BMEN3350 EXAM 1 Solution

Problem 1 (20 points):

#Q1. (3 points) A 14-bit analog-to-digital converter (ADC) has an input range of 1V to 6 V. If the output

of the ADC is 74, what is the voltage at its input? Ignore quantization error.

 Vin​=(2bits−1ADC Output×(Vmax−Vmin)​)+Vmin​

2 −1#Q1. (3 points) A 12-bit analog-to-digital converter (ADC) has an input range of 2V to 5 V. If the output

of the ADC is 47, what is the voltage at its input? Ignore quantization error.

Vin​=(2bits−1ADC Output×(Vmax−Vmin)​)+Vmin​

Substituting the values:

$$V_{\text{in}} = \left(\frac{47 \times (5 - 2)}{2^{12} - 1} \right) + 2$$ $$= \left(\frac{47 \times 3}{4095} \right) + 2$$ $$= \left(\frac{141}{4095} \right) + 2$$ $$= 0.0344 + 2$$ $$= 2.0344V$$

#Q2. (3 points) Briefly state the purpose of using voltage followers.

Used as a buffer between two stages since it has infinite input impedance and zero output impedance.

#Q3. (3 points) An analog signal contains three sinusoidal components with frequencies 5, 7 and 12 Hz.

What is the minimum sampling rate required in order to avoid aliasing?

24 sps

#Q3. (3 points) An analog signal contains three sinusoidal components with frequencies 5, 7 and 24 Hz.

What is the minimum sampling rate required in order to avoid aliasing?

48 SPS