Question

A dual slope A/D converter has resolution of 12-bits. If the clock rate is $100KHz,$ what is the maximum rate at which samples can be converted?

• A. $10Hz$
• B. $12Hz$
• C. $14Hz$
• D. $16Hz$

Answer 1

The correct option is B $12Hz$


Total conversion time,$$\begin{array}{cc}t& =2^N{T}_C+\frac{V_a}{V_R}{.2}^N{T}_C\end{array}$$
Where N = Number of bits of converter
$T_C$ = Time period of the clock
$V_a$=Analog voltage
$V_R$ = Reference voltage
The largest $V_a$ can be equal to $V_R$ therefore,
$$\begin{array}{cc}{V}_a& =V_R\\ t& =2^{N+1}{T}_C\\ t& =2^{12+1}.T_C\\ t& =2^{12+1}.T_C\\ t& =2^{13}\times \frac{1}{100\times {10}^3}sec\\ t& =\frac{8192}{{10}^5}\\ f& <\frac{{10}^5}{8192}\\ f& <12.20\\ \therefore f_{max}& =12Hz\end{array}$$