LT_network_theor

EE 2274
Network Theorems
Completed Prior to Coming to Lab
PreLab:
Note for the prelab you must show all your work and the prelab is to be handwritten.
1. Using mesh current analysis, find the three mesh currents of the circuit illustrated in Figure 2-1.
Use the mesh currents to find the voltages across the five resistors. Then, using KVL, show that
the sum of the voltages around each of the six loops is zero.
2. Use nodal analysis to find the actual currents flowing in each of the five resistors in the circuit of
Figure 2-1. Then, use KCL to show that the sum of the currents at each of the two nodes B and
C is zero.
3. Create a LTspice solution of Figure2-1 after you run the .OP simulation, left click on the
schematic – View - a node voltage and a branch current by for each element voltage and current
from Figure 2-1 include LTspice schematics with node voltages (place a label on all nodes) and
branch currents, mark the loop currents and their values.
4. Calculate the theoretical Thevenin’s voltage and resistance of the circuit used in Figure 2-2. Any
valid method will be accepted. Find Voc ( open circuit voltage), ZTH ( Thevenin’s impedance), and
ISC (short circuit current)
5. The power absorbed by a load resistance, Rload, is given by equation below. To find the value of
RL that will absorb maximum power, find VL in terms of the Thevenin’s voltage VOC and resistance
ZTH and substitute this information into the PL equation below. This should all be done
symbolically. Next, take the derivative of the power with respect to Rload and set this derivative
equal to zero. Finally, solve for RL. Show all steps of the handwritten symbolic derivation.
𝑃𝐿𝑜𝑎𝑑 = 𝑉𝐿𝑜𝑎𝑑 𝐼𝐿𝑜𝑎𝑑 =
2
𝑉𝐿𝑜𝑎𝑑
𝑅𝐿𝑜𝑎𝑑
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Lab 2 Revised: January 16, 2015
6. Using the expression of PL found in terms of VOC, ZTH, and RLoad from part 5, make a LTspice plot
circuit and plot Pload vs. Rload, with Rload running from ZTH-100Ω to ZTH+100Ω. From your plot,
select five values above the value of RL calculated using parts 4 and 5, and select five values
below this calculated RL value. These will be used in PART 4, Step d. of this lab. Include plot and
schematic from LTspice.
LTspice tips:
1. Use edit to place components Voltage source, Resistors, and commands on the
schematic. Place a label on all nodes that you want to measure. Each components
has a Name and a Value for Rload, select the part value to {Rvar}
2. Instead of Rload having a numerical value for its resistance, place name of variable
parameter, { Rvar.} We use the spice dot directive “.STEP PARAM Rvar StartValue
EndValue StepSize“ and place on schematic to step the value of Rload through a range
of values from the start to end by the step size.
3. Select the Parametric Sweep. Click Global parameter. Set Parameter name to "RVAR".
Start Value Zth - 100, End value Zth + 100 with 5 Ohm increments.
4. Edit the simulation and set to .OP and place on schematic.
5. Run the simulation. On the plot window, select Add Trace and select proper Voltage
across Rload times the current through Rload from the pull down list to plot the power
Pload = I(Rload)*V(vload)
6. Your plot should be parabolic and hit a peak at Zth. If the plot is upside down, simply
multiply expression by -1 as the sign is dependent on how LTspice has assumed the
current direction.
7. Left click on the expression of the trace and select attach cursor, move cursor to what
you want to mark.
8. Open plot setting - notes and annotations – label curser position.
7. Design for before coming to the laboratory
PART V: SYNTHESIS: copied from the lab procedure.
For lab: Create a circuit, similar to Figure 2-6, which has a Thevenin's equivalent VOC = 4V and ZTH =
455Ω. (Hint: Write the equations relating the given values of VOC and ZTH to the unknown values of
R1, R2, R3, and VIN) then you must make some initial assumptions. Show all work.
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Lab 2 Revised: January 16, 2015
PreLab Data Sheet
Network Theorems
PART 1: KIRCHHOFF'S VOLTAGE LAW PreLab (circuit Figure 2.1).
Must include units.
Loop ABGH IABGH = ________________
VAB __________
VBG __________
VGH __________
VHA __________
VCF __________
VFG __________
VDE __________
VEF __________
VCF __________
VFG __________
∑ all = ____________________
Loop GBCF IGBCF = _______________
VGB __________
VBC __________
∑ all = ____________________
Loop FCDE IFCDE = ____________
VFC __________
VCD __________
∑ all = ____________________
Loop ABCFGH
VAB __________
VBC __________
VGH __________
VHA __________
∑ all = _____________________
Loop ABCDEFGH
VAB __________
VBC __________
VCD __________
VDE __________
VEF __________
VFG __________
VGH __________
VHA __________
VCD __________
VDE __________
∑ all = _____________________
Loop GBCDEF
VGB __________
VBC __________
VEF __________
VFG __________
∑ all = ____________________
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Lab 2 Revised: January 16, 2015
PART 2: KIRCHHOFF'S CURRENT LAW PreLab (circuit Figure 2.1)
Node B
IBA __________
IBG __________
IBC __________
∑ all = ____________________
Node C
ICB __________
ICF __________
IDE __________
∑ all = ____________________
PART 3: Nodal and loop analysis with Pspice PreLab ( circuit Figure 2.1)
Include PSPICE schematics with all currents and voltages shown
PART 4: THEVENIN’S VOLTAGE AND RESISTANCE PreLab ( circuit of Figure 2.2)
1. Theoretical values. From LTspice plot
VOC = _______________
ZTH = _______________
ISC = _______________
PART 5: MAXIMUM POWER TRANSFER PreLab
1. Maximum power derivation.
Show all steps of the handwritten symbolic derivation.
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Lab 2 Revised: January 16, 2015
PART 6: MAXIMUM POWER TRANSFER PreLab (Build circuit Figure 2-2)
From part 4 use Voc and Zth equivalent circuit Figure 2.5
Fiill in table for using Zth from LTspice plot. Include LTspice schematics and plots
Decade Box Rload
Ohms Rload RL
Volts Load VL
Current Load IL
Power in Rload PL
Zth -100
Zth -80
Zth -60
Zth -40
Zth -20
Zth
Zth +20
Zth +40
Zth +60
Zth +80
Zth +100
PART 7: SYNTHESIS PreLab
1. Record values used for VIN, R1, R2 and R3 in the sketch below. Show calculations used to
determine these values. Note : there many, solutions show all calculations and assumptions.
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Lab 2 Revised: January 16, 2015
Lab procedure
Lab Techniques:
Measuring voltage and current, calculating power, finding Thevenin’s
equivalent circuit.
Comments:
Check data sheet for results needed. Record your data as the lab progresses.
PART 1: KIRCHHOFF'S VOLTAGE LAW (KVL) (procedure)
Construct the circuit of Figure 2-1. Through measurement, show that the sum of the voltages
around each of the six loops is approximately zero. Use a multimeter set on DCV to measure the
voltage across each resistor. Make sure it is connected in parallel with the resistors in your
circuit. Use the first subscript to denote the positive lead of the multimeter. After you check the
comparison of VCF with VFC, use this information so that you don't have to make all
measurements twice.
PART 2: KIRCHHOFF'S CURRENT LAW (KCL) (procedure)
Using your circuit of Part 1. Measure the currents and show that the sum is zero at each of the
nodes B and C. Use the multimeter set on DC mA to measure the current through each
individual resistor. Make sure the multimeter is connected in series with the resistors in your
circuit.
PART 3: Nodal and loop analysis with LTspice was done in PreLab ( circuit Figure 2.1)
Include LTspice schematics with all currents and voltages shown
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Lab 2 Revised: January 16, 2015
PART 4: THEVENIN’S VOLTAGE AND RESISTANCE (procedure)
a. In your Prelab, you calculated the theoretical Thevenin’s voltage and resistance of the circuit in
Figure 2-2 as seen by any load across terminals x-y. (Hint: The Thevenin’s voltage will be the open
circuit voltage measured across the 470Ω resistor. The Thevenin’s resistance will be the equivalent
resistance of the circuit (as seen from nodes X-Y) with the voltage source removed and replaced by
a short circuit.)
b.
Measure the Thevenin’s voltage and resistance directly from your circuit and compare your
measured values to your calculated ones. To measure the Thevenin’s voltage, measure the open
circuit voltage across the 470Ω resistor. To measure the Thevenin’s resistance, replace the voltage
supply with a short circuit, as shown in Figure 2-3, and measure the resistance of the circuit at points
x-y. How do your measured values compare?
c.
The Thevenin’s resistance can also be found by measuring the open circuit voltage and the short
circuit current (ISC ). (To measure the short circuit current, place a 10Ω resistor from x-y, measure
the 10Ω resistor current with the multimeter set on DC mA.?) The Thevenin’s resistance can be
found using formula.
(2-1)
Where VOC is the open circuit voltage and ISC is the short circuit current. How does this value of
ZTH compare with the theoretical and measured values of ZTH found in Steps 1 and 2?
d. Using the computed value of VOC and ZTH, construct Figure 2-4. Using the +25V supply on the E3631A
adjusted to the VOC value and the decade box adjusted to the ZTH value, measure the voltage, V, and
the current, I, of the 560Ω resistor. Compare results with those obtained in parts 1 and 2. Would you
say the Thevenin approach permits replacement by an equivalent circuit?
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Lab 2 Revised: January 16, 2015
PART 5: was done in prelab derivations of equations.
PART 6: MAXIMUM POWER TRANSFER (procedure)
The power absorbed by a load resistance RL in Figure 2-5 is given by Equation (2-2).
𝑃𝐿𝑜𝑎𝑑 = 𝑉𝐿𝑜𝑎𝑑 𝐼𝐿𝑜𝑎𝑑 =
2
𝑉𝐿𝑜𝑎𝑑
𝑅𝐿𝑜𝑎𝑑
(2-2)
To find the value of Rload that will absorb the maximum power, find VL in terms of the Thevenin’s voltage
VOC and resistance ZTH and substitute this information into Equation (2-2). Next, take the derivative of the
power with respect to RL and set this derivative equal to zero. Finally, solve for R L. Make sure that you
include this derivation in your report. *Note: This is the same derivation that was done in the prelab.
Construct Figure 2-5. Set RL equal to ZTH by measuring the resistance of the decade resistance box and
adjusting the resistance box dials until you get the proper value ( do not adjust the decade resistance
box with the power turned on). Then, measure VL and IL and calculate the power PL absorbed by this
new load resistor with a value of ZTH.
Vary the decade resistance box five values above, and five values below your calculated value of R L and
repeat the power calculation for each Rload setting. Is the power absorbed by your value of Rload from
Step 2 the maximum compared to the power absorbed by these ten resistance values? Include a hand
drawn plot of the power calculations done after varying Rload and submit this plot with your report.
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Lab 2 Revised: January 16, 2015
PART 7: SYNTHESIS (procedure)
Create a circuit, similar to Figure 2-6, which has a Thevenin's equivalent VOC = 4V and ZTH = 455Ω.
Record the values used on the data sheet. (Hint: Write the equations relating the given values of VOC
and ZTH to the unknown values of R1, R2, R3, and VIN). Measure Vin, Voc, Isc, measure ZTH to
measure ZTH remove VIN short circuit that connection to the circuit and measurer the output of the
circuit with an ohmmeter.
1. Demonstrate the circuit to your instructor.
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Lab 2 Revised: January 16, 2015
Student #1_______________ Student # 2 _____________________ Bench # ______ Date ______
Lab Procedure Data Sheet
Network Theorems
PART 1: KIRCHHOFF'S VOLTAGE LAW ( circuit Figure 2.1)
Hints: Place the positive voltmeter lead on first subscript.
From loop to loop, some voltages are negative of previously measured value.
Loop ABGH IABGH = ________________ (Calculate from a voltage across a known resistor I = V/R)
VAB __________
VBG __________
VGH __________
VHA __________
∑ all = ____________________
Loop GBCF IGBCF = _______________(Calculate from a voltage across a known resistor I = V/R)
VGB __________
VBC __________
VCF __________
VFG __________
∑ all = ____________________
Loop FCDE IFCDE = ____________(Calculate from a voltage across a known resistor I = V/R)
VFC __________
VCD __________
VDE __________
VEF __________
∑ all = ____________________
Loop ABCFGH IABCFGH = ____________(Calculate from a voltage across a known resistor I = V/R)
VAB __________
VBC __________
VGH __________
VHA __________
VCF __________
VFG __________
∑ all = _____________________
Loop ABCDEFGH IABCDEFGH = ____________(Calculate from a voltage across a known resistor I = V/R)
VAB __________
VBC __________
VCD __________
VDE __________
VEF __________
VFG __________
VGH __________
VHA __________
∑ all = _____________________
Loop GBCDEF IGBCDEF = ____________(Calculate from a voltage across a known resistor I = V/R)
VGB __________
VBC __________
VEF __________
VFG __________
VCD __________
VDE __________
∑ all = ____________________
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Lab 2 Revised: January 16, 2015
PART 2: KIRCHHOFF'S CURRENT LAW (circuit Figure 2.1) use Ammeter
Remember: Current is a series or through parameter.
Hint: Positive (red) input to ammeter connected to first subscript.
Node B
IBA __________
IBG __________
IBC __________
∑ all = ____________________
Node C
ICB __________
ICF __________
IDE __________
∑ all = ____________________
PART 3 : prelab LTspice already turned in
PART 4: THEVENIN’S VOLTAGE AND RESISTANCE
a.
Theoretical values. (From prelab)
VOC = _______________
ZTH = _______________
ISC = _______________ (Calculated using theoretical values)
b.
Measured values.
VOC = _______________
ZTH = _______________
Compare the theoretical and measured values of VOC and ZTH (include % Error):
c.
Measured value. (Short Circuit) use ammeter
ISC = _______________ Measured with ammeter
ISC = _______________ (Calculated using measured values of part 3.b I = V/R)
How does this value compare with ISC from parts 3.a and 3.c (include % Error)?
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Lab 2 Revised: January 16, 2015
d. Thevenin’s Replacement.
Values measured from the Thevenin’s Equivalent Circuit (Figure 4-4):
560Ω voltage ____________
560Ω current ____________
Values measured from the Original Circuit (Figure 2-1):
560Ω voltage (VDE , Part I) ____________
560Ω current (IDE , Part II) ____________
How does the voltage and current with the Thevenin’s equivalent circuit compare to the original
voltage and current (include % Error)?
PART 5: prelab derivations of equations already turned in.
PART 6: MAXIMUM POWER TRANSFER
a.
Measured values from Figure 2-5 (with RL equal to ZTH).
RL = __________
VL = __________
IL = __________
PL = __________
b. Fiill in table for using Zth from part 4
Decade Box Rload
Ohms Rload RL
Volts Load VL
Current Load IL
Power in Rload PL
Zth -100
Zth -80
Zth -60
Zth -40
Zth -20
Zth
Zth +20
Zth +40
Zth +60
Zth +80
Zth +100
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Lab 2 Revised: January 16, 2015
PART 7: SYNTHESIS
Record values used for VIN, R1, R2 and R3 in the sketch below. Show calculations used to determine
the values.
Measured values.
VOC = __________
Isc = ___________ ZTH = __________
Have instructor sign: _____________________________
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Lab 2 Revised: January 16, 2015

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