3/10/16 - Super Meshes, Transistors, and Gummel Plots

Today we are beginning class with a concept that can be related to our node voltage analysis. Just like how we can define a super node for voltage nodes to only contain a voltage source, we can define a super mesh to be just a branch that contains just a current source. We still define the currents to be ground around the loop, but we now have an equation for the branch we took out.

Here we list traits of a circuit that it would be beneficial to use one method over the other, such as the goal of finding current or voltage, or what is in the circuit.

An example of a mesh problem that we failed to solve.

The same circuit in EveryCircuit.

Next, we begin setting up the same circuit on the breadboard. We have the resistors used in the circuit on the board and used the strips on them to read their values.

Here we have the actual measured resistances of the resistors on the board measured with the multi meter.

Hooked up to the Analog Discovery, we power up the circuit and measure the potentials across resistors.

 

Here we measure v_1 and v_2 respectively.

Now we compare our actual values compared to the expected values from the calculations.

We also measure a current in the circuit and compared it to our expected value.

From our observations, the recorded experimental values are very close to our calculated theoretical values.

We are introduced to a new circuit element, the transistor. Here we can see that the equivalent circuit to a transititor is a voltage source, a branch going out, and a dependent current source. The voltage source is due to the transistor requiring some potential to activate the element, once the threshold is passed, current can flow though as normal. 

The beta constant for the dependent source is based on the transistor itself, higher grade resistors have a largest constant to amplify the current passing though. Most standard transistors have a multiplier of 50, so that's what we assumed in this example.

Next, we are setting up a circuit based on what we have just learned. Again, we use the Analog Discovery instrument and attach it as shown to create the circuit.

We will be feeding it a step function and a linear voltage source as inputs and we are measuring the potential from across the resistor and across the transistor collector and emitter.

We are inputing a linearly increasing and decreasing voltage for channel 1 and a step function that has half the period of channel 1 on channel 2.

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When we measure the voltages, we can plot them against each other with an XY plot. Doing so reveals this unique graph. This graph is known as a Gummel Plot, which measures current going into the collector vs. current coming out of the emitter. It has a logarithmic shape and we know from Ohm's Law that voltage is simply a scalar of current with a factor of resistance.

3/8/16 - Mesh Analysis and More Circuits

Today we start with a node analysis problem and we're introduced to the concept of a super node. The super node involves a branch that only contains a voltage source, we can "eliminate" a variable in our calculations as we have an equation based off of the branch and can substitute without doing much work.

Next up, we have a simple two branch circuit to find the voltages across certain various elements in the circuit. We calculate the different voltages that one node can have based on the E-12 resistance variations.

Here is a picture of the circuit on a breadboard, we hook up the Analog Discovery's waveform generator and voltage supply to the circuit.

So we begin measuring the potentials across the various elements with the multimeter.

The voltage across v2, which we compare to our calculations, it turns out to be fairly off of the expect values.

The voltage measured at v1, which is roughly what we expected.

The voltage measured at v3, which is roughly what we expected again.

The voltage at v4, which is also roughly what we expected. 

A general overview of our set up and how we measured the values.

Here is a table of our recorded values.

Next, we are introduced to Mesh Analysis, which is nearly the same thing and the node voltage method, except it finds currents rather than voltages. 

We start by drawing two loops and labeling them i_1 and i_2. We then write KVL equations to form a system of equations to solve. Both loops run clockwise regardless of which way the current is actually flowing by standard practice. We solve the system and find the currents in the loop. Now knowing the currents, we can find every other item in the loop.

Lastly, we are given practice reading resistor labels, with the table of resistance colour labels, Professor Mason gives us examples on the board and we find the resistances of each strip set.

With higher grade resistors, there is less uncertainty in the resistor and the resistor provides another strip of precision to find the value.

We compile our found values and even added the chicken in the middle.

3/3/16 - Thermal Sensors and Microcontrollers

Today, Professor Mason starts us off with an introduction to microcontrollers and what they do. He tells us that a very 8-bit chip is in a lot of electronics and brings up the topic of a 3D printer. A 3D printer has a nozzle where the plastic filament is fed and melted, and to read the temperature on the nozzle, there is a material that has a negative temperature coefficient. This can be attached in series with a resistor to create a varying voltage source. 

So we're given the design problem of the set up to vary in voltage of 0.5V for 12 degress Celsius, from room temperature to the melting point of the plastic.We're also told that the microcontrolleris popular for its analog to digital signal converter, which will take a voltage reading and convert it into an 8-bit digital signal.

Since the voltage can vary from 0V to 5V, we found the voltage resolution to be 0.0196V per bit of data.

Now we find the temperature resolution of the reading.

Since we know the voltage resolution, we can find approximately how many bits can represent a 0.5V change in voltage. We find it to be around 25 or 26 bits and we divide 0.5V by the nearest whole number of bits to find our temperature resolution.

A finalized version of the work shown above.

Next, we measure the resitances that the temperature probe has when exposed to different temperatures, one at room temperature and one at what we believed to be body temperature.

We calcuated the resistances solve for resistance values that would return our 0.5V range. We chose the 12k resistor since that was the closest we had to the E-12 series present in the classroom.

We find what our expected voltages are and then start setting up the circuit.

Again, we take the Analog discovery and breadboard to set up the circuit and use a mutli meter to measure the voltage out.

This is its reading at room temperature.

This is the reading at our "body temperature".

The measured values are very close to our expected.

Professor Mason also showed us that our multi meters could also measure temperature, so we plugged a probe in and tested its functionality.

This is the actual room temperature.

And this is the actual "body" temperature.

Then, we are shown a new way to solve circuit problems, using node analysis.

This method is called the node voltage method and begins by identifying the essential nodes. We define an essential node as a node with 3 or more connections. Then we deem one to be our reference node and write KCL equations to make a system of equations in order to solve for the node voltages in reference to the ground node.

Though many substitutions, we solve for one voltage, and found the other shortly afterwards.

Lastly, since we only had 25 bits in our design of the temperature probe, we were told to find the ideal resistor to give us the maximum resolution possible.

The easiest way to do this was to take the derivative and set it equal to zero, which we did and found our ideal resistance to give the maximum scope of resolution. But plugging this number back in, we can see the our voltage gap barely increased by a hundredth of a bolt, which won't give us another bit to work with since the voltage resolution isn't that high.

3/1/16 - Hotdogs, BJTs (Not BLT), and LEDs

Today we start off the class with a demonstration, a hot dog connected to two prongs hooked up to the 120VAC wall outlet. We were asked what would happen to the hot dog once it was connected and draw a current versus time graph.

We assumed that since the hot dog has water in it, current will flow though it and slowly cook it as the water evaporates. Once the hot dog was powered, we saw it slowly steam and then start smoking as the electricity burned the hot dog at the point of contact. Then, LEDs were inserted on the hot dog, and we were asked what the LEDs would do. We said the the LEDs that had legs parallel to the hot dog would light, with more spread out legs lighting more, and the ones perpendicular to the hot dog would not light at all.

The hotdog with LEDs stuck in it.

The hot dog being powered and we see that our predictions are correct. 

There a a potential drop across the hot dog, and with the LEDs being powered at two different spots, we see a potential difference and current flows through the LED, obviously the further the spread, the more potential and the parallel ones receive no current as there is no potential drop.

Next we're given a simple KCL problem to be introduced to dependent sources. We're told that the current source is dependent on the current flowing though the middle branch. We do a simple KCL equation and find the unknown current flowing though the branch, then we found the potential drop across the resistor.

We're given a KCL problem and told to find i_0 and v_0, we solve and find   is equal to 4A and v_0 is equal to 8V.

Professor Mason shows us that there a much simpler method to solve the problems and avoid so many currents, we can redraw the circuit to cluster the top wire into a single connection and eliminate many of the currents we were dealing with.

Next up, we were given the problem of the varying voltage source. It's a simple circuit with a power source v_s, a voltage out v_out, and two resistors with resistance R1 and R2.

We solve for the current though the whole loop to and multiply it by R1, and since we know that is the potential drop the second resistor has to have, we can conclude that the potential between the resistors is that value.

Next, we are given a design problem involving an an LED that has specific requirements to run off of a 12VDC supply. We set up the initial loop and solve for R1 and R2 using the formula derived from the previous step. We first found total resistance and then found values of resistance that would give us our maximum operating voltage from the 12VDC source.

Professor Mason then tells us that resistors do not come in those values we have just solved for, and to obtain such a resistor, it is extremely expensive. So,with a table of E-12 grade resistor values, we found two that would be proportionally close to our values we solved for. We calculated the new voltage and current and found the voltage is nearly identical and the current is roughly halved.

Another problem, we have a LED that runs off of a specified voltage and we need to find a resistor that would drop the potential down. So we find the maximum drop possible and the maximum current possible and solve for resistance.

There is also a lovely comment from our neighboring group.

Next, another resistor problem that we found the equivalence resistance to be just a simple answer. We were quite disgruntled when we solved it.

Lastly, for the lab, we were introduced to a light sensor that has a variable resistance based on the amount of light received. We're also introduced to a new circuit element called a Bipolar Junction Transistor, or BJT for short. The BJT works similar to the MOSFET from last time except that rather than using voltage as a activation value, it uses current. The light sensor varies between a very high resistance and a lower resistance when in the dark, with the circuit, we cam make a LED light turn on an off dependent on the light level. We solve for the current that would flow and the potential at each value.

Here we have the circuit set up on the breadboard with the Analog Discovery as a power source. We also have a multimeter set up to measure the potential across various elements.

Here the sensor is uncovered so the potential across the bulb is not enough to turn on the LED.

Here we cover the sensor and we notice the potential across the bulb increases to turn on the LED.

Here we have the measured values of the light sensor's resistance and calculated our expected voltage across the LED, and then compared it to the actual voltage. We found that the voltage when it was off was close, but the voltage when it was on was fairly off.