I work for the Navy, doing testing and repair of Electronic Warfare (RADAR detection and jamming) systems. A fundamental understanding of Radio Frequency (RF) Wave Propagation is required to effectively troubleshoot system operations. Part of this process is conduct Voltage Standing Wave Ratio (VSWR) testing of RF pathways, such as millimeter Waveguides and Heliax.

VSWR is the measure of how efficiently RF power is transmitted in to a load. For example, if a power amplifier is connected to an antenna through a transmission line, such as a Waveguide, ideally there will be no reflections and all the signal from the power amplifier will be transmitted to the antenna. However, in the real world, there will be some mismatches that will cause some of the signal to be reflected back in to the transmission line. VSWR is the measure of how much signal is reflected back in to the system. It is the ratio between transmitted and reflected waves. A high VSWR indicates poor transmission-line efficiency and performance, in most cases requiring component or pathway replacement.

To calculate VSWR, a specialized Signal generator and Spectrum Analyzer are used, as well as an assortment of loads and couplers. Some of the basic formulas for VSWR include:

Where (r) is the Reflection Coefficient, (RL) is the Return Loss, and (ML) is the Mismatch Loss (Microwave101, 2022).

To be honest though, I’ve really never looked at nor understood the formulas required for the calculations. The test equipment I use is designed to generate the needed signals, measure the reflected energy for a given frequency range, and then provide a graph with the resulting calculations. From there, I compare the loss values based on the specifications for the pathway or antenna under test.

References

Microwave101. (2022, November 01). Voltage standing wave ratio (VSWR). Retrieved from microwave101.com: https://www.microwaves101.com/encyclopedias/voltage-standing-wave-ratio-vswr

(69) Understanding VSWR and Return Loss – YouTube

# Category: Calculus homework help

While in the Navy, I work on radar systems. Thus, I will be talking about pulse integration and fluctuation loss in a radar which is in a way a part of what my job/career is thus far. Typically, you need more than a single pulse to meet the required performance for a pulsed radar. Thus, we use pulse integration to improve SNR or (Signal-to-Noise Ratio) to average out any interferences. The following list is used to process multiple high-velocity tracks over several resolution cells during the integration time. Or simply put multiple incoming potentially hostile targets at a very high speed over a large area.

The result of loss is the difference in the Signal-to-Noise required over a set area M-of-N Integration and when Signal-to-noise is required for all CPI (Coherent Processing Interval) within that area.

I never personally use calculation since the computer does most of this on the fly and even gives us updates on when this is occurring. That way, as an operator and technician, I can focus on threats, take a clean picture, and keep the status of my gear up to date with what fixes are required.

References:

Mathworks. 1994-2022. The Mathworks, Ink.

https://www.mathworks.com/help/radar/ug/introduction-to-integration-and-fluctuation-losses-in-radar.html

I choose the COMPTIA approach mainly for its structured steps that really helps break down problems and find solutions faster and also records the issue as a record in case further issues arise and if they are the same or similar it will help with finding the problems occurring. The steps are very straightforward, and they are:

Step 1: Collecting information—Identifying symptoms and issues

Step 2: Develop a Probable Cause Theory

Step 3: Test the Theory to Find Out What’s Causing It

Step 4: Create an Action Plan

Step 5: Put The Solution Into Action

Step 6: Check For Full System Functionality and Put Preventive Measures In Place

Step 7: Create a Record of The Problem

The reason I choose the CompTIA troubleshooting approach is because it’s a very good system when it comes to troubleshooting network issues. For this discussion board I will explain my problem and how I implemented this step-by-step approach to find the solution. The problem I am experiencing is that my home network speeds are very slow in areas other than the room with the actual router in it and I found this by using step one of the CompTIA method because I went room to room and tested my network speed on my laptop and discovered this. After finding this trend throughout my home I moved to step two which is developing a probable cause theory for this issue and my theory was that my house is built with stucco which is very thick concrete material that hinders Wi-Fi signal in other areas of the house besides the living room with the router. For my action plan I decided to test this by running an ethernet cable to a repeater near a room with low network speed and see if the speeds would be higher than before. After doing this test I found that the speeds were maintained throughout the house where the repeater was near. The results of the test helped me develop my action plan of running ethernet cable to multiple repeaters throughout the house to expand the network signal range. After putting this plan into my house, it was evident that my theory was correct regarding the slow network speeds and after implementing the repeaters all of my devices had way better network speeds throughout the whole house. When I got to step six everything functioned as planned and no more symptoms were found throughout the whole house. The next thing I did was made a word document stating my network setup and what devices were using the repeaters and what speeds each device maintained when the repeaters were first installed in case I run into another issue down the road. The biggest reason I choose this method is because finding problems and troubleshooting is most effective and efficient if there is a process/system of doing it that way no time is waisted, and you don’t get discouraged and you stay on track throughout the troubleshooting process.

## Find y’ for

Finding Derivatives:

Find y’ for

(A) y = 3e^x + 5 ln x

(B) y = x^4 – ln x^4

Please help me solve these two questions.

Thank you (:

Find a resource with a tutorial/information that will help you create a specific, original, math problem related to your topic. Remember, you are NOT teaching the whole topic, but just how to solve ONE PROBLEM You’ve created. You must cite your source in APA format. (Even if you know how to create and solve a problem related to your topic, you still must include a source that your classmates can reference to read more about what you are teaching.)

Tell us the problem you’ve created. Remember, your problem must be ORIGINAL: made up by YOU. DO NOT use a problem that has a full solution from a resource.

Tell us how to solve your problem step by step. Your solution should include all mathematical steps as well as explanations in your own words. You can type this with the equation editor right here in the reply box, you can use an image file to show hand-written work, or you can make a video using the media tool to provide your explanations! I encourage you to get creative with how you explain your solution!

Please research at least one source of information on engineering applications of integration. Important: The purpose of this assignment is for you to share your engineering expertise and teach us how integral calculus is applied in your field. Under no circumstances should you copy and paste any content from a web reference. Instead, explain these applications in your own words.

In your original post, answer the following:

Create a summary of what you found (in your own words!) and describe an example application. Keep your post clear and concise, under 500 words.

You can use any source you like, including (but not limited to) the Internet, ECPI Library Resources, and your Electric Circuits textbook. Be sure to include the citation of your source in APA format.

There are many types of derivatives used in real life engineering situations but, the one I am going to talk about is tangents used in daily life. I specifically want to explain an example of a secant tangent line used in daily life for engineers. A secant line is a line that connects to two points on a circle. Astronauts use this to find things like the distance from the moon while it is orbiting to many different locations on earth. The formula used for this real life equation is y-b=[(d-b)/(c-a)](x-a). For example, if you are using this equation and are given the values (5-3)/(-2-1). Your equation of the secant line should look like so y-3=-2/3(x-1) then y=(-2/3)x+2/3+3 with the solution being y=(-2/3)x+11/3.

Reference:

Application of tangents and normal in real life. Unacademy. (2022, April 19). Retrieved October 19, 2022, from https://unacademy.com/content/upsc/study-material/mathematics/application-of-tangents-and-normal-in-real- life/#:~:text=of%20the%20tangent.-,For%20example%2C%20when%20a%20cycle%20travels%20down%20a%20road%2C%20that,and%20turned%20from%20another%20endLinks to an external site..

For my discussion, I choose to talk about how derivatives are used for servo motor controls. First, we need to discuss what a servo motor is and what it does. A servo motor is a current and voltage-controlled electrical motor. This motor works on a closed-loop system through the commands of a servo controller which uses a feedback device to control the velocity and position of the servo. A great example of this would be the cruise control in a car. The servo controller would be the driver setting cruise control to a set speed which sends a voltage signal and varying current to the servo which controls the throttle until you get to a certain speed, then maintains that speed. The feedback device would be your tachometer telling the servo to lower the current being sent if you go over the set speed and to raise the current if you go under the set speed. The servo is using Proportional Integral Derivative or PID which changes the motor’s output based on the set speed and what the tachometer reads. The PID algorithm uses Proportional feedback which tells the servo that it needs to go faster to reach the set speed increasing current sent to the servo. Derivative feedback tells the servo that we are over the set speed, and it doesn’t need to run anymore decreasing current sent to the servo. Integral feedback holds the current at its set amps and holds the position of the servo to keep the set speed without any outside interactions that would call for the need of the other two. Below is an image of how the PID algorithm works.

(Collins, 2022)

When put into an equation it will look something like this:

Apmonitor.com (n.d.)

Thank you for reading.

References:

Collins, D. (2022, October 17). FAQ: What are servo feedback gains, overshoot limits, and position error limits? Motion Control Tips. https://www.motioncontroltips.com/faq-what-are-servo-feedback-gains-overshoot-limits-position-error-limits/Links to an external site.

Proportional Integral Derivative (PID). (n.d.). https://apmonitor.com/pdc/index.php/Main/ProportionalIntegralDerivativeLinks to an external site.

Using a simulation of the manufacturing process Mr. Gürkan found a method to find the optimal location to place buffers to help machines run smoother and longer without breaking down. The simulation ran a maximum of 50 machines and took data on cycle times and downtime to set up the production process. Then using the data collected and forming a directional derivative could be used to infer the approximate location where the process became too loud or uneven. These points were isolated and selected for the optimal location for the buffers. Once added into the simulation the productivity of the process was found to increase as was the time between break down on the production line.

To further test the simulation additional production line simulations were produced. These additional simulations were made with fewer machines used in the process. These simulations were tested utilizing the directional derivative and more traditional stochastic testing methods and the level of error found between the two on the location of buffers was found to be negligible.

References

Gürkan, G. (2000). Simulation optimization of buffer allocations in production lines with unreliable machines. Annals of Operations Research, 93(1–4), 117–216. https://libproxy.ecpi.edu:2111/10.1023/a:1018900729338

Let’s go beyond the mechanics. Differential calculus is a tool, invented to solve the most challenging problems in science and engineering. For instance, Newton used differential calculus to express the equations of planetary motion around the Sun, as well as the rate at which a warm object cools off in a colder environment. This week, you’ll become familiar with more of those applications by presenting them to your classmates.

Please research at least one source of information on engineering applications of derivatives.

Create a summary of what you found (in your own words!) and describe an example application. Keep your post clear and concise, under 500 words.

You can use any source you like. Be sure to include the citation of your source in APA format.