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###### 日期：2021-12-03 09:28

ECE 20001 Fall 2021 – Group Project

(Due on Gradescope by Dec 6th Monday by 5pm ET)

(Only 1 submission per Group; you must select all group members on Gradescope during submission)

A) Maximum Power Transfer Theorem (Graphical) [30 points]

The amount of power received by a load is an important parameter in electrical and electronic

applications. In DC circuits, we can represent the load with a resistor having resistance of RL ohms.

Similarly, in AC circuits, we can represent it with a complex load having an impedance of ZL ohms.

Maximum power transfer theorem states that the DC voltage source will deliver maximum power to

the variable load resistor only when the load resistance is equal to the equivalent Thevenin resistance.

Similarly, Maximum power transfer theorem states that the AC voltage source will deliver maximum

power to the variable complex load only when the load impedance is equal to the complex conjugate of

equivalent Thevenin impedance.

1) [4 points] Find the equation governing the Power (PLoad) delivered to the load (ZLoad) in terms of

Vth, and ZLoad, Zth in Figure 1.

(Hint: This is not the max power transfer equation)

Figure 1

Figure 2

2) [15 points] Using the circuit in Figure 2, evaluate the following for radial frequency ω = 1 rad/s

a) [6 points] Find the Thevenin equivalent (Vth and Zth) of the circuit in Figure 2.

b) [6 points] Assuming: ? = 1∠? = ∠

Using the equation derived in Part 1, plot the Power (PLoad) vs phase angle () of ZLoad. Vary

(?180° < < 180°) 45°.

c) [3 points] From the graph, evaluate the phase angle for which PLoad is maximum. Give

comments on the value observed.

3) [11 points] Using the same circuit in Figure 2, for radial frequency ω = 2 rad/s,

a) [8 points] Find the Thevenin equivalent (Vth and Zth) of the circuit in Figure 2 and calculate

the maximum power delivered to the load (PLoad).

b) [3 points] Give reasons why the power delivered by the load for the two different

frequencies are different.

B) Diode Current [15 points]

The diode equation gives an expression for the current through a diode as a function of voltage.

The Ideal Diode Law, expressed as:

= 0 (exp (1)

where:

= The net current flowing through the diode;

0 = Reverse saturation current

= Applied voltage across the terminals of the diode;

q = Absolute value of electron charge = 1.6 × 10?19 = 1; Figure 3

k = Boltzmann's constant = 8.617 × 10?5 /

T = Absolute temperature (K).

The "reverse saturation current" (0) is an extremely important parameter which differentiates one

diode from another. 0 is a measure of the recombination in a device. A diode with a larger

recombination will have a larger 0 .

Figure 4

1) [4 points] From the plot shown in Figure 4, find the value of 0(Reverse saturation current in

mA) and T (temperature in K).

2) [6 points] Plot the load line on the graph as derived from KVL of the diode circuit in Figure 3,

find the approximate operating point (Q) of the diode from the plot.

[Given: VA = 1 V; RD = 125 M?]

C) Rectifier Design using Diodes [30 points]

Rectifiers are circuits which transform AC signals to have some DC component. Recall, that if you have a

voltage signal of the form () = cos ( + ), if we take an average over the time-period: =

2

,

then the average is zero. This average value is the same as the DC component of the signal. Now if we

want to transform () into a signal that has a non-zero average value (or non-zero DC component), we

need to design circuits which are known as rectifiers. And for the rectifier design, diodes are useful and

widely employed. In this problem, we will explore the design of two kinds of rectifiers using diodes.

1) Half Wave Rectifier [15 points]

Consider the circuit below, which is known as the half-wave rectifier.

Let () = (). Assuming the ideal model for a diode,

a) Find out the expression for ().

b) Sketch () and () with respect to time t.

c) Find the average value of () (which is also the DC component of ()).

d) [Bonus (5 points)]: Repeat parts (a) and (b) assuming a constant voltage model for the diode

with diode drop 0.7V in the forward bias.

2) Full Wave Rectifier [15 points]

Now, consider the circuit below, which is known as the full-wave bridge rectifier.

Let () = (). Assuming the ideal model for a diode,

a) Find out the expression for ().

b) Sketch () and () with respect to time t.

c) Find the average value of () (which is also the DC component of ()).

D) Real-world circuit application [30 points]

In the class, we have introduced two basic circuit components: electrical (e.g., resistors, capacitors,

inductors, ideal transformers) and electronic (e.g., diodes and transistors). In this part, we will explore

real-world circuits that make use of electrical and/or electronic components to achieve a useful

functionality. You are asked to research and describe via a short 5 min video a real-world circuit that uses

electrical and/or electronic components to achieve its functionality (the circuit you pick must use more

than one component to achieve its primary functionality; for e.g., an electric bulb using ‘resistor’ as the

core element to achieve its functionality would not qualify). As concrete tasks, structure your video

describing the circuit by answering following questions about it. Your video must include all your team

members. The video can also be a recorded zoom meeting amongst all the team members.

a) Describe the functionality you are focusing on.

b) Provide a simple circuit diagram for the functionality you are focusing on.

c) Describe the essential role played by the components you picked in the circuit to achieve the

functionality (highlight any connections you can make to the concepts learnt in the class for this

part)

E) Group Contribution

Please write down the names of everyone in your group and let us know who did what contribution to

this group project?

[Contributions could be research, managing meet times, working part of the problems, learning and

then contributing, editing, and recording video, etc. If there is very little to no contribution we may

deduct 30%-80% of the overall group project score for that particular individual with little to no

contribution. This is there to prevent inactive group members not helping the project.]