Question 29.8: Show the value of the output voltage at the end of each cycl......
Show the value of the output voltage at the end of each cycle for a 6-bit cyclic DAC with an input value of D_5D_4D_3D_2D_1D_0 = 110101. Assume that V_{REF} = 5 V.
We can predict the value of the output based on our previous experience with DACs. The digital input 110101 corresponds to 53_{10}. Therefore, the output voltage due to this input should be
\nu_{O U T}=\frac{53}{64}\cdot V_{R E F}=4.140625~\mathrm{V}Now examine the cyclic converter in Fig. 29.17. By performing a 6-bit conversion and using Eq. (29.39), the outputs occurring at the end of each cycle can be seen in Fig. 29.18.
\nu_{O U T}(n)=\left\lgroup D_{n-1}\cdot V_{R E F}\ +\ \frac{1}{2}\cdot\nu_{A}(n-1)\right\rgroup \cdot\frac{1}{2} (29.39)
The output voltage at the end of the sixth cycle is precisely what was predicted. Note that had this been a 3-bit conversion, the output voltage at the end of cycle 3 would correspond to the value of the 3-bit DACs studied previously with an input of 101.
