Question

A delta modulated system is designed to operate 4 times the Nyquist rate for a signal with 3 kHz bandwidth. The quantization step size is 260 mV. The maximum amplitude of a 3 kHz input sinusoidal for which the delta modulator does not show slope overload is

• A. 1.041 V
• B. 2.085 V
• C. 0.331 V
• D. 0.662 V

Answer 1

The correct option is C 0.331 V

$\text{To avoid slope overload,}$
$\begin{array}{cc}\Delta f_s& \ge {\left|\frac{d}{dt}\right(m\left(t\right)\left)\right|}_{max}\\ \text{now}{f}_s& =4\times \left(2f_m\right)\\ f_s& =4\times 2\times 3=24kHz\\ \therefore \Delta f_s& \ge 2\pi A_m{f}_m\\ 260\times {10}^{-3}\times 24\times {10}^3& \ge \left(2\pi \right)A_m\times (3\times {10}^3)\\ A_m& \le 0.331V\end{array}$