Do Question 5 and 6 What is the function (express mathematically) represented by

Question

Do Question 5 and 6 What is the function (express mathematically) represented by this frequency spectrum? Plot this expression y(t) = 15 cos 2 pi t + 4 sin 2 pi t. Do not use a calculator or a computer to either obtain the answer or make the plot. Show your work. Plot what the FFT frequency spectrum will look like for this series of sine waves. V(t) = 10 sin(100 pi t) + 5 sin(200 pi t) + 3 sin(300 pi t) + 1 sin(400 pi t) If the TC voltage is input to a 12-bit ADC having a plusminus 5 V range, estimate the percent quantization error in the digital value. You have purchased an 8-bit digital to analog converter to control the joint position on a robot arm (which is proportional to input voltage) a. The DAC shows an output voltage of 1.01 V when the binary value of 00100101 is applied. What is the full scale analog output range of this DAC in Volts? b. What voltage does the DAC output with a binary value of 01010 applied? c. If the joint rotates 8.6 degrees/V applied, what is the minimum joint rotation increment you can achieve with this DAC? A 0 to 3V 8-bit ADC is used to measure an input voltage of 1.230 V. a. Determine the binary representation and the analog voltage approximation of the input signal. Explain your answer in terms of the quantization error of the ADC. b. If we wanted to ensure that the analog approximation be within 1 mV of the actual input voltage, how many bits would we require in our ADC?

Explanation / Answer

DAC output , 00100101 = 25 + 22 + 20 = 37

8 - bits count starts from 0 to 7 when the bit is on its value is 2n

when all 7 bits are on its value is 128+64+32+16+8+4+2+1 = 255

The DAC range is from 0 to 255

37 = 1.01 V

value per digit =1.01 /37 = 0.027297 V

full range = 0.027 *255 = 6.9608 V

bit value , 11101010 = 234

analog value = 0.027*234 = 6.3876 V

joint rotation 8.6 deg /V

minimum voltage we can read with DAC = 0.027297 V

minimum rotation = 8.6 *0.027297 = 0.235 deg

6) 3V DAC

3 V   - 255 digital value

1.23 V = (255/3)*1.23 = 105.55 = 106 digtial value

binary value : 01011010

1 mv - 1 digit

for 3 V we shall have 3000 digital value

this corrosponds to 12 bits = 212 -1 = 4095

i.e 0 to 4095 mV

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