(𝜕 𝑑 𝑢 + 𝜒 𝑢 ) 2 Phase domain Phase noise 𝜒 𝑢 Linear 6

You can linearize the behaviour in the phase domain PFD + CP LF VCO DIV 7

The BLA combines concepts from both the linear and Volterra theory 1 Linear model + Easy to use / widespread − Neglects nonlinearities Best Linear Approximation + Linear + Strong nonlinearities 2 Volterra theory + Models nonlinearities − Difficult − Weak nonlinearities 8

The BLA extracts a linear model from nonlinear systems Linear Distortions 9

Multisines make odd and even NLs distinguishable 10

Multisines give more control over the excited frequencies Noise Multisine Wanted profile Frequency Frequency 11

Applying multisines as time jitter allows to characterise the distortions 1 Non-ideal oscillator Phase domain multisine 2 Digital reference clock Time jitter 12

Phase domain multisines need to be quantised 13

Phase domain multisines are applied as the reference signal 14

A 4 th -order type-II PLL is analysed using the BLA 15

PFD behaves linearly in phase domain 𝑍 𝑄𝐺𝐸 Even 𝑍 𝑇 Odd 𝑍 𝑇 16

Introduce nonlinear behaviour in the CP 1 Asymmetric delay 𝜐 𝑉𝑄 ≠ 𝜐 𝐸𝑂 2 Mismatch in current sources 𝐽 𝑉𝑄 ≠ 𝐽 𝐸𝑂 17

Effects of non-idealities in CP are significant Mismatch of 1% Asymmetry of 1 ‰ 𝑍 𝐷𝑄 𝑍 𝐷𝑄 Even 𝑍 𝑇 Even 𝑍 𝑇 Odd 𝑍 𝑇 Odd 𝑍 𝑇 18

Analysis of Phase-Locked Loops using the Best Linear Approximation 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 19