The DC Reference being the first thing in our project we had a few different iterations. For the sake of complexity, I will focus on the 2 designs we had to choose between. We started with a simple Digital to Analog Converter (DAC). We designed a voltage divider with a 1000 ohm resistor and a digital potentiometer that we could vary using the Raspberry pi. By manipulating the the value of the digital potentiometer we could vary the voltage coming from the split in the divider. This design worked for the requirements placed for the project being able to get a voltage range from around 0.25-4.2v. We ultimately decided that due to the limit of the digital potentiometers enforced by the constraints of the project, we decided to go with another method. 

The next design was a sallen key low pass filter. By using the filter with the pulse width modulation (PWM) from the pi we could manipulate the voltage from 0-3.3v by varying the duty cycle of the square wave. Essentially what this does it take the average voltage across the whole duty cycle. The higher the duty cycle, i.e. 100%, the higher the voltage and vice versa. The project requirements stated that the voltage outputted from the DC Reference needed to be 0-4v in .25v increments. Knowing that the range we were currently getting for this design was 0-3.3v, we added a non-inverting operational amplifier (OP AMP) to increase our range 0-4v to be within the specification required. Through meticulous testing and measuring of different duty cycles we were able to characterize and ensure the best possible accuracy of our reference voltage.

To design the voltmeter we knew we need to design an Analog to Digital Converter (ADC). When researching for this a few design constraints we focused on were the amount of raspberry pi pins we were going to use and the accuracy we could get out of our system. So, ADCs like the flash ADC were not in consideration for our project. After we gathered a better understanding of what was required and what we wanted to achieve we went with a mix of successive bit approximation and using our DC Reference. By using a comparator OP AMP we could feed in a voltage that we know and the voltage we wanted to test multiple times. By using the successive bit approximation we could spend significantly less time testing every combination of voltage within our range and test by halving the amount each time. The range starts by testing if the input voltage is higher or lower than 2v. Depending on if it was higher or lower then it would move to 1v or 3v respectively and so on until it satisfied the .25v threshold. To ensure our voltmeter was able to test the difference in voltages across a component and not just a point voltage, we added a differential amplifier to essentially turn the original 2 test points into one. After significant testing we were able to confirm that the voltmeter worked as intended. We also were able to create a chart of what voltages would read as in our design and this can be seen in the appendix.

The ohmmeter design was inspired by how we were creating the voltmeter. By using 1 of the 5 digital potentiometers we were allotted in the beginning of the project we could create 2 voltage dividers. In these 2 voltage dividers there would be 2 set resistors. Originally the values of these resistors were the same, but due to not being able to reach the desired range we had to make them separate values, but these values are values we knew. In one of the dividers we implemented the digital potentiometer which we had characterized and knew all the values that it would output for all 128 steps. Knowing this information we could simply check the voltage outputted by the side with the digital potentiometer to the side with the unknown resistor, the resistor we wanted to the get value of. For simplicity of this process we checked values individually at this point and did not implement something like the successive bit approximation. Checking each step of the digital potentiometer until the voltage had change from higher to lower on the output of the comparator we could get a pretty good idea on the value of the resistor. Knowing in the beginning that the values chosen for resistors in the dividers there was a conversion factor we had to do to get it to be the correct value.

The sine wave generator was the most difficult and most time consuming part of the whole project. We had many iterations of trials and errors trying to get the perfect design to fit the requirements. We started by trying to manipulate our DC Reference to make a sine wave like wave form by changing the voltage super quick, but unfortunately we were not able to get it to change quick enough to meet the requirements. Looking back we could have added filters to limit the amount of voltage steps we needed to go through but in the end we did not use this method. The method we actually went with was using a wein bridge oscillator and 4 digital potentiometers. We carefully tested different methods of using this oscillator with different capacitors to get the range we needed. After getting the capacitors to have the range we wanted we needed to be able to control the frequency and amplitude. To control this we used 2 resistors that controlled the frequency and 2 that controlled the amplitude. By taking each of the 4 potentiometers and testing every possible value of each we were able to create a lookup table. This table allowed us to send a desired value of each and have it find the values the potentiometers needed. By using this method we were able to create a sine wave with a range of 0-.5v to 0-5v and have a frequency of 1000-10000Hz.

At this point in the project we got a really good understanding of how we wanted to try and tackle this task. This is one of the only parts of the project I would say we nailed in the first iteration. By using a comparator OP AMP we could test a wave's frequency by checking how many times the comparator triggers. Becuase we knew that the value of the wave had to be higher than .5v we chose a value under that to compare to. The incoming wave would go in to one side of the comparator and the other side of the comparator had a .4v input. Using some interrupts and math we could count the amount of times it crossed the threshold and back calculate out the frequency. Overall this worked exactly how we wanted and only had to make minor changes to get it to be as accurate as possible.