3000 is hexadecimal 3000 Suppose that there is a 14bit AD co

$3000 is hexadecimal 3000

Suppose that there is a 14-bit A/D converter with V_RL = 1 .OV and V_RH = 4.0V, operating at a sampling rate of 50k samples/sec. Assuming that the converter generates unsigned digital values: What would you expect the (hex) digital output to be when the converter samples an input equal to 2.3V? What analog input voltage would correspond to an output of $3000 ? What is the maximum frequency component that may be present in the input signal if we are to avoid aliasing?

Solution

Ans) As V_RL=1.0 V and V_RH=4.0 V

The range is:4-1= 3 V

The resolution is: 3 / 2^14 = 0.183 mV

As input equal to 2.3 V,resultant input to ADC is 2.3-V_RL=1.3 V

Decimal Value of ADC= 1.3/Resolution=1.3/0.183 m=7099.7

Hex output will be $1BBB

For Hex value of $3000 the input voltage is

Decimal value=3*16^3=12288

Input Voltage =12288*resolution+V_RL=3.25 V

Input Voltage =3.25 V

Maximum Frequency without aliasing is Sampling Frequency /2 as per Nyquist sampling theorem

Maximum Frequency=50k/2=25kHz