1. Variable unit16_t dac_value = 0x0800 is written by software to DAC channel used in 12-bit right-aligned mode. DAC reference voltage is 3V. determine DAC output voltage. Show your work.
To determine the DAC output voltage, we need to use the formula:
Output voltage = (DAC value / (2^n - 1)) * Reference voltage
Where DAC value is the value written to the DAC (in this case, 0x0800), n is the number of bits used by the DAC (12 bits in this case), and the reference voltage is 3V.
Plugging in the values:
Output voltage = (0x0800 / (2^12 - 1)) * 3V
First, let's calculate (2^12 - 1):
2^12 = 4096
(2^12 - 1) = 4096 - 1 = 4095
Now we can plug in the values:
Output voltage = (0x0800 / 4095) * 3V
Since 0x0800 is equal to 2048 in decimal,
Output voltage = (2048 / 4095) * 3V
Simplifying,
Output voltage = (0.5) * 3V
Output voltage = 1.5V
Therefore, the DAC output voltage is 1.5V.
2. Determine the output frequency fout of a DDS system having 32-bit phase accumulator if DDS clock frequency fclk is 120 kHz and the value of the frequency tuning code M is 196608. Show your work.
To determine the output frequency, we can use the formula:
fout = (M * fclk) / (2^32)
Where M is the frequency tuning code (196608 in this case), fclk is the DDS clock frequency (120 kHz in this case), and 2^32 is the maximum value of the phase accumulator for a 32-bit system.
Plugging in the values:
fout = (196608 * 120 kHz) / (2^32)
To simplify the calculation, we can rewrite the division as a multiplication by the reciprocal:
fout = (196608 * 120 kHz) * (1 / (2^32))
Now, let's calculate (2^32):
2^32 = 4294967296
Plugging in the values:
fout = (196608 * 120 kHz) * (1 / 4294967296)
Simplifying,
fout = (23592960 kHz) * (1 / 4294967296)
Now we can calculate the output frequency:
fout = 5.48 Hz
Therefore, the output frequency fout of the DDS system is 5.48 Hz.
3. Indicate the component of a digital signal processing system that converts discrete digital signal into analog signal.
a) DAC
b) CPU
c) ADC
d) FPU
a) DAC (Digital-to-Analog Converter)
The component of a digital signal processing system that converts a discrete digital signal into an analog signal is a DAC. A DAC takes in a series of digital values and converts them into continuous analog signals that can be used by analog devices or systems. This conversion allows digital signals to be processed and utilized in analog domains.
4. An analog input signal x(t) = 1.5 +0.5 sin(100t) is sampled with 2 kHz sampling frequency fs. Assuming that sampling starts at t = 0 compute the value of the sample x [20]. Show your work.
To compute the value of the sample x[20], we need to use the given analog input signal and the sampling frequency.
The formula to calculate the sample index "n" is:
n = (t * fs)
Where t is the time at which the sample is taken and fs is the sampling frequency.
In this case, we have t = 20/fs, as the sampling starts at t = 0.
So, we can calculate the sample index:
n = (20 * 2 kHz)
n = 40,000
Now, we can calculate the value of the sample using the given analog input signal:
x[n] = 1.5 + 0.5 * sin(100 * n / fs)
Plugging in the values:
x[40,000] = 1.5 + 0.5 * sin(100 * 40,000 / 2,000)
Simplifying,
x[40,000] = 1.5 + 0.5 * sin(100 * 20)
Since sin(100 * 20) = sin(2000), we can calculate the value using a calculator or approximation techniques:
x[40,000] ≈ 1.5 + 0.5 * sin(2000)
x[40,000] ≈ 1.5 + 0.5 * 0.89
x[40,000] ≈ 1.5 + 0.445
x[40,000] ≈ 1.945
Therefore, the value of the sample x[20] is approximately 1.945.