#### yefj

##### Full Member level 4

Hello,I am trying to develop the expression for the DNL of DAC

the worst case DNL is the transtion between 011..11 and 1..000 (assume between the MSB is N+1 )

for 01..111

For binary weighted:

\[ I_{dac}=Vref*2^{n+1}*N(G,\delta G) \\ 2^0+..+2^n=\frac{2^0(2^{n+1}-1)}{2-1}=2^{n+1} \]

so for 1000..0

\[ I_{dac}=Vref*2^{n}*N(G,\delta G) =Vref*N(G,\sqrt{2^{n}}\delta G) \\ \]

so if we substract the two current for DNL the variance of the DNL is:

\[ \sqrt{2^{n+1}}-\sqrt{2^{n}}=\sqrt{2^{n}}(\sqrt{2}-1) \]

which is different form the formal expression shown bellow.Where did i go wrong?

Thanks.

the worst case DNL is the transtion between 011..11 and 1..000 (assume between the MSB is N+1 )

for 01..111

For binary weighted:

\[ I_{dac}=Vref*2^{n+1}*N(G,\delta G) \\ 2^0+..+2^n=\frac{2^0(2^{n+1}-1)}{2-1}=2^{n+1} \]

so for 1000..0

\[ I_{dac}=Vref*2^{n}*N(G,\delta G) =Vref*N(G,\sqrt{2^{n}}\delta G) \\ \]

so if we substract the two current for DNL the variance of the DNL is:

\[ \sqrt{2^{n+1}}-\sqrt{2^{n}}=\sqrt{2^{n}}(\sqrt{2}-1) \]

which is different form the formal expression shown bellow.Where did i go wrong?

Thanks.

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