لا خطية التفاضل

في الرياضيات ، تعتبر خطية عملية التفاضل احدى أهم الخواص الأساسية للمشتق ، في حساب التفاضل.

Demonstrates A. Differential Linearity where a change in the input produces a corresponding change in output and B. Differential Non-linearity, where the relationship is not directly linear

تنتج هذه الخاصية قاعدة الجمع في التفاضل و قاعدة العامل الثابت في التفاضل . لذا يمكننا القول أن عملية التفاضل خطية أو ان معمل التفاضل معامل خطي .

لا خطية التفاضل Differential nonlinearity (واختصارها DNL) هي مصطلح يصف الانحراف بين two analog values corresponding to adjacent input digital values. It is an important specification for measuring error in a digital-to-analog converter (DAC); the accuracy of a DAC is mainly determined by this specification. Ideally, any two adjacent digital codes correspond to output analog voltages that are exactly one Least Significant Bit (LSB) apart. Differential non-linearity is a measure of the worst case deviation from the ideal 1 LSB step. For example, a DAC with a 1.5 LSB output change for a 1 LSB digital code change exhibits 1⁄2 LSB differential non-linearity. Differential non-linearity may be expressed in fractional bits or as a percentage of full scale. A differential non-linearity greater than 1 LSB may lead to a non-monotonic transfer function in a DAC. It is also known as a missing code.

خطية التفاضل Differential linearity تشير إلى علاقة ثابتة بين التغير في المـُخرَج والمـُدخل. For transducers if a change in the input produces a uniform step change in the output the transducer possess differential linearity. Differential linearity is desirable and is inherent to a system such as a single-slope analog-to-digital converter used in nuclear instrumentation.

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 الصيغة

${\text{DNL(i)}}={{V_{\text{out}}(i+1)-V_{\text{out}}(i)} \over {\text{ideal LSB step width}}}-1$

 تأثير DNL

• If the DNL of an ADC is smaller than -1, missing codes appear in the transfer function, i.e. there are codes for which there is no input voltage to get the at the ADC output.
• If the DNL of a DAC is bigger than 1, the transfer function of the DAC becomes non-monotonic. A non-monotonic DAC is especially not desired in closed-loop control application as it may cause stability problems, i.e. it may cause oscillations.

 انظر أيضاً

• Integral nonlinearity

 وصلات خارجية

• INL/DNL Measurements for High-Speed Analog-to-Digital Converters (ADCs) Application Note 283 by Maxim
• Understanding Data Converters