Instrumentation for measurement and characterization of mixed-signal devices

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Universidade de Aveiro Departamento deElectrónica, Telecomunica¸cões e Informática, 2018

Diogo Carlos Alcobia

Ribeiro

Instrumentation for Measurement and

Characterization of Mixed-Signal Devices

Instrumenta¸

c˜

ao para medida e caracteriza¸

c˜

ao de

dispositivos anal´

ogico-digitais

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Universidade de Aveiro Departamento deElectrónica, Telecomunica¸cões e Informática, 2018

Diogo Carlos Alcobia

Ribeiro

Instrumentation for Measurement and

Characterization of Mixed-Signal Devices

Instrumenta¸

c˜

ao para medida e caracteriza¸

c˜

ao de

dispositivos anal´

ogico-digitais

PhD Thesis submitted to request the evaluation by the PhD Scientific Committee and by the jury panel that will be nominated.

This PhD Thesis was supervised by Prof. Dr. Nuno Miguel Gon¸calves Borges de Carvalho, Full Professor from the Department of Electronics, Telecommunications and Informatics (DETI), University of Aveiro, and co-supervised by Dr. Pedro Miguel Duarte Cruz.

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the jury / o j´uri

president / presidente Professor Doutor Ant´onio Manuel Rosa Pereira Caetano

Professor Catedr´atico, Universidade de Aveiro

examiners committee / vogais Professor Doutor Jos´e Carlos Esteves Duarte Pedro

Professor Catedr´atico, Universidade de Aveiro

Professor Doutor Jos´e Alberto Peixoto Machado da Silva

Professor Associado, Universidade do Porto

Professor Doutor Jo˜ao Carlos da Palma Goes

Professor Associado com Agrega¸c˜ao, Universidade Nova de Lisboa

Doutor Dylan Forrest Williams

Investigador, National Institute of Standards and Technology

advisor / orientador Professor Doutor Nuno Miguel Gon¸calves Borges de Carvalho

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acknowledgments / agradecimentos

I want to thank everyone who supported me during this long journey. Especially, I want to thank Dylan Williams and Kate Remley for having received me at NIST, in Boulder, and for allowing me to learn from them, in such a great place.

I want to thank all the researchers from NIST, in particular Rob Horansky, for helping me with every difficult problem I encountered.

I want to thank all the friends with who I could take a break, enjoy the outdoors, or visit new places. Thank you all. . .

Thank you Al´ırio Boaventura for your huge help.

Jerome, Damir and Jelena, thank you my great friends! You managed to make all the time I spent with you, in Boulder, seem a lot shorter.

Thank you all so very much!

Quero também agradecer aos meus orientadores. Ao Prof. Nuno Borges de Carvalho pelas oportunidades proporcionadas, pela motiva¸cão, e por sempre acreditar que é poss´ıvel. Ao Doutor Pedro Cruz, por todo o apoio cient´ıfico, durante as partes interessantes e principalmente durante as partes chatas. Quero agradecer a toda a malta do instituto de telecomunica¸cões por todas as interessantes discussões e por me ajudarem a estar sempre a par de todas as noticias (cient´ıficas e de foro geral).

A todos os meus amigos e companheiros de aventuras, porque sem eles, seria certamente muito mais dif´ıcil ter chegado ao fim desta etapa.

`

A Inês por todo o carinho, dedica¸cão e paciência. E por todas as grandes experiências vividas por esse mundo fora.

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A ti Dulce, ao Jo˜ao e `a Maria Rita da Silva Teixeira, por todo o apoio durante esta (longa) parte final do doutoramento.

Aos meus pais e irm˜a, por todo o apoio incondicional, sempre. A todos, um grande muito obrigado!

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Keywords Mixed-signal (analog & digital), analog-to-digital converters (ADCs), digital-to-analog converters (DACs), software defined radios (SDRs), mi-crowave network analysis, device characterization, scattering parameters (S-parameters), radio frequency (RF) instrumentation, vector network ana-lyzers (VNAs)

Abstract This PhD thesis work is about the development of radio frequency oriented measurement and characterization approaches for mixed-signal devices. Mixed-signal devices are an important building block for newer, higher data-rate and smart radios. However, intuitive and simple characterization approaches have not yet been developed.

The most basic mixed-signal device is an ADC or a DAC. The ADCs and DACs will be considered in this work, as well as, more complex mixed-signal devices and even entire (integrated) radio front-ends.

A microwave network analysis approach, in an S-parameters like fashion, will be used to augment the modeling techniques of mixed-signal devices. This type of behavioral modeling approach is extensively supported within the tools used during the RF design stages. This will allow RF engineers to account for the non-ideal effects of these devices in a simpler way.

The final outcome may be used to establish an instrument capable to characterize both basic and more complex mixed-signal devices, in the same way a traditional VNA does for fully analog devices.

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Palavras-chave Sinais analógico-digitais, conversores analógico-digital (ADCs), conversores digital-analógico (DACs), rádios definidos por software (SDRs), análise de circuitos de micro-ondas, caracteriza¸cão de dispositivos electrónicos, parâmetros S, instrumenta¸cão de radiofrequência (RF), analisadores de redes vectoriais (VNAs).

Resumo Este trabalho de doutoramento aborda o desenvolvimento de técnicas de medida e caracteriza¸cão, usando uma perspetiva de radiofrequência, para dispositivos analógico-digitais. Os dispositivos analógico-digitais são blocos importantes no desenho de novos rádios, com maior velocidade de troca de dados, ou mesmo rádios inteligentes.

As ADCs e DACs podem ser consideradas como os dispositivos anal´ ogico-digitais mais simples. Neste trabalho vão ser consideradas as ADCs e DACs, bem como dispositivos analógico-digitais mais complexos, ou mesmo cadeias completas de rádio.

Uma abordagem baseada na análise de circuitos de micro-ondas, semel-hante à utilizada pelos ‘parâmetros S’, vai ser utilizada para expandir as técnicas de caracteriza¸cão dos dispositivos analógico-digitais. Este tipo de caracteriza¸cão comportamental é suportada amplamente pelas ferramentas utilizadas durante o desenvolvimento de aparelhos rádio. Esta técnica vai permitir aos engenheiros de RF considerar os efeitos não-ideais deste tipo de dispositivos, de uma forma mais simples.

O resultado final deste trabalho poderá vir a ser utilizado para estabelecer um instrumento capaz de caracterizar dispositivos analógico-digitais sim-ples ou mais complexos, da mesma forma que um VNA é utilizado para dispositivos puramente analógicos.

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List of Figures

1.1 Mobile data traffic growth prediction for the global market, based on [9]. . . . 2

2.1 Illustration of the sampling process effects in the frequency domain. . . 6

2.2 Detailed illustration of the down- and up-conversion effects that happen in mixed-signal converters due to the sampling process. . . 7

(a) Receiver configuration (ADC): down-conversion. . . 7

(b) Transmitter configuration (DAC): up-conversion. . . 7

2.3 Shape of the three main baseband pulses that DAC may use. The pulse shape is shown over the time of one sample period, from 0 to TS. . . 8

(a) NRZ . . . 8

(b) RZ . . . 8

(c) Manchester-like . . . 8

2.4 DAC ideal frequency response, in magnitude and phase, considering the three main baseband pulse shapes. The frequency response is shown for a normalized frequency, from 0 to 6_{× f}S. . . 9

(a) NRZ . . . 9

(b) RZ . . . 9

(c) Manchester-like . . . 9

2.5 Ideal SDR transceiver architecture. . . 11

2.6 Receiver front-end using a baseband digitization architecture, where the digi-tization is performed at BB using an I/Q approach. . . 12

2.7 Receiver front-end using an IF digitization architecture, performing digitization at IF. . . 13

2.8 Receiver front-end using a direct digitization architecture, performing digitiza-tion of the incoming signal directly at RF. . . 13

2.9 Oscilloscope versus logic analyzer waveforms. . . 16

2.10 S-parameters representation of a 2-port device. . . 19

2.11 Architecture of a traditional VNA. . . 19

2.12 Illustration of the new instrument, capable of measure and characterize mixed-signal devices and systems: the Mixed-Signal Network Analyzer. . . 22

2.13 Reference planes in coaxial PC 3.5 mm, 2.4 mm or 1.85 mm connectors, from [74, p. 89] . . . 24

2.14 Error in measuring the reflected traveling wave, b1, due to the limited direc-tional coupler directivity. The measured value, b1m, is vectorial affected by ed, b1m= b1+ ed. . . 24

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2.15 One-port microwave network analysis error models represented by signal-flow

diagrams. . . 25

(a) 4-terms error model. . . 25

(b) 3-terms error model using an alternative notation. . . 25

2.16 2-port microwave network analysis error models represented by signal-flow diagrams. . . 26

(a) 8-terms error model. . . 26

(b) 12-terms error model. . . 26

2.17 Electrical characteristics of coaxial Open standard, from [74, p. 92]. . . 29

2.18 Offset equivalent model for the Open and Short standards. . . 29

2.19 Illustration of the absolute calibration procedure. It involves 2 steps: step one uses a power meter, and step two uses a comb-generator. . . 30

2.20 Signal-flow diagram of the sampler front-end error model, used with the equivalent-time sampling oscilloscope (ETSO). . . 31

2.21 Traceability path illustration, from the EOS fundamental calibration up to the LSNA’s phase calibration using a characterized commercial CG. At the EOS system the traceability to the SI is assured through the direct link of the measurement to the meter (m), second (s) and Volt (V) units. The Volt is an SI derived unit, V = m2_{· kg · s}−3_{· A}−1_{. . . .} ₃₂

3.1 Representation of the two main mixed-signal characterization approaches. . . 36

(a) Signal integrity approach. . . 36

(b) System-level behavioral approach. . . 36

3.2 Illustration of the conversion from binary representation to state values. . . . 37

3.3 Simulation of the maximum amplitude and phase error in an ideal digitization process (sampling and quantization) of sinewaves, at each of the frequencies of the considered frequency grid. Errors obtained for 3 ENOB values: 6, 8 and 12 bits. Number of divisions per two Nyquist zones (NZs) considered for the frequency grid: 64 and 61 (prime number). Results shown over a frequency axis normalized to the CLK value. . . 42

(a) 64 divisions. . . 42

(b) 61 divisions. . . 42

3.4 Illustration of the (required) frequency mapping used during the linear charac-terization of a mixed-signal transmitter. A simple mixed-signal device is being considered, a device without an integrated frequency translation circuitry (a mixer stage), such as a mixed-signal data converter (DAC), for example. The digital stimulus frequency, fstim, is within the 1st NZ frequency region. The digital input (adig₂ ) is mapped to each analog output (b1) frequency component. ∗ _{stands for the complex conjugate operator. . . .} ₄₆

4.1 Block diagram of the measurement strategy to be employed in the extraction of the proposed D-parameters characterization. . . 55

4.2 Block diagram of the analog-side instrumentation, when using a mixer-based or a sampler-based receiver. Have in mind that the wave-separation structures are connected to a signal generation structure (after the dotted line), as represented in Fig. 4.1. . . 57

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(b) Sampler-based. . . 57 4.3 Block diagram of the calibration procedures to apply at the analog-side, when

using a mixer-based or sampler-based instrument. Have in mind that the wave-separation structures are connected to a signal generation structure (after the dotted line), as represented in Fig. 4.1. . . 61 (a) Mixer-based. . . 61 (b) Sampler-based. . . 61 4.4 Block diagram of the ‘optimum’ strategy to achieve phase synchronization

between digital- and analog-sides. The analog receivers and wave-separation structures are not represented, see Fig. 4.1. . . 64 4.5 Illustration of the trigger waveforms for the synchronization of the signals from

the analog- and digital-sides. Considering: divCLK = 1 and divDIG = divREC.

ks1 and ks2 are integer values. . . 67

4.6 Illustration of the phase traces, at the intermediate steps, when calculating the proposed phase minimization. Based on a hypothetical DUT’s D21 phase

response. . . 67 5.1 Block diagram and photo of the measurement setup, based on an NVNA, used

to characterize the RF DAC. . . 75 (a) Block diagram. . . 75 (b) Photo. . . 75 5.2 Nominal D21 results, from 10 MHz to 10 GHz, in 10 MHz frequency steps. The

DAC operated in ‘Normal’ mode, for all the 4 considered CLK frequencies. . 78 5.3 Nominal D21 results, from 10 MHz to 10 GHz, in 10 MHz frequency steps. The

DAC operated in ‘Mix’ mode, for all the 4 considered CLK frequencies. . . . 78 5.4 Nominal D22results, from 10 MHz to 10 GHz, in 10 MHz frequency steps. For

all the considered DAC operating conditions (‘Normal’ and ‘Mix’ modes of operation, and all the 4 CLK frequencies). . . 79 5.5 Sensitivity and Monte-Carlo uncertainty intervals of D21, from 10 MHz to

10 GHz, in 10 MHz frequency steps. DAC operated in ‘Normal’ mode, at 2.5 GHz. . . 80 (a) Sensitivity. . . 80 (b) Monte-Carlo. . . 80 5.6 Sensitivity and Monte-Carlo uncertainty intervals of D22, from 10 MHz to

10 GHz, in 10 MHz frequency steps. DAC operated in ‘Normal’ mode, at 2.5 GHz. . . 80 (a) Sensitivity. . . 80 (b) Monte-Carlo. . . 80 5.7 Closeup in the y-axis of the Monte-Carlo uncertainty intervals of both D21and

D22. Results shown from 10 MHz to 10 GHz, in 10 MHz frequency steps. DAC

operated in ‘Normal’ mode, at 2.5 GHz. . . 81 (a) D21 . . . 81

(b) D22 . . . 81

5.8 Monte-Carlo 95% confidence intervals for each D21 measurement extraction.

Results calculated relatively to the Nominal values of the average of all 4 measurement iterations. Results shown from 10 MHz to 10 GHz, in 10 MHz frequency steps. DAC operated in ‘Normal’ mode, at 2.5 GHz. . . 82

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5.9 Sensitivity 95% confidence intervals for each D21 measurement extraction.

Results calculated relatively to the Nominal values of the average of all 4 measurement iterations. Results shown from 10 MHz to 10 GHz, in 10 MHz

frequency steps. DAC operated in ‘Normal’ mode, at 2.5 GHz. . . 82

5.10 Block diagram of the measurement setup used for the extraction of the nonlinear D-parameters model of the integrated transmitter. . . 83

(a) During the measurement (for extraction) stage. . . 83

(b) During the absolute calibration. . . 83

5.11 Extracted nonlinear D-parameters of the integrated transmitter. CLK fre-quency of 62.5 MHz, fundamental input of 9 MHz. Equivalent input power swept from -14 to +2 dBm, in 4 dB steps. . . 84

(a) Input fundamental to output fundamental, at the 1st NZ. . . 84

(b) Input fundamental to output fundamental, at the 2nd _{NZ. . . .} ₈₄

5.12 Simulated and measured output spectrum from the integrated transmitter. Simulation done considering its extracted nonlinear D-parameters. Results shown in a span of 6.5 MHz around the carrier frequency. . . 86

(a) At the fundamental, in the 4th NZ. . . 86

(b) At the 2nd harmonic, in the 2nd NZ. . . 86

5.13 Illustration of ideal frequency expansion performed to the modulated sig-nals, from the first NZ to all the upper NZs, before the application of the D-parameters linear model to calculate the simulation results. . . 86

5.14 Illustration of the mismatch correction procedure used to calculate the wave coming from the DAC into an ideal 50 Ω load (bDAC), based on the calibrated measured waves (bi and ai). . . 87

5.15 Complete procedure work-flow to achieve the wave from the DAC into an ideal 50 Ω load: from the acquisition of raw data, to the mismatch correction. . . . 88

5.16 Spectra of the measured (and calibrated) non-predistorted 16-QAM modulated signal (after mismatch correction). Traces shown from 10 MHz to 4 GHz, in 1.25 MHz frequency steps. DAC operated in ‘Normal’ mode, at 2 GHz. . . 89

(a) 470 MHz carrier. . . 89

(b) 630 MHz carrier. . . 89

5.17 Spectra of the calibrated waves measured during the phase calibration stage, with the (CAL) CG connected. Measurements from 10 MHz to 10 GHz, in 10 MHz frequency steps. The CG was also set to produce an output with a tone separation of 10 MHz (input of 10 MHz with an internal divider of 1). The NVNA IF BW was set to 100 Hz. . . 90

(a) Single measurement. . . 90

(b) Average of the 20 raw measurements. . . 90

5.18 Spectra (magnitude and phase) of the calibrated waves measured during the phase calibration stage, with the (CAL) CG connected. Measurements from 10 MHz to 4 GHz, in 1.25 MHz frequency steps. The CG was also set to produce an output with a tone separation of 1.25 MHz (input of 10 MHz with an internal divider of 8). The NVNA IF BW was set to 30 Hz. . . 90

(a) Single measurement (magnitude). . . 90

(b) Average of the 1600 raw measurements (magnitude). . . 90

(c) Single measurement (phase). . . 90

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5.19 Spectra of the calibrated incident and reflected waves (before the mismatch correction step) of the non-predistorted 16-QAM modulated signal. DAC operated in ‘Normal’ mode, at 2.4 GHz. Traces shown from 10 MHz to 4 GHz, in 1.25 MHz frequency steps. The wave notation, a2 and b2, follows the DUT

port numbering shown in 5.1a. . . 92

5.20 Spectral comparison between measured and simulated nominal results. Signals considered: non-predistorted 16-QAM, at 470 and 630 MHz carriers. DAC operated in ‘Normal’ mode, at 2.5 GHz. Results shown from 10 MHz to 4 GHz, in 1.25 MHz steps. . . 94

5.21 Differences, over frequency, between measured and simulated nominal results, for a non-predistorted 16-QAM modulated signal input, at a 630 MHz carrier frequency. DAC operated in ‘Normal’ mode, at 2.5 GHz. Traces shown in a span of 712.5 MHz around the carrier frequency, at the three first NZs. . . 94

5.22 Monte-Carlo uncertainty intervals, over frequency, of the measured non-predistorted 16-QAM modulated signal, at a 630 MHz carrier. DAC operated in ‘Normal’ mode, at 2.5 GHz. Results shown for each one of the three first NZs, for a bandwidth of 712.5 MHz around the carrier. . . 95

(a) for the 1st _{NZ. . . .} ₉₅

(b) for the 2nd NZ. . . 95

(c) for the 3rd NZ. . . 95

5.23 Monte-Carlo 95% confidence intervals, over frequency, for the measured and simulated results. Signal shown: non-predistorted 16-QAM, at a 630 MHz carrier frequency. DAC operated in ‘Normal’ mode, at 2.5 GHz. Results shown in a span of 712.5 MHz around the carrier frequency at the three first NZs. All the shown results are relative to the Nominal simulated values. . . 96

5.24 Sensitivity 95% confidence intervals, over frequency, for the measured and simulated results. Signal shown: non-predistorted 16-QAM, at a 630 MHz carrier frequency. DAC operated in ‘Normal’ mode, at 2.5 GHz. Results shown in a span of 712.5 MHz around the carrier frequency at the three first NZs. All the shown results are relative to the Nominal simulated values. . . 96

5.25 Procedure used to generate the predistorted waveform. . . 98

5.26 Spectra of the measured predistorted 64-QAM modulated signals, at a 630 MHz carrier. DAC operated in ‘Normal’ mode, at 2 GHz. Results shown from 10 MHz to 4 GHz, in 1.25 MHz frequency steps. Predistortion performed for one of the two first NZs. . . 99

(a) Predistorted for the 1st NZ. . . 99

(b) Predistorted for the 2nd _NZ. _{. . . .} ₉₉

5.27 Differences, over frequency, between measured nominal results and simulated (ideal) signal. Signals shown: predistorted 64-QAM, at a 630 MHz carrier. DAC operated in ‘Normal’ mode, at 2 GHz. Results shown for each one of the three first NZs, for a bandwidth of 712.5 MHz around the carrier. . . 99

(a) for the 1st NZ. . . 99

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(c) for the 3rd _{NZ. . . .} ₉₉

5.28 Signal constellations for both the non-predistorted and predistorted signals. Signals shown: 64-QAM, at a 630 MHz carrier, in the 1st NZ. DAC operated in ‘Normal’ mode, at 2 GHz. . . 101

(a) Considering the non-predistorted signal. . . 101

(b) Considering the predistorted signal. . . 101

5.29 Differences, over frequency, between demodulated measured signals and the ideal baseband signal, for both the non-predistorted and predistorted signals. Signals shown: 64-QAM, at a 630 MHz carrier, in the 1st NZ. DAC operated in ‘Normal’ mode, at 2 GHz. . . 102

5.30 Differences, over frequency, between demodulated measured signals and the ideal baseband signal, for both the non-predistorted and predistorted signals. Signals shown: 64-QAM, at a 630 MHz carrier, in the 3rd NZ. DAC operated in ‘Normal’ mode, at 2 GHz. . . 102

5.31 Monte-Carlo uncertainty intervals, over frequency, of the measured predistorted 64-QAM signals, at a 630 MHz carrier. DAC operated in ‘Normal’ mode, at 2 GHz. Results shown for each one of the three first NZs, for a bandwidth of 712.5 MHz around the carrier. . . 103

(a) for the 1st NZ. . . 103

(b) for the 2nd NZ. . . 103

(c) for the 3rd _{NZ. . . .} ₁₀₃

5.32 Monte-Carlo 95% confidence intervals, over frequency, for the measured pre-distorted and simulated results. Signals shown: prepre-distorted 64-QAM, at a 630 MHz carrier frequency. DAC operated in ‘Normal’ mode, at 2 GHz. Results shown in a span of 712.5 MHz around the carrier frequency at the three first NZs. All the shown results are relative to the nominal simulated values. . . . 105

(a) for the 1st _{NZ. . . .} ₁₀₅

(b) for the 2nd _{NZ. . . .} ₁₀₅

(c) for the 3rd NZ. . . 105

5.33 Two measured results (of predistorted signals), over frequency, are shown: the 95% confidence intervals after demodulation, relative to the nominal result after demodulation; and the differences between the ideal demodulated (baseband) signal and measured nominal result after demodulation. Signal shown: predistorted 64-QAM, at a 630 MHz carrier, in the 1st _{NZ. DAC} operated with a 2 GHz CLK, in ‘Normal’ mode. . . 105

(a) from Monte-Carlo analysis. . . 105

(b) from Sensitivity analysis. . . 105

5.34 Various EVMRMS uncertainty results from the measured predistorted signals. Results shown: Monte-Carlo histogram, the nominal value, the MC mean (which includes the statistical bias), the MC higher and lower 95% confidence intervals, and the Gaussian distribution from the Sensitivity analysis. Signals evaluated: predistorted 64-QAM, at a 630 MHz carrier, in the three first NZs. DAC operated in ‘Normal’ mode, at 2 GHz. . . 106

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(a) at the 1st _NZ. _{. . . .} ₁₀₆

(b) at the 2nd _{NZ. . . .} ₁₀₆

(c) at the 3rd _NZ. _{. . . .} ₁₀₆

5.35 Block diagram and photo of the measurement setup using the equivalent-time sampling oscilloscope (ETSO). . . 109 (a) Block diagram. . . 109 (b) Block diagram. . . 109 5.36 Illustration of the signals generated by the AWG to feed the scope. . . 110 5.37 Spectra of the measured predistorted 64-QAM modulated signals, at a 630 MHz

carrier. Comparison between scope and NVNA measurements. DAC operated in ‘Normal’ mode, at 2 GHz. Results shown from 0 to 6 GHz, in 1.25 MHz frequency steps. Predistortion performed for one of the two first NZs. . . 111 (a) Predistorted for the 1st NZ. . . 111 (b) Predistorted for the 2nd NZ. . . 111 5.38 Differences, over frequency, between measured nominal results from the scope

and from the NVNA. Signals shown: predistorted 64-QAM, at a 630 MHz carrier. DAC operated in ‘Normal’ mode, at 2 GHz. Results shown for each one of the three first NZs, for a bandwidth of 712.5 MHz around the carrier. . 112 (a) for the 1st _{NZ. . . .} ₁₁₂

(b) for the 2nd NZ. . . 112 (c) for the 3rd NZ. . . 112 5.39 Differences, over frequency, between measured nominal results from the scope

and simulated (ideal) signal. Signals shown: predistorted 64-QAM, at a 630 MHz carrier. DAC operated in ‘Normal’ mode, at 2 GHz. Results shown for each one of the three first NZs, for a bandwidth of 712.5 MHz around the carrier. . . 112 (a) for the 1st NZ. . . 112 (b) for the 2nd NZ. . . 112 (c) for the 3rd NZ. . . 112 5.40 Monte-Carlo uncertainty intervals, over frequency, of the scope measurements.

Signals shown: predistorted 64-QAM, at a 630 MHz carrier. DAC operated in ‘Normal’ mode, at 2 GHz. Results shown for each one of the three first NZs, for a bandwidth of 712.5 MHz around the carrier. . . 114 (a) for the 1st _{NZ. . . .} ₁₁₄

(b) for the 2nd _{NZ. . . .} ₁₁₄

(c) for the 3rd _{NZ. . . .} ₁₁₄

5.41 Two scope measured results (of predistorted signals), over frequency, are shown: the Monte-Carlo 95% confidence intervals after demodulation, rela-tive to the nominal result after demodulation; and the differences between the ideal demodulated (baseband) signal and measured nominal result after demodulation. Signals shown: predistorted 64-QAM, at a 630 MHz carrier, in the 1st and 3rd NZs. DAC operated with a 2 GHz CLK, in ‘Normal’ mode. . . 114 (a) at the 1st _NZ. _{. . . .} ₁₁₄

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5.42 Various EVMRMS uncertainty results obtained from the demodulation of the

predistorted signals measured with the scope and with the NVNA. Results shown: Monte-Carlo histogram, the nominal value, the MC mean (which includes the statistical bias), the MC higher and lower 95% confidence intervals, and the Gaussian distribution from the Sensitivity analysis. Signals evaluated: predistorted 64-QAM, at a 630 MHz carrier, in the three first NZs. DAC operated in ‘Normal’ mode, at 2 GHz. . . 115 (a) at the 1st _NZ. _{. . . .} ₁₁₅

(b) at the 2nd NZ. . . 115 (c) at the 3rd NZ. . . 115 5.43 Differences, over frequency, between the demodulated measured signals

(nom-inal values) and the ideal baseband signals. Results shown for (predistorted) signals measured with the NVNA and with the scope. Signals evaluated: predistorted 64-QAM, at a 630 MHz carrier, in the 1st and 3rd NZs; and, 64-QAM, at a 470 MHz carrier, in the 3rd NZ. DAC operated in ‘Normal’ mode, at 2 GHz. . . 118 (a) 630 MHz carrier, at the 1st NZ. . . 118 (b) 630 MHz carrier, at the 3rd NZ. . . 118 (c) 470 MHz carrier, at the 3rd NZ. . . 118 A.1 Simplified block diagram of the measurement setup. . . 134 A.2 Phase variation of the CW signal used as CLK, during the extraction of the

linear D-parameters of the DAC, shown in section 5.1.1. Results shown for different measurement iterations, at the four CLK frequencies used during the characterization. The phase variation was calculated relatively to the phase of the CG output (at the CLK frequency). . . 134 (a) High phase variations. . . 134 (b) Low phase variations. . . 134 A.3 Uncertainty of the clock (CLK) phase variation measurements, uncertainty

calculated using a Sensitivity and Monte-Carlo uncertainties analyses. Results shown along the acquisition time. . . 136 (a) from Sensitivity analysis. . . 136 (b) from Monte-Carlo analysis. . . 136 A.4 Uncertainty of the CLK phase variation measurements, uncertainty calculated

using a Sensitivity and Monte-Carlo uncertainties analyses. Results shown along the acquisition time. . . 136 (a) from Sensitivity analysis. . . 136 (b) from Monte-Carlo analysis. . . 136 B.1 Nominal EVMRMS along the considered number of CG averages used during

the calibration stage. Results for two carrier frequencies, at the first NZ. . . . 138 (a) with a 470 MHz carrier. . . 138 (b) with a 630 MHz carrier. . . 138 B.2 Uncertainty EVMRMSalong the considered number of CG averages used during

the calibration stage. Uncertainty calculated using a Sensitivity and Monte-Carlo uncertainties analyses. . . 139 (a) from Sensitivity analysis. . . 139

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(b) from Monte-Carlo analysis. . . 139 B.3 Monte-Carlo histograms for each number of CG averages used during the

calibration stage. . . 140 (a) Histograms on a linearly spaced x-axis. . . 140 (b) Histograms on a logarithmic x-axis. . . 140 E.1 Representation of the hybrid model idea, to be adjustable to any DAC CLK

frequency. . . 159 E.2 Illustration of the parametric model, with two parameters, based on the

pulse-shape of the quad-switch current steering DAC architecture. Illustration representing the considered non-ideal pulse-shape, along the duration of one sampling period, from 0 to TS. . . 160

E.3 Frequency response of the pulse-shape parametric model considered. Results shown in a normalized frequency grid relative to the CLK frequency, from 0 to 5 fs. Considered parametric values: β = 0.6824 and α = 0.05. . . 162

E.4 Frequency response of the filter to cascade with the pulse-shape parametric model. Results shown from 10 MHz to 10 GHz, in 10 MHz step. Considered parametric values: β = 0.6824 and α = 0.05. . . 162

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List of Tables

5.2 NMSE when considering the Nominal measured and Nominal simulated results. Values obtained for a non-predistorted 16-QAM modulated signal, at both carrier frequencies. DAC operated in ‘Normal’ mode, at 2.5 GHz. . . 94 5.3 Nominal EVMRMS results from the NVNA measured non-predistorted

(‘non-PD’) and predistorted (‘PD’) signals. Signals considered: 64-QAM (480 MSymb/s), at a 630 MHz carrier frequency. All the DAC operating conditions are considered: both DAC operation modes, at each of the four CLK frequencies. Values shown for the first three NZs. . . 101 5.4 EVMRMS uncertainty results from the Monte-Carlo analysis of the NVNA

measurements. Signals considered: predistorted 64-QAM (480 MSymb/s), at both 470 MHz and 630 MHz carrier frequencies, for the first three NZs. DAC operated in ‘Normal’ mode, at 2 GHz. . . 107 5.7 EVMRMS uncertainty results from the Monte-Carlo analysis of the NVNA and

scope measurements, of predistorted signals. Signals considered: predistorted 64-QAM (480 MSymb/s), at both 470 MHz and 630 MHz carrier frequencies, for the first three NZs. DAC operated in ‘Normal’ mode, at 2 GHz. . . 116 C.1 Nominal EVMRMS results from the NVNA measured non-predistorted

(‘non-PD’) and predistorted (‘PD’) signals. Signals considered: QPSK (480 MSymb/s), at a 470 MHz carrier frequency. All the DAC operating conditions are considered: both DAC operation modes, at each of the four CLK frequencies. Values shown for the first three NZs. . . 142 C.2 Nominal EVMRMS results from the NVNA measured non-predistorted

(‘non-PD’) and predistorted (‘PD’) signals. Signals considered: QPSK (480 MSymb/s), at a 630 MHz carrier frequency. All the DAC operating conditions are considered: both DAC operation modes, at each of the four CLK frequencies. Values shown for the first three NZs. . . 142 C.3 Nominal EVMRMS results from the NVNA measured non-predistorted

(‘non-PD’) and predistorted (‘PD’) signals. Signals considered: 16-QAM (480 MSymb/s), at a 470 MHz carrier frequency. All the DAC operating conditions are considered: both DAC operation modes, at each of the four CLK frequencies. Values shown for the first three NZs. . . 143

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C.4 Nominal EVMRMS results from the NVNA measured non-predistorted

(‘non-PD’) and predistorted (‘PD’) signals. Signals considered: 16-QAM (480 MSymb/s), at a 630 MHz carrier frequency. All the DAC operating conditions are considered: both DAC operation modes, at each of the four CLK frequencies. Values shown for the first three NZs. . . 143 C.5 Nominal EVMRMS results from the NVNA measured non-predistorted

(‘non-PD’) and predistorted (‘PD’) signals. Signals considered: 64-QAM (480 MSymb/s), at a 470 MHz carrier frequency. All the DAC operating conditions are considered: both DAC operation modes, at each of the four CLK frequencies. Values shown for the first three NZs. . . 144 D.1 EVMRMS uncertainty results from the Monte-Carlo analysis of the NVNA and

scope measurements, of predistorted signals. Signals considered: predistorted QPSK (480 MSymb/s), at both 470 MHz and 630 MHz carrier frequencies, for the first three NZs. DAC operated in both ‘Normal’ and ‘Mix’ modes, at 2 GHz. . . 146 D.2 EVMRMS uncertainty results from the Monte-Carlo analysis of the NVNA and

scope measurements, of predistorted signals. Signals considered: predistorted QPSK (480 MSymb/s), at both 470 MHz and 630 MHz carrier frequencies, for the first three NZs. DAC operated in both ‘Normal’ and ‘Mix’ modes, at 2.2 GHz. . . 147 D.3 EVMRMS uncertainty results from the Monte-Carlo analysis of the NVNA and

scope measurements, of predistorted signals. Signals considered: predistorted 16-QAM (480 MSymb/s), at both 470 MHz and 630 MHz carrier frequencies, for the first three NZs. DAC operated in both ‘Normal’ and ‘Mix’ modes, at 2 GHz. . . 150 D.6 EVMRMS uncertainty results from the Monte-Carlo analysis of the NVNA and

scope measurements, of predistorted signals. Signals considered: predistorted 16-QAM (480 MSymb/s), at both 470 MHz and 630 MHz carrier frequencies, for the first three NZs. DAC operated in both ‘Normal’ and ‘Mix’ modes, at 2.2 GHz. . . 151 D.7 EVMRMS uncertainty results from the Monte-Carlo analysis of the NVNA and

scope measurements, of predistorted signals. Signals considered: predistorted 16-QAM (480 MSymb/s), at both 470 MHz and 630 MHz carrier frequencies, for the first three NZs. DAC operated in both ‘Normal’ and ‘Mix’ modes, at 2.4 GHz. . . 152

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D.8 EVMRMS uncertainty results from the Monte-Carlo analysis of the NVNA and

scope measurements, of predistorted signals. Signals considered: predistorted 64-QAM (480 MSymb/s), at both 470 MHz and 630 MHz carrier frequencies, for the first three NZs. DAC operated in both ‘Normal’ and ‘Mix’ modes, at 2 GHz. . . 154 D.10 EVMRMS uncertainty results from the Monte-Carlo analysis of the NVNA and

scope measurements, of predistorted signals. Signals considered: predistorted 64-QAM (480 MSymb/s), at both 470 MHz and 630 MHz carrier frequencies, for the first three NZs. DAC operated in both ‘Normal’ and ‘Mix’ modes, at 2.5 GHz. . . 157

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Abbreviations and Acronyms

1G first generation 2G second generation 3G third generation 4G fourth generation 5G fifth generation

ADC analog-to-digital converter ADS advanced design system AM amplitude modulation

AM-AM amplitude modulation to amplitude modulation conversion AM-PM amplitude modulation to phase modulation conversion AWG arbitrary waveform generator

BB baseband BER bit error rate BPF bandpass filter

BPSK binary phase-shift keying BW bandwidth

CAD computer-aided design CG comb-generator

CLK clock

CMOS complementary metal–oxide–semiconductor CW continuous wave

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DC direct current DLL delay-locked loop DNL differential nonlinearity DPD digital predistortion DUT device under test

ENOB effective number of bits EOS electrooptical sampling ETS equivalent-time sampling

ETSO equivalent-time sampling oscilloscope EVM error vector magnitude

FFT fast Fourier transform FM frequency modulation FMC FPGA Mezzanine Card FoM figure of merit

FPGA field programmable gate array FS full scale

GPIB General Purpose Interface Bus

GSM global system for mobile communications GSPS Giga-samples per second

GUM Guide to the Expression of Uncertainty in Measurement HPR harmonic phase reference

I/Q In-phase/Quadrature IC integrated circuit IF intermediate frequency IMD intermodulation distortion

IMD3 third-order intermodulation distortion INL integral nonlinearity

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IoT internet of things IP intellectual property IS-95 interim standard 95

ISO International Organization for Standardization LA logic analyzer

LO local oscillator LPF low-pass filter

LSNA large signal network analyzer LSOP large-signal operation point LVDS low-voltage differential signaling MC Monte-Carlo

mm-Wave millimeter-wave MSO mixed-signal oscilloscope

MUF microwave uncertainty framework NI National Instruments

NIST National Institute of Standards and Technology NMSE normalised mean square error

NRZ Non-Return-to-Zero

NVNA nonlinear vector network analyzer NZ Nyquist zone

OFDM orthogonal frequency-division multiplexing OSM Open, Short, Match

P1dB 1 dB compression point PC precision connector

PHD polyharmonic distortion PLL phase-locked loop

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QAM quadrature amplitude modulation QPSK quadrature phase-shift keying RF radio frequency

RMS root mean square RT real-time

RTO real-time oscilloscope RZ Return-to-Zero

S-parameters scattering parameters SDR software defined radio

SFDR spurious-free dynamic range SI international system of units

SINAD signal-to-noise and distortion ratio SMA sub-miniature version A

SNR signal-to-noise ratio SoC system-on-chip SOL Short, Open, Load

SOLR Short, Open, Load, Reciprocal SOLT Short, Open, Load, Thru TBC timebase correction TBD timebase distortion TI time-interleaving

TMTT Transactions on Microwave Theory and Techniques TOSM Through, Open, Short, Match

TRL Trough, Reflect, Line TTL transistor–transistor logic

UOSM Unknown through, Open, Short, Match USB Universal Serial Bus

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VNA vector network analyzer VSA vector signal analyzer VSG vector signal generator Wi-Fi wireless fidelity

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Chapter 1 Introduction

Wireless communication technology has been growing since its inception. Every year, the number of devices sharing information wirelessly increases and the volume of information shared with each device also increases.

At the beginning, the popularity of wireless communications increased slowly. Starting with the appearance of analog based solutions: first the radio broadcast (using both AM and FM technology), then the television broadcast, and later with the first generation (1G) of mobile telephone technology.

With the migration to the digital era and with the development of digital based wireless modulations, the usage rate of mobile communication systems got an impressive boost. It started with the appearance of the second generation (2G) mobile telephone technology, the GSM in Europe and the IS-95 in the United States of America. And, it never stopped growing when stepping to the third generation (3G) of mobile communications, where a transition to a new paradigm began: voice was no longer the only information to be shared, instead users wanted to communicate “data”. At this point, Wi-Fi brought wireless Internet and multimedia services to computers and other equipments. These services kept on evolving forming a big network that interconnects every single one of us. That is where we are right now: in the internet of things (IoT) era, where wireless communications are present in almost every device on our planet.

Nowadays, a plenitude of wireless standards are available in order to cover all the possible usage needs, from low-distance high data-rate to high-distance low data-rate communications. In the mobile phone sector, the fourth generation (4G) is now in place with increasing transfer speeds, with users demanding for even more multimedia content, which keeps on generating higher and higher data traffic every single year. Cisco Visual Networking Index forecasts a continuous growth in global mobile data traffic, reaching 49 Exabytes/month in 2021 [9], as shown in Fig. 1.1.

In order to cope with this fast growth in data traffic and transfer speed, higher modulation bandwidths (BWs) combined with higher modulation schemes are required. Predictions say: the future fifth generation (5G) will be operating at millimeter-wave (mm-Wave) frequencies, [10], to allow the allocation of these very high signal BWs.

In this context, mixed-signal devices have an increasingly higher importance in the design of radios. The use of mixed-signal devices, such as high-speed converters (these being analog-to-digital converters (ADCs) or digital-to-analog converters (DACs)), brings several advantages to the radio technology: they enable the communication of high BW signals

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2.1 3.7 7 11 17 24 35 49 2014 2015 2016 2017 2018 2019 2020 2021 EB ytes / M o n th Year

Global Mobile Data Traffic Forecast

Source: Cisco VNI mobile, 2017

EB = Exabyte (1000 PB) PB = Petabyte (1000 TB)

Figure 1.1: Mobile data traffic growth prediction for the global market, based on [9].

with/or more than one signal at once, allowing the use of carrier aggregation [11].

Additionally, software defined radio (SDR) technology, which is coupled with the usage of mixed-signal devices, is also being used in order to: increase the flexibility of radios (see section 2.2.1), reduce costs, and time-to-market of new products.

1.1 Motivation

This PhD work intends to characterize radio oriented mixed-signal devices and systems. Mixed-signal data converters (ADCs or DACs) are the fundamental mixed-signal devices and throughout this manuscript they will be referred as: core ‘mixed-signal devices’. But, bare in mind that the characterization to be proposed will also seek to be applied to more complex mixed-signal devices.

The use of mixed-signal devices, including high-speed converters, in the design of radios has been increasing due to the previously mentioned advantages. However, the measurement techniques for the characterization of their behavior is still underdeveloped.

As shown in [12], high-speed mixed-signal data converters are a valuable asset to employ in the design of new radio handsets and base-stations, despite the modeling approaches currently applied to predict the behavior of these devices are still insufficient. Presently, a designer that needs a model to simulate the behavior of ADCs and DACs may only have available a generic functional description of an ideal converter (based in an hardware description approach such as Verilog). These modeling techniques are still too simple and they are not capable to correctly predict many of important effects that these devices show, under real-world scenarios.

In many situations, the nonlinear effects or other complex effects (such as the linear dynamic effects) of the employed mixed-signal converter may be neglected when compared to the remaining building blocks of a system, and an ideal characterization approach may be used to successfully design a final product. But, with these devices being driven at higher-speeds and closer to the radio antenna, the previous scenario is rapidly changing, because their non-ideal effects will introduce a stronger impact on the final system performance.

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Therefore, the development of a measurement technique and characterization approach capable of fully characterize the most important non-ideal effects that these core mixed-signals devices present is of paramount importance.

Furthermore, integration is another very important trend in the radio industry [13]. By making use of integration, smaller and lower-cost final products are possible to produce. Presently, mixed-signal converters are being built together with analog counterparts inside the same single chip, which is often called system-on-chip (SoC). This leads to a difficult situation where the fully analog blocks are impossible to be measured apart from the mixed-signal converter, because everything is now combined into a single system, which becomes a single more complex mixed-signal device. Thus, the previous single block left uncharacterized because of limited characterization techniques, has now increased to the size of a full system left uncharacterized and the assumption of an ideal behavior is now extended into possible unbearable dimensions. Having this as the scenario in the years to come, once again, the test and characterization through measurements of mixed-signal devices reveals itself as a truly essential area to evolve.

Following a set of several works, the MSc and PhD works of Pedro Cruz [14],[15], and my own MSc work [16], the purpose of this PhD work is to improve the current state of the techniques available for the measurement and characterization of mixed-signal devices and systems. Being those either core mixed-signal devices or more complex mixed-signal devices.

1.2 Main Goals

The main goal of this work is to define a measurement apparatus and develop the necessary tools to characterize mixed-signal devices (or systems) – being those integrated circuits (ICs) or complete transceivers built with discrete parts. To achieve this, several main steps are necessary: the first one is the design and conception of a new measurement system to acquire the correlated inputs and outputs of such systems. Next, a calibration method has to be addressed to correct for the systematic errors in the proposed measurement technique. In the end, to complement the previous work, an extension of the actual nonlinear analog behavioral models should be proposed and validated for general mixed-signal devices and systems.

In summary, two main goals were established:

Development of suitable measurement techniques for linear and nonlinear characteriza-tion of mixed-signal devices.

Development of linear and nonlinear behavioral models for mixed-signal systems that keep the same mindset of traditional radio approaches (following a microwave network analysis methodology - see section 2.3.5).

The proposed piece of instrumentation will be determinant to speed up the development of new radio solutions built using mixed-signal devices. Meaning that, in the future, the proposed research work may be a very useful tool due to the growing importance of the high-speed mixed-signal technology in the telecommunications’ world.

The outcome of this thesis has the expected capability to be a time saving tool for radio designers and manufacturers due to the new proposed method that will allow to directly measure and consistently evaluate complete mixed-signal systems.

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1.3 Main Contributions

This thesis is largely supported by the following publications: [1–8]. These publications are annexed to this thesis manuscript in Appendix F.

For convenience of the reader, a list with the bibliography details of each publication and the specific appendix section where they are located in this manuscript, is shown below:

Transactions on Microwave Theory and Techniques (TMTT) journal, annexed in Ap-pendix F.1:

[1] D. C. Ribeiro, A. Prata, P. M. Cruz, and N. B. Carvalho, “D-parameters: A novel framework for characterization and behavioral modeling of mixed-signal systems,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 10, pp. 3277–3287, Oct 2015.

TMTT journal, annexed in Appendix F.2:

[2] D. C. Ribeiro, P. M. Cruz, and N. B. Carvalho, “Synchronous oversampled measure-ments for the extraction of mixed-signal behavioral models in digital to analog integrated transmitters,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 12, pp. 3183–3192, Dec 2014.

Conference paper, annexed in Appendix F.3:

[3] ——, “Large-signal characterization of a mixed-signal SoC receiver for multiband SDR/CR designs,” in 44nd European Microwave Conf. (EuMC), Oct 2014, pp. 1424– 1427.

[4] ——, “Characterization of SDR/CR front-ends for improved digital signal processing algorithms,” in 22nd European Signal Processing Conf. (EUSIPCO), Sept 2014, pp. 586–590.

[5] D. C. Ribeiro, P. M. Cruz, A. Prata, and N. Carvalho, “Automatic characterization of RF DACs for software defined radio applications,” in IEEE MTT-S Int. Microwave Symp. (IMS), June 2014, pp. 1–4.

[6] D. C. Ribeiro, P. M. Cruz, and N. B. Carvalho, “Synchronous frequency domain measurements for the extraction of X-parameters in digital to analog transmitters,” in IEEE MTT-S Int. Microwave Symp. (IMS), June 2013, pp. 1–4.

[7] ——, “Corrected mixed-domain measurements for software defined radios,” in 42nd European Microwave Conf. (EuMC), Oct. 2012, pp. 554–557.

[8] ——, “Towards a denser frequency grid in phase measurements using mixer-based receivers,” in 85th ARFTG Microwave Measurements Conf., May 2015, pp. 1–5.

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Chapter 2 State-of-the-Art

2.1 Mixed-signal data converters - as the core mixed-signal

device

The core mixed-signal device can be considered as being: the mixed-signal converter, namely analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). These devices perform the basic function of converting a signal from one domain, either analog or digital, to the other. Around them, a multitude of other blocks, with very different functions, can be used to perform tasks with various complexity levels. More specifically, the combination of mixed-signal converters with the right blocks enables the design of complete radios, as will be seen in section 2.2.

Mixed-signal converters operate differently from any other device. Primarily, the charac-teristics that immediately standout come from the sampling process, i.e. the conversion from one of the domains to the other.

In this chapter, a summarized review of some of the main mixed-signal converters’ char-acteristics will be made. A brief overview of the practical limitations of these devices and the performance metrics typically used to characterize their behavior will also be addressed, notwithstanding a more in-depth look into these topics can be found in [17–20].

2.1.1 Sampling process description

A sampling process, with sampling frequency fS, can be mathematically described as the

multiplication of the original signal x(t) by a periodic impulse train, p(t), with period TS = _f1_S.

The sampled signal xS(t) can be described as, [21]:

xS(t) = x(t) p(t) = +∞

X

n=−∞

x(t) δ(t− n TS) (2.1)

Equation (2.2) expresses the Fourier transformation of the sampled signal xS(t). From

equation (2.2), it can be noticed that the spectrum of the resulting signal is a train of replicas of the original signal spectrum spaced by fS, see Fig. 2.1.

XS(f ) = fS +∞

X

k=−∞

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fS 2fS fS 2 3fS 2 - fS 2 Sampling Process 0 1stNZ 2ndNZ 3rdNZ 4thNZ

Figure 2.1: Illustration of the sampling process effects in the frequency domain.

If the sampling process is applied to a real signal, the resultant sampled spectrum can be split into NZs, spaced by fS/2. In each one of these zones, the spectrum will be the mirror

image of the adjacent NZs. In addition to the mirroring effect, the spectral components at even NZs will also be the complex conjugate of the correspondent (mirrored) spectral components at the odd NZs, and vice-versa, [21, Ch. 8].

To prevent superposition of the original spectrum that consequently causes degradation of information, the original signal must be bandwidth-limited to a maximum of fS/2. This

frequency limitation is widely known as the Nyquist theorem.

The same effect that up-converts an original baseband signal within the first NZ to every others zones, will also down-convert a signal at a higher NZ to the first NZ (0 Hz up to fS/2).

In telecommunications, both processes are very useful, with the up-conversion being more used at the transmitter, whereas the down-conversion, more at the receiver side.

If the Nyquist theorem limits are followed, a signal can be directly down-converted by the ADC (from a high carrier frequency directly to baseband (BB)), in the case of a receiver; or up-converted by the DAC (from BB directly to a high carrier frequency), in the case of a transmitter. This is the concept that enables the design of bandpass sampling receivers and transmitters [22].

The sampling process characteristics can also be used to down-convert multiple signals to the first NZ [23], as may be perceived from Fig. 2.1. For that to be achieved without any signal degradation, all the folded spectra needs to be accommodated in the first NZ without any superposition. As a fundamental rule, the sum of all signals’ BWs must not be higher than fS/2. However, caution must be taken, because even in this situation the position of

each folded signal may cause a superposition of the signals’ spectra. The frequency position where each carrier will fall can be calculated using equation (2.3), see below.

Transmitter and Receiver Examples

In order to better illustrate the very useful up- and down-conversion effects that happen in mixed-signal data converters due to the sampling process, both situations are represented in Fig. 2.2. In this example the discrete-time domain is represented in the first NZ only, since, as seen before, the spectrum repeats for all the other NZs.

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fS 2 fS 2 fS 3fS2 1st_NZ ₂nd_NZ ₃rd_NZ Con�nuous-�me [Analog domain] Discrete-�me [Digital domain] 0 0 Rx

(a) Receiver configuration (ADC): down-conversion. Input Output 0 fS 2 fS 2 fS 3fS2 1stNZ 2ndNZ 3rdNZ Discrete-�me [Digital domain] Con�nuous-�me [Analog domain] 0 Tx

(b) Transmitter configuration (DAC): up-conversion.

Figure 2.2: Detailed illustration of the down- and up-conversion effects that happen in mixed-signal converters due to the sampling process.

It should be noted that, when using the sampling effects to down-convert a signal, at a carrier frequency fC within an even NZ, it will lie at the first NZ as a mirrored image of the

original signal. While, if the fC frequency was within an odd NZ, the signal will lie at the

first NZ as the non-mirrored (direct) image of the original signal. This effect is illustrated in Fig. 2.2a. The same effect will also occur when up-converting a signal, thus a signal at the first NZ will appear at an even NZ as its mirrored image and at an odd NZ as its direct image. This effect is also illustrated in Fig. 2.2b.

In Fig. 2.2a is represented the down-conversion effect that happens in a receiver config-uration mixed-signal converter (ADC). As can be seen multiple signal bands can be down-converted without superposition of one another.

A carrier frequency fC will fall to the first NZ, down-converted to the carrier frequency

ffold, according to the following expression:

ffold= fC− fC fS fS (2.3)

where ffoldis the folding frequency in the first NZ,b...e is the rounding operation towards the

nearest integer, and|...| is the absolute value.

In Fig. 2.2b is represented the up-conversion effect that happens in a transmitter config-uration mixed-signal converter (DAC). In this situation all the signal bands at baseband (in the digital domain) will be up-converted to all the upper NZs. Subsequent filters may be used to select the wanted signal carrier.

In this case, the up-converted carrier frequency (fup) that will lie at the kth NZ can be

calculated using the piecewise function below:

fup =    k−1 2 fS+ fC , for k odd k 2 fS− fC , for k even (2.4)

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2.1.2 Practical remarks

In practical converters, several characteristics limit the usage extent of mixed-signal data converters. One of those factors is the analog BW of the mixed-signal device, which limits the maximum analog frequency that can be digitized or generated.

In ADCs, their input analog BW, is limited by multiple factors, such as: how fast the sampling circuit can get a sample from the analog signal (the acquisition time), the faster this can be performed the higher the possible analog BW of the ADC can be; the time taken to perform the conversion from the sampled analog voltage to its digital representation (the conversion time); and by the BW of the structures around the ADC itself.

Different ADC architectures may be used depending on speed and power requirements, as discussed in [24, 17]. Typical high-speed ADCs use Pipeline or Flash architectures. For even higher sampling rates, time-interleaving (TI) sampling is also commonly used, however further issues may arise, mainly, from the differences between interleaving branches, [25].

The maximum digitized and generated signal frequencies are also limited by the jitter associated with the conversion CLK. For this, both the jitter of the CLK signal and the jitter added by the converter itself (typically named aperture jitter) need both to be considered [19, Sec. 6-5]. The total jitter limits the dynamic range of the converter for higher frequencies, because the higher the digitized/generated signal frequency the higher the noise level (due to the jitter) will be, as evaluated in [26].

Switching now to DACs: they may also be built using different architectures, [17]. How-ever, for high-speed applications, the current-steering architecture is the most adopted one, [27]. Generally, DACs do not use a very short pulse to generate the output analog signal, instead a baseband pulse with the duration of one sampling period is used. The shape of this baseband pulse dictates the shape of the DAC’s frequency response.

Mainly, three different baseband pulse shapes can be often used with commercial DAC devices (assuming vlevelas the voltage level that the DAC is required to generate at a particular

sampling period):

Non-Return-to-Zero (NRZ): traditional baseband pulse shape, where the level to gener-ate (vlevel) is maintained throughout the entire sampling period. It is shown in Fig. 2.3a.

Return-to-Zero (RZ): the level to generate (vlevel) is kept for half the sampling period,

and for the other half the value 0 is generated. It is shown in Fig. 2.3b.

Manchester-like: the level to generate (vlevel) is kept for half the sampling period and

for the other half the symmetric value (_−vlevel) is generated. It is shown in Fig. 2.3c.

Usually, for a DAC operating with this baseband pulse shape, the correspondent mode of operation can also be called ‘mix’ mode or ‘RF’ mode.

(a) NRZ (b) RZ (c) Manchester-like

Figure 2.3: Shape of the three main baseband pulses that DACs may use. The pulse shape is shown over the time of one sample period, from 0 to TS.

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0 fS 2fS 3fS 4fS 5fS 6fS -60 -40 -20 0 Mag. (dB) 0 fS 2fS 3fS 4fS 5fS 6fS Norm. Freq. 0 90 180 Phase (deg) (a) NRZ 0 fS 2fS 3fS 4fS 5fS 6fS -60 -40 -20 0 0 fS 2fS 3fS 4fS 5fS 6fS Norm. Freq. 0 90 180 (b) RZ 0 fS 2fS 3fS 4fS 5fS 6fS -60 -40 -20 0 0 fS 2fS 3fS 4fS 5fS 6fS Norm. Freq. 0 90 180 (c) Manchester-like

Figure 2.4: DAC ideal frequency response, in magnitude and phase, considering the three main baseband pulse shapes. The frequency response is shown for a normalized frequency, from 0 to 6_{× f}S.

The magnitude and phase of the ideal frequency response obtained when using each baseband pulse shape is shown in Fig. 2.4. The mathematical descriptions that allow to get the shown traces are the following: Considering Vout,NORM the output normalized to

the output full-scale amplitude value (_|Vout,FS|), such that Vout,NORM = Vout/|V_out,FS|. And,

considering Din,NORM the input normalized to the input full-scale amplitude (|Din,FS|), such

that Din,NORM=Din/_|D_in,FS_|.

NRZ: Vout,NORM Din,NORM f= sinc f fS RZ: Vout,NORM Din,NORM f= 1 2 sinc f 2fS Manchester-like: Vout,NORM Din,NORM f= j sinc f 2fS sin πf 2fS

(Further information can be found in [28–30]).

Furthermore, state-of-the-art DACs commonly present differential outputs. These are very important, because they allow to cancel the even-order distortion, [31], and therefore diminish its effects.

As was briefly reviewed, the practical implementations of ADCs and DACs present par-ticular properties that need to be considered when working with these type of devices. Both ADCs and DACs are subject to a constant evolution throughout the years. Even if the maximum speed of these devices does not increase at a steady pace, other metrics are always being pushed forward, [32, 24, 27].

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2.1.3 Characterization of mixed-signal data converters

The characterization of mixed-signal data converters has been subject of research since a long time ago, always with a major interest from the community. Currently the main figures of merit (FoMs) and their proper measurement procedures are standardized in [33] for ADCs, and in [34] for DACs. Different FoMs and performance metrics are specified in order to address and characterize the multiple performance topics of mixed-signal converters.

Even some radio-oriented metrics are specified in [33, 34], as for example, the impedance at the analog port of the converter, or its intermodulation distortion (IMD) behavior.

However, for the most part, the considered performance metrics are traditional mixed-signal converters’ FoMs, oriented to general purpose devices. These FoMs were developed to evaluate the converters from a time-domain and digital perspective, looking for non-idealities on each converted level value, or in the transition between converted levels. The FoMs addressed in [33, 34], and in the majority of the surveyed literature, mainly include:

Integral nonlinearity (INL) Differential nonlinearity (DNL) Effective number of bits (ENOB) Spurious-free dynamic range (SFDR)

Signal-to-noise and distortion ratio (SINAD)

An explanation about the meaning of each one of these FoMs will not be addressed here, because this topic is extensively reviewed in the literature, as in [33, 34, 19, 35].

These metrics were subject to an extensive research throughout the years with successive evolutions in their definitions and/or measurement methods, such as in: [36–42]. They are currently very mature, thus the standardization documents mentioned before. These concepts are widely used by researchers designing state-of-the-art mixed-signal converters and by commercial vendors, when describing the performance of their products.

Nonetheless, since these metrics provide limited information about the frequency domain behavior of the mixed-signal devices, they might be of difficult use for a radio engineer. For example, when developing the frequency plan strategy to use inside of a radio product, i.e. when choosing the intermediate frequency(ies) (IF(s)) and CLK frequency(ies). Moreover, some of these traditional FoMs can only be applied to discrete mixed-signal converters and cannot be used to characterize more complex systems, such as integrated SoC transceivers.

Still, regarding the mixed-signal converters characterization approaches: besides the men-tioned FoMs, more complex methods were also researched along the years, [43–45]. More specifically, Volterra series were a subject of multiple studies to model ADCs, as in: [46–50]. Yet, in the opinion of the author, it is still not available a characterization approach that allows to obtain an easy to measure and easy to simulate mixed-signal device model. Particularly, a model which provides the radio engineer with a comprehensive frequency domain response of the device.

Finally, it is worth to highlight, once more, that the measurement and modeling ap-proaches, which will be proposed and discussed along this PhD work, are not intended to solely characterize mixed-signal converters. Instead, the characterization approach to be addressed is intended to be applied to simple or complex mixed-signal devices and/or systems (even integrated radios, as SoC transceivers/receivers/transmitters), so that an additional portion of their behavior can be measured and characterized.

Instrumentation for measurement and characterization of mixed-signal devices

Diogo Carlos Alcobia

Ribeiro

Instrumentation for Measurement and

Characterization of Mixed-Signal Devices

Instrumenta¸

c˜

ao para medida e caracteriza¸

c˜

ao de

dispositivos anal´

ogico-digitais

Diogo Carlos Alcobia

Ribeiro

Instrumentation for Measurement and

Characterization of Mixed-Signal Devices

Instrumenta¸

c˜

ao para medida e caracteriza¸

c˜

ao de

dispositivos anal´

ogico-digitais

Contents

List of Figures

List of Tables

Abbreviations and Acronyms

Chapter 1

Introduction

Global Mobile Data Traffic Forecast

1.1

Motivation

1.2

Main Goals

1.3

Main Contributions

Chapter 2

State-of-the-Art

2.1

Mixed-signal data converters - as the core mixed-signal

device