Differential nonlinearity

<h2 id="formula">Formula</h2>
<p>
  
    
      
        
          DNL(i)
        
        =
        
          
            
              
                V
                
                  out
                
              
              (
              i
              +
              1
              )
              −
              
                V
                
                  out
                
              
              (
              i
              )
            
            
              ideal LSB step width
            
          
        
        −
        1
      
    
    {\displaystyle {\text{DNL(i)}}={{V_{\text{out}}(i+1)-V_{\text{out}}(i)} \over {\text{ideal LSB step width}}}-1}

</p>
<h2 id="effects-of-dnl">Effects of DNL</h2>
<ul><li>If the DNL of an ADC is smaller than -1, <i>missing codes</i> appear in the transfer function, i.e. there are codes for which there is no input voltage to get the code at the ADC output.</li>
<li>If the DNL of a DAC is bigger than 1, the transfer function of the DAC becomes <a href="/facts/Monotonic_function/MjQK0YL2">non-monotonic</a>. A non-monotonic DAC is especially not desired in <a href="/facts/Closed-loop_transfer_function/D1A3AA7q">closed-loop</a> control application as it may cause stability problems, i.e. it may cause oscillations.</li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Integral_nonlinearity/T2nXCzdI">Integral nonlinearity</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="https://www.analog.com/en/technical-articles/inldnl-measurements-for-types-of-highspeed-adcs.html">INL/DNL Measurements for High-Speed Analog-to-Digital Converters (ADCs)</a>  Application Note 283 by Analog Devices</li>
<li><a href="http://focus.ti.com/lit/an/slaa013/slaa013.pdf">Understanding Data Converters</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>INL and DNL definitions "A DNL error specification of less than or equal to 1LSB guarantees a monotonic transfer function with no missing codes. "  https://www.analog.com/en/technical-articles/inldnl-measurements-for-types-of-highspeed-adcs.html <a href="https://www.analog.com/en/technical-articles/inldnl-measurements-for-types-of-highspeed-adcs.html" target="_blank">https://www.analog.com/en/technical-articles/inldnl-measurements-for-types-of-highspeed-adcs.html</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Differential nonlinearity open-in-new

Differential nonlinearity