LAB 3a

Equivalent Circuits

Prelab

Read the lab exercise and familiarize yourself with the procedure.
Familiarize yourself with the network theorems using texts, course notes, or internet sources.

***Note: No hand analysis of the circuit is required for this lab.****

Theory

The theorems investigated in the following lab are: Thevenin's Theorem, and Norton's Theorem and Maximum Power Transfer.

Thevenin's Theorem: Any network of voltage sources, current sources, and resistors can be reduced to a voltage source and resistor in series.

The source voltage, in this case the Thevenin voltage, is referred to as Vth.
The equivalent series resistance, in this case the Thevenin resistance, is referred to as Rth.
The current through nodes a and b will be Vth / Rth.

Norton's Theorem: Any network of voltage sources, current sources, and resistors can be reduced to a current source and resistor in parallel.

The source current, in this case the Norton current, is referred to as INo.
The equivalent series resistance, in this case the Norton resistance, is referred to as RNo.
The voltage across nodes a and b will be INo x Rth.

Please see the Tutorial page for help with the procedure, and the Equipment & Components page for help identifying materials.

Problem

AP Engineering manufactures speaker amplifiers for several sound system companies. Rival engineering firm AKM Engineering has just released a competing amplifier system that you are tasked to reverse engineer and duplicate based on the circuit provided. The marketing team has purchased and supplied the rival amplifier for you to work on. They have asked that you do not disassemble the device.

Determine the voltage, current, and equivalent resistance seen by the load resistor. Create the Thevenin equivalent circuit for use in the initial testing phase.

Equipment & Components

In the Circuit below:
- R1= 47Ω
- R2= 1kΩ
- R3= 1kΩ
- R4= 47Ω
- R5= 100Ω
- R6= 100Ω
- R7= 1.2kΩ
- R8= 1kΩ
- R9=1kΩ
- R10=1.2kΩ
- RL = Rth
DC Power Supply
2x Banana to Aligator Clip cable
Multimeter
Potentiometer
220Ω and 332Ω resistors

Circuit 3a.1

Simplified (Thevenin) circuit.

Procedure

Part 1

Simulate circuit 3a.1 using PSpice as follows:
- Calculate the open circuit voltage Voc
  - In PSpice make RL very large ~999G Ω in Circuit 3a.1.
  - Screenshot this Voc Result
- Calculate the short circuit current Isc
  - In PSpice make RL very small ~0.001n Ω in Circuit 3a.1.
  - Screenshot this Isc result.
- Calculate the Thevenin resistance Rth= Voc/Isc
Draw the Thevenin circuit for circuit 3a.1 as seen by the load resistor including calculated values.
Simulate the Thevenin Circuit with RL = Rth
- Screenshot the maximum power result.
- Then simulate again with RL = 332Ω and 220Ω to show that the value chosen does provide the maximum power.
- Record these two values, but you do not have to screenshot them.

Part 2

See simplified circuit below Circuit 3a.1 for more detail.

Using the potentiometer supplied, and the Thevenin voltage determined above (set on your DC supply):

Build the Thevenin equivalent.
- A potentiometer is a variable resistor. The resistance between the centre and either end pin is adjustable using the knob.
- Measure the resistance with your multimeter while turning the knob to set the desired resistance (Rth determined above)
- Be sure to use the same two pins for test and build!
After setting potentiometer, insert as Rth.
The power supply should be set to Vth and the Potentiometer is set to Rth.
Note that there is no connection between nodes a and b in the simplified circuit shown!

Part 3

Measure Voc across node a & b:
- With no load: Just DC supply and Resistance in series measure voltage across nodes a and b.
Measure Isc through node a & b :
- With no load: Just DC supply and resistance measure the current from node a to node b.
Insert the 330 ohm resistor across node a and b and test the voltage and current in the resistor.
Repeat this test with the 220 ohm resistor.

*** We do not have a resistor with the value determined for Rth. We can however see that it must be between 220 and 332 by the central value theorem***

Results

What was the Thevenin Resistance?
Complete the table below the results section and include it in your report.
Show your designs for the amplifiers that mimic the performance of the tested one.
- Simply draw the Thevenin and Norton circuits including the values for each parameter.
Show screenshots from all three PSpice simulations.

Questions

Explain the term "Impedance Matching" and list an instance where it is commonly applied.
Speaker systems are typically rated by a resistance value (referred to as characteristic impedance), what resistance is this amplifier designed for?
What is the power delivered to the speakers in Watts?

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