03/22/2016

Day 03/22/2016: Max Power Delivered using Thevenin Approach

I. Introduction:

Today we were back to the Thevenin concept we learned from last lesson. Power maximizing using Thevenin circuit is what we learned today.

Using the Thevenin equivalent circuit, we find the dissipated power of the resistor, the formula is shown above. Power is directly related to cR_L but indirecly related to c/R_L^2. Combine the two graphs, we should come up with a nice bell-shaped curved. The power would be maximized at x=Rth

Here is how we proved the power would be maximized if Rth=R_l. First we got the Power eqution  int term of R_L. We replaed the R_L with x for easier referecen. Then we took the first derivate of power with respect to x and let it equal to 0 to find the x that maximized the power, which is x= Rthevenein

 II. More Example:
We concluded that max power is transfered to the load resistance if it equals Rth. Professor Mason assigned us a couple more examples to do

In this photo,we  obtain the Thevenin equivalent at terminals a-b and Find R_L for maximum power. We used the source transformation partially to find the power dissipated when R_l=24, 8 ohms respectively

 III. Real Life Problem
Professor Mason gave us a real problem of a robot design, we were asked to find the maximum power delived to the circuit.

We attemped to solve the problem by first find the Rth which in this case equivalent to Req due to the fact that there is no dependent source. And we applied maximized power theorem by letting Rload=Rth

One more example to find the Rth. In this case we redraw the circuit to find Rth first, and open circuit the RL to find the Vth. Then we applied maximized power delivered theorem

 IV. Lab: Proving the maximized power transfer theorem with numerical values:

Here is how we set up the circuit. We varied the pot (variable resistors) to obtain our desired value of resistance

Here is our data table. Notice that as we the Rl approaching the Rth, the power transfer is increasing, after that the power decreased . we change the value of RL and make a table about Vout and the power and we find that max power is 1.33*10^-3 when RL=5K ohms, which is same as Rs=4.7k ohms.

Here is the graph of Power vs. R. Power is maximized at Rl=5kohms

Here we had to calculate the source voltage V_s and internal resistance R_s (unideal source of voltage) . Then we determine the voltage when an 8-Ohm load is connected to the source.

V. Summary:
Today we further our learning of thevanin to find the max power transfer to the circuit. The max power transfer theorem stated that, and we already proved, that power is max delivered when RL=Rth. We also did the lab to use the numerical value to prove that max power transfer theorem is true, which was shown in the graph.