Lab7 lab - Homework assignment for Allen Turner PDF

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Homework assignment for Allen Turner...

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Yu Liu Due: 3/19/2018 Section: 1A76

Lab 7: Digital to Analog Conversion/ Butterworth Filter Design Pre-Lab Introduction In this lab, a 4-bit Digital to Analog converter and a Butterworth Filter is built. Based on the design of the circuit, the 4-bit digital to analog circuit adds its own voltage to the analog output. First it adds input/2 and then input/4 and then input/8 and lastly input/16 and adds it all up which gives almost that initial input value.

Discussion Using the MCP6024 and the patterns waveform option, a 4-bit DAC was built. Figure 1a shows the derivation of the equation for the 4 bit DAC. Adjusting B0-B3 so that only one input is high while the other ones are low, Vo does indeed vary B 3 B2 B 1 B 0 + + + . As shown in figures 1b-1e, by having a according to the equation: Vo= 8 16 4 2 wavegen input of around 5 Volts and some losses associated with the system, with only B3 high, it gets about 2V, with only B2 high, it gets about 1V, with only B1 high, it gets about .5V and with only B0 high, it gets about .25V which is what is expected according to the equation. Using the patterns waveform option, a sawtooth waveform results. By changing the frequency from 1kHz to 2kHz, the timing for the binary counter changes from 16ms to 8ms and so does the period of the sawtooth (each period is now 8ms). Changing the frequency to 4kHz further reduces the period to 4ms as shown in figure 1h. Vo is consistent with the binary input values. The circuit would only need more inputs and resistors in order to make this into a 5,6,7 or 8 bit digital to analog converter.

Figure 1a: Analysis of 4 bit DAC

Figure 1b: B3 High

Figure 1c: B2 High

Figure 1d: B1 High

Figure 1e: B0 High

Figure 1f: 1K Hz with period 16ms

Figure 1g: 2K Hz with period 8ms

Figure 1f: 4K Hz with period 4ms

Butterworth Filter Parts (g,h) The low pass active Butterworth filter was built and set to a frequency 500 Hz, 200Hz and 50 Hz as seen in Figures 2a, 2b, 2c. The circuit behaved like a low pass filter with cutoff frequency of 100 Hz. At 50 Hz, the input signal passes through uninterrupted but at 200 Hz and 500 Hz, the input signal starts to become lower as it becomes farther from 100 Hz. At 500 Hz, the output signal is seen to be about 0 V.

Figure 2a: 500 Hz

Figure 2b: 200 Hz

Figure 2c: 50 Hz

Conclusion In this lab, the 4-bit DAC was created and using the pattern waveform it steps up the voltages by adding each individual voltage from B3-B0 to get Vout. By adding more resistors in the same way that is being done in the circuit, it can be changed into a 5,6,8, or any other extension bit DAC. By changing the input patterns from binary to decimal, the number of steps will decrease from 16 to 10. Since this is a 4-bit input pattern, whenever one of the inputs are 1, it adds about a .3 input voltage, for example if B1 and B0 are high where as B3 and B2 are low, Vout would be the sum of B1 and B0 which is about 1V. It turns inputs which are either high or low and adds it up to an analog output....