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Ivan I. Ovchinnikov 2023-03-10 18:02:23 +03:00
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04-complex-electronic-devices-developing.tex
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@ -322,25 +322,31 @@ $z$ -- номер зоны. Пусть ширина полосы = 4МГц, це
\section{Квантование} \section{Квантование}
Дискретный сигнал -- это сигнал с конечным количеством отсчётов, но разрядность пока бесконечна, поэтому возможно применить разрядность АЦП. Передаточная характеристика идеального квантователя Дискретный сигнал -- это сигнал с конечным количеством отсчётов, но разрядность пока бесконечна, поэтому возможно применить разрядность АЦП. Передаточная характеристика идеального квантователя
(5) \begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-sig-sampling-err.svg}
\caption{Квантование}
\end{figure}
явно теряем в точности. Явно теряем в точности. Основной параметр -- Signal-Noise-Ratio
Signal-Noise-Ratio
\[SNR = 6,02N + 1,76dB\] \[SNR = 6,02N + 1,76dB\]
N -- разрядность. Сигнал -- нестационарный процесс, имеет равномерное распределение от 0 до $f_s/2$, не коррелирует со входным сигналом, матмодель - входной сигнал умножается на шум квантования. N -- разрядность. Сигнал -- нестационарный процесс, имеет равномерное распределение от $0$ до $f_s/2$, не коррелирует со входным сигналом, матмодель -- входной сигнал умножается на шум квантования. Если аналоговая частота больше -- есть более общий вариант
Если аналоговая частота больше -- есть более общий вариант
\[SNR = 6,02N + 1,76dB +10\log_{10}(\frac{f_s}{2f_a})\] \[SNR = 6,02N + 1,76dB +10\log_{10}(\frac{f_s}{2f_a})\]
Если частота дискретизации много больше - частота увеличилась, а разрядность не увеличитася, тогда шум уменьшается. Шум всегда будет коррелировать с сигналом, это можно использовать, подав собственный шум на низкой частоте. Если частота дискретизации много больше -- частота увеличилась, а разрядность не увеличитася, тогда шум уменьшается. Шум всегда будет коррелировать с сигналом, это можно использовать, подав собственный шум на низкой частоте.
\section{Характеристики АЦП} \section{Характеристики АЦП}
(6) \begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-sig-sampling-check.svg}
\caption{}
\end{figure}
память+пэвм -- способ проверить АЦП для своей системы. память+пэвм -- способ проверить АЦП для своей системы.
Характеристики могут быть статические и динамические. Характеристики могут быть статические и динамические.
@ -354,62 +360,136 @@ N -- разрядность. Сигнал -- нестационарный про
\item ошибка смещения offset error \item ошибка смещения offset error
\end{itemize} \end{itemize}
(7) ПХ идеального АЦП, все центры кода лежат на прямой \begin{figure}[H]
(8) пример ПХ реального АЦП. \centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-perfect-tc.svg}
\caption{Передаточная характеристика идеального АЦП}
\end{figure}
ПХ идеального АЦП -- все центры кода лежат на прямой линии симметрии
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-real-tc.svg}
\caption{Пример ПХ реального АЦП}
\end{figure}
Дифференциальная нелинейность -- наибольшее отклонение ширины кода от идеального значения в МЗР или процентах от полной шкалы. Дифференциальная нелинейность -- наибольшее отклонение ширины кода от идеального значения в МЗР или процентах от полной шкалы.
Интегральная нелинейность -- наихудшее отклонение центра кода от прямой, также измеряется в МЗР или процентах от полной шкалы. Интегральная нелинейность -- наихудшее отклонение центра кода от прямой, также измеряется в МЗР или процентах от полной шкалы.
Пропущенные коды формируется из первых двух. в примере 8 кода 011 не будет, в даташите будет написано no missing code если например (N=14) то на младших разрядах можем уже не видеть биты. Пропущенные коды формируется из первых двух. в примере 8 кода 011 не будет, в даташите будет написано no missing code если например ($N=14$) то на младших разрядах можем уже не видеть биты. Эти ошибки невозможно исправить
Эти ошибки невозможно исправить Ошибка смещения -- это аддитивная добавка напряжения на входе проценты от шкалы.
Ошибка смещения - это аддитивная добавка напряжения на входе проценты от шкалы Ошибка усиления -- угол начального наклона (мультипликативная ошибка). Эти ошибки возможно исправить программно или внешними аналоговыми цепями.
ошибка усиления - угол начального наклона (мультипликативная ошибка)
Эти ошибки возможно исправить программно или внешними аналоговыми цепями.
\subsection{Динамические характеристики} \subsection{Динамические характеристики}
\begin{itemize} \begin{itemize}
\item Реальное отношение сигнал-шум ($SNR_{real}$). Реальная характеристика точно будет отличаться. Точность разрядности возможно посчитать по формуле \item Реальное отношение сигнал-шум ($SNR_{real}$). Реальная характеристика точно будет отличаться. Точность разрядности возможно посчитать по формуле
\[\frac{1}{LSB} \cdot 100\%\] \[\frac{1}{LSB} \cdot 100\%\]
для N=8 это 0.4\%. SNR = 48dB(1,76dB). Младшие биты АЦП всегда шумят, тест нужно делать на постоянном токе (например, замкнуть на землю, при условии, что земля не дрожжит). для $N=8$ это $0.4\%$. $SNR = 48dB(+1,76dB)$. Младшие биты АЦП всегда шумят, тест нужно делать на постоянном токе (например, замкнуть на землю, при условии, что земля не дрожжит).
$N=8$, $SNR=49,7dB$. реальный может быть 48,1 или 47,1 (первый лучше) зависит от частоты
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-typical-snr.svg}
\caption{Типовой график}
\end{figure}
N=8, SNR=49,7dB. реальный может быть 48,1 или 47,1 (первый лучше) зависит от частоты типовой график
(9)
обратный график - эффективное число бит обратный график - эффективное число бит
\[ENoB = \frac{SNR_{real} - 1,76dB}{6,02}\] \[ENoB = \frac{SNR_{real} - 1,76dB}{6,02}\]
\item Коэффициент гармонических искажений Total Harmonic Distortion -- отражает качество и линейность кармоник. Чем меньше брать в расчёт гармоник - тем легче продать. $THD=\frac{A_1}{\sqrt{A_2^2+A_3^2...}}\%$. AD -- считает по 5 гармоникам, TI -- по 7. \item Коэффициент гармонических искажений Total Harmonic Distortion -- отражает качество и линейность кармоник. Чем меньше брать в расчёт гармоник - тем легче продать. $THD=\frac{A_1}{\sqrt{A_2^2+A_3^2...}}\%$. AD -- считает по 5 гармоникам, TI -- по 7.
(10) \begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-typical-thd.svg}
\caption{Типовой график}
\end{figure}
\item сигнал шум и искажение (SINAD) типовая схема 4096 отсчётов. более качественный параметр. \item сигнал шум и искажение (SINAD) типовая схема 4096 отсчётов. более качественный параметр.
\item свободный динамический диапазон (SFDR spurious free dynamic range) -- свободный от наиболее мешающих компонент. иногда указывают самый мешающий компонент peak spurious (dB). эта характеристика всегда больше СШ. ДД замеряется по самой высокой гармонике. \item свободный динамический диапазон (SFDR spurious free dynamic range) -- свободный от наиболее мешающих компонент. иногда указывают самый мешающий компонент peak spurious (dB). эта характеристика всегда больше СШ. ДД замеряется по самой высокой гармонике.
(11)
\item частотная характеристика: полномощная полоса пропускания (full-power bandwidth) -- частота на которой амплитуда реконструируемой синусоиды отличается на -3дБ. \begin{figure}[H]
(12) \centering
\item частотная характеристика: полнолинейная полоса (Full linear bandwidth) срез -0,1дБ, показывает где АЧХ максимально плоская. \fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-sfdr.svg}
\end{figure}
\item частотная характеристика: полномощная полоса пропускания (full-power bandwidth) -- частота на которой амплитуда реконструируемой синусоиды отличается на $-3$дБ.
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-fpb.svg}
\end{figure}
\item частотная характеристика: полнолинейная полоса (Full linear bandwidth) срез $-0,1$дБ, показывает где АЧХ максимально плоская.
\item при интермодуляции в общем случае появляются гармоники каждой частоты (кубические составляющие). \item при интермодуляции в общем случае появляются гармоники каждой частоты (кубические составляющие).
(13) продукт интермодуляционных искажений \begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-imd.svg}
\caption{Продукт интермодуляционных искажений}
\end{figure}
\begin{equation*}
\begin{gathered}
2: f_2-f_1, f_2+f_1;\\
3: 2f_1+f_2, 2f_1-f_2, f_1+2f_2, f_1-2f_2;\\
...
\end{gathered}
\end{equation*}
Intermodulation distortion (IMD). обычно используется сигнальный тест на два компонента и используются продукты второго и третьего порядка. Intermodulation distortion (IMD). обычно используется сигнальный тест на два компонента и используются продукты второго и третьего порядка.
\[ IMD = \frac{\sqrt{a_{f_1}^2 + a_{f_2}^2}}{\sqrt{\text{сумма квадратов коэффициентов интермодуляции}}} \%\] \[ IMD = \frac{\sqrt{a_{f_1}^2 + a_{f_2}^2}}{\sqrt{\sum(\text{коэффициенты интермодуляции})^2}} \%\]
В ВЧ и радиочастотных цепях -- это критическая характеристика. Измеряется также через БПФ. В ВЧ и радиочастотных цепях -- это критическая характеристика. Измеряется также через БПФ.
\item время восстановления после перенапряжения. overvoltage recovery. \item время восстановления после перенапряжения. overvoltage recovery.
(14) время восстановления измерения с приемлемой точностью (1МЗР) \begin{figure}[H]
Может возникнуть от помех или наводок, индустриальные помехи, итд. \centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-ovr.svg}
\end{figure}
время восстановления измерения с приемлемой точностью (1МЗР). Может возникнуть от помех или наводок, индустриальные помехи, итд.
\item время установления выходного напряжения (setting time, $t_{set}$) -- фактически, переходная характеристика. \item время установления выходного напряжения (setting time, $t_{set}$) -- фактически, переходная характеристика.
(15) \begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-set.svg}
\end{figure}
характеристика может быть критична для многоканальных систем (мультиплексор перед АЦП) частота переключения каналов. характеристика может быть критична для многоканальных систем (мультиплексор перед АЦП) частота переключения каналов.
\item апертурная неопределённость (апертурный джиттер, aperture jitter). дрожание фазы \item апертурная неопределённость (апертурный джиттер, aperture jitter). дрожание фазы
(16)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-jitter.svg}
\end{figure}
Если это тактовый сигнал который подаётся на АЦП, даётся среднеквадратичное значение. Если это тактовый сигнал который подаётся на АЦП, даётся среднеквадратичное значение.
(17) \begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-slope.svg}
\end{figure}
влияет на динамический диапазон (напрямую зависит от скорости нарастания сигнала (вольт/мкс)). Если величина этой ошибки превышает 1МЗР -- она становится определяющей. Тогда это нужно определять выходную частоту. влияет на динамический диапазон (напрямую зависит от скорости нарастания сигнала (вольт/мкс)). Если величина этой ошибки превышает 1МЗР -- она становится определяющей. Тогда это нужно определять выходную частоту.
(18) \begin{equation*}
Фазовые шумы ТИ накладываются на внутренние фазовые шумы АЦП и так теряются разряды. ТИ должны идти в ту же сторону, что и распространение сигнала. Обязательно через внешние драйверы ТИ с нулевой задержкой. Эмиттерно-селективная логика, дифференциальные сигналы. Снизить шумы позволяют clock-cleaner на основе ФАПЧ. \begin{gathered}
\left.\frac{dv}{dt}\right|_{t_0} = U_a\omega_{\max}\\
\Delta v = u_a\omega_{\max} \Delta t_a\\
\Delta v = \frac{1}{2}LSB = \frac{2u_a}{2^{N+1}}\\
\omega_{max} = \frac{1}{2\pi\Delta t_a 2^{N+1}}
\end{gathered}
\end{equation*}
где N -- разрядность АЦП. Фазовые шумы ТИ накладываются на внутренние фазовые шумы АЦП и так теряются разряды. ТИ должны идти в ту же сторону, что и распространение сигнала. Обязательно через внешние драйверы ТИ с нулевой задержкой. Эмиттерно-селективная логика, дифференциальные сигналы. Снизить шумы позволяют clock-cleaner на основе ФАПЧ.
\end{itemize} \end{itemize}

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