cedd lec pics
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@ -322,25 +322,31 @@ $z$ -- номер зоны. Пусть ширина полосы = 4МГц, це
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\section{Квантование}
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Дискретный сигнал -- это сигнал с конечным количеством отсчётов, но разрядность пока бесконечна, поэтому возможно применить разрядность АЦП. Передаточная характеристика идеального квантователя
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(5)
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-sig-sampling-err.svg}
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\caption{Квантование}
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\end{figure}
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явно теряем в точности.
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Signal-Noise-Ratio
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Явно теряем в точности. Основной параметр -- Signal-Noise-Ratio
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\[SNR = 6,02N + 1,76dB\]
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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.
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Если аналоговая частота больше -- есть более общий вариант
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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
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\[SNR = 6,02N + 1,76dB +10\log_{10}(\frac{f_s}{2f_a})\]
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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.
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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.
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\section{Характеристики АЦП}
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(6)
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-sig-sampling-check.svg}
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\caption{}
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\end{figure}
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память+пэвм -- способ проверить АЦП для своей системы.
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Характеристики могут быть статические и динамические.
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@ -354,62 +360,136 @@ N -- разрядность. Сигнал -- нестационарный про
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\item ошибка смещения offset error
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\end{itemize}
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(7) ПХ идеального АЦП, все центры кода лежат на прямой
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(8) пример ПХ реального АЦП.
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-perfect-tc.svg}
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\caption{Передаточная характеристика идеального АЦП}
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\end{figure}
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ПХ идеального АЦП -- все центры кода лежат на прямой линии симметрии
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-real-tc.svg}
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\caption{Пример ПХ реального АЦП}
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\end{figure}
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Дифференциальная нелинейность -- наибольшее отклонение ширины кода от идеального значения в МЗР или процентах от полной шкалы.
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Интегральная нелинейность -- наихудшее отклонение центра кода от прямой, также измеряется в МЗР или процентах от полной шкалы.
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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.
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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
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Эти ошибки невозможно исправить
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Ошибка смещения -- это аддитивная добавка напряжения на входе проценты от шкалы.
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Ошибка смещения - это аддитивная добавка напряжения на входе проценты от шкалы
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ошибка усиления - угол начального наклона (мультипликативная ошибка)
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Эти ошибки возможно исправить программно или внешними аналоговыми цепями.
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Ошибка усиления -- угол начального наклона (мультипликативная ошибка). Эти ошибки возможно исправить программно или внешними аналоговыми цепями.
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\subsection{Динамические характеристики}
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\begin{itemize}
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\item Реальное отношение сигнал-шум ($SNR_{real}$). Реальная характеристика точно будет отличаться. Точность разрядности возможно посчитать по формуле
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\[\frac{1}{LSB} \cdot 100\%\]
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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).
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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).
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N=8, SNR=49,7dB. реальный может быть 48,1 или 47,1 (первый лучше) зависит от частоты типовой график
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(9)
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обратный график - эффективное число бит
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$N=8$, $SNR=49,7dB$. реальный может быть 48,1 или 47,1 (первый лучше) зависит от частоты
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-typical-snr.svg}
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\caption{Типовой график}
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\end{figure}
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обратный график - эффективное число бит
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\[ENoB = \frac{SNR_{real} - 1,76dB}{6,02}\]
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\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.
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(10)
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-typical-thd.svg}
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\caption{Типовой график}
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\end{figure}
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\item сигнал шум и искажение (SINAD) типовая схема 4096 отсчётов. более качественный параметр.
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\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.
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(11)
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\item частотная характеристика: полномощная полоса пропускания (full-power bandwidth) -- частота на которой амплитуда реконструируемой синусоиды отличается на -3дБ.
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(12)
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\item частотная характеристика: полнолинейная полоса (Full linear bandwidth) срез -0,1дБ, показывает где АЧХ максимально плоская.
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-sfdr.svg}
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\end{figure}
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\item частотная характеристика: полномощная полоса пропускания (full-power bandwidth) -- частота на которой амплитуда реконструируемой синусоиды отличается на $-3$дБ.
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-fpb.svg}
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\end{figure}
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\item частотная характеристика: полнолинейная полоса (Full linear bandwidth) срез $-0,1$дБ, показывает где АЧХ максимально плоская.
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\item при интермодуляции в общем случае появляются гармоники каждой частоты (кубические составляющие).
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(13) продукт интермодуляционных искажений
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-imd.svg}
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\caption{Продукт интермодуляционных искажений}
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\end{figure}
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\begin{equation*}
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\begin{gathered}
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2: f_2-f_1, f_2+f_1;\\
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3: 2f_1+f_2, 2f_1-f_2, f_1+2f_2, f_1-2f_2;\\
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...
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\end{gathered}
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\end{equation*}
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Intermodulation distortion (IMD). обычно используется сигнальный тест на два компонента и используются продукты второго и третьего порядка.
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\[ IMD = \frac{\sqrt{a_{f_1}^2 + a_{f_2}^2}}{\sqrt{\text{сумма квадратов коэффициентов интермодуляции}}} \%\]
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\[ IMD = \frac{\sqrt{a_{f_1}^2 + a_{f_2}^2}}{\sqrt{\sum(\text{коэффициенты интермодуляции})^2}} \%\]
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В ВЧ и радиочастотных цепях -- это критическая характеристика. Измеряется также через БПФ.
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\item время восстановления после перенапряжения. overvoltage recovery.
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(14) время восстановления измерения с приемлемой точностью (1МЗР)
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Может возникнуть от помех или наводок, индустриальные помехи, итд.
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-ovr.svg}
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\end{figure}
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время восстановления измерения с приемлемой точностью (1МЗР). Может возникнуть от помех или наводок, индустриальные помехи, итд.
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\item время установления выходного напряжения (setting time, $t_{set}$) -- фактически, переходная характеристика.
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(15)
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-set.svg}
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\end{figure}
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характеристика может быть критична для многоканальных систем (мультиплексор перед АЦП) частота переключения каналов.
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\item апертурная неопределённость (апертурный джиттер, aperture jitter). дрожание фазы
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(16)
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-jitter.svg}
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\end{figure}
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Если это тактовый сигнал который подаётся на АЦП, даётся среднеквадратичное значение.
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(17)
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\begin{figure}[H]
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\centering
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\fontsize{12}{1}\selectfont
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\includesvg[scale=1.01]{pics/04-cedd-00-slope.svg}
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\end{figure}
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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.
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(18)
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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.
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\begin{equation*}
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\begin{gathered}
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\left.\frac{dv}{dt}\right|_{t_0} = U_a\omega_{\max}\\
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\Delta v = u_a\omega_{\max} \Delta t_a\\
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\Delta v = \frac{1}{2}LSB = \frac{2u_a}{2^{N+1}}\\
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\omega_{max} = \frac{1}{2\pi\Delta t_a 2^{N+1}}
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\end{gathered}
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\end{equation*}
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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.
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\end{itemize}
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After Width: | Height: | Size: 16 KiB |
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Reference in New Issue