Nodal Analysis

Motivational Analysis Problem:

In most real-world situations, it is important to design a system so that it can take damage and still deliver the necessary results. An example of this in circuit design is building in redundant power supplies. However, it is very seldom as simple as just adding in another battery. New power sources mean that the overall system must be redesigned in order to handle variances in voltage and current while still remaining operational.

We were given the task of designing a simple circuit which consisted of two voltage supplies and a total of five resistors.

Design Parameters:

We are given that in the outer loop there is a 100 Ohm resistor followed by two 220 Ohm resistors in series. There is a 12V source connected by the positive terminal to the 100 Ohm resistor and a 9V supply connected by its positive resistor to the outside 220 Ohm resistor. The two negative negative terminals are connected to each other and ground. There are two branches connected between the ground consisting of 1000 Ohm resistors, one between the 100 Ohm resistor and the inside 220 Ohm resistor and the other between the two 220 resistors.

Setup:

Results:

We measured the voltage across the 1000 Ohm resistors along with the currents through the batteries and compared these to our predicted values.

Theoretical Value Measured % Error

Current Battery1 -17.5 mA 17.84 mA 1.94

Current Battery2 -1.8 mA 1.57 mA 12.78

Voltage1 10.25 V 10.25 V 10.35 V 1.00

Voltage2 8.6 V 8.6 V 8.76 V 1.86

Voltage Dividers

Motivational Design Problem:

Here, we were to design a system which consisted of an unregulated power supply connected to three loads in parallel. The objective is to be able to design a system which stays within operational parameters no matter how many of the loads are on or off.

Design Parameters:

We are given that all three loads have a resistance of 1kOlms. No matter what combination of loads are on or off the the voltage must remain between 4.75V and 5.25V.

System Model:

Pictured is the model which we developed. It consists of a voltage supply set to 6V connected to a variable resister box (VRB) in series set to 55Olm. The VRB is connected to three 1kOlm resisters in parallel which are in connected back to the voltage supply. We measured the current through each resistor as well as through the voltage supply.

Results:

The circuit operated within the desired parameters.

Introduction to Biasing

Motivational Design Problem:

We are to design a simple circuit that consists of a 9V Alkaline battery and two LEDs, with distinct voltage and current demands, which are used to indicate whether a device is on or off. We were to determine the most efficient layout for the circuit and the resistance needed in order to keep the LEDs from burning out.

Design Parameters:

The circuit is to be designed to handle a 9V Alkaline battery, one LED rated for 5V and 22.75mA and another LED rated for 2V and 20mA.

System Model:

Shown above is the circuit we built to model the desired system. In the configuration pictured it consists of a supply source set to supply 9V, a bread board with a red and a yellow LED installed, a resistor placed in front of both LEDs in parallel, a multimeter measuring Amps in one of the branches in front of the red LED and another multimeter which is measuring the voltage across the red LED.

Results:

By using the given requirements of the system and a few initial measurements we were able to use Kirchhoff's circuit laws in order to determine the values for the required resistors. 175.8 Olms were needed for the yellow LED's resistor while 360 Olms were required for the red one. However due to restraints on the available equipment we were forced to use a 150 and 360 Olm resistor respectively.

Introduction To DC Circuits

Motivational Design Problem:

In this exercise we are asked to consider a hypothetical situation where we are to connect a piece of electrical equipment, with specific energy demands, to a battery source that maybe a significant distance away from it. With increasing distance the natural resistance of the connecting wires steadily adds up and this leads to a decrease of the actual power that the electrical equipment will be able to draw. If the total resistance becomes too great then the piece of equipment may no longer function at all.

Design Parameters:

We must determine the maximum distance that the battery and equipment, or load, may be separated from each other if we must connect them by using AWG #30 cable. Also, we are to determine the distribution efficiency and the approximate time before the battery discharges.

We are given that the load is rated to consume 0.144W when supplied with 12V and that it will no longer operate properly when it is supplied with less than 11V. The battery will supply a constant 12V and has a capacity of 0.8Ahr.

System Model:

Above is a photograph of the experimental model which we designed to mimic the demands of the system required by the design problem. It consists of a power supply which is connected in series with a variable resistor box and a mounted resister which simulated our load. We used a multimeter in the circuit to measure the systems amps and another multimeter connected across the load to measure the voltage there.

The variable resistor box allowed us to determine the highest possible resistance which would allow the necessary voltage at the load. By using this highest possible resistance we were able to determine the greatest possible length of cable given the known resistance of AWG #30 cabling.

Results:

We determined that the maximum resistance possible is 142.3 ohms. This allows a maximum cable distance of 412.3 meters connecting the battery source and the load.

It would take the battery about 83.68 hrs to discharge and the system operates at around 92% efficiency.