Electronics I for M.E.
ECE 09-311 2
Load Line Exercises
James K. Beard, Ph.D.
Rowan Hall 238A
beard@rowan.edu
http://rowan.jkbeard.com
April 24, 2007
The Load Line
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Definition: v-i curve of Thévenin equivalent of a
linear circuit
Purpose: To provide a graphical interface with a
nonlinear circuit element such as a diode or
transistor
Usage:
 Draw v-i curve of the nonlinear element,
 Draw load line over it, and
 Intersection of the lines is the operating point.
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Examples follow for BJT, MOSFET, and diode
April 24, 2007
Electronics I for M.E.
Slide 2
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Electronics I for M.E.
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25
Collector Current, mA
20
0.0 uA
10.0 uA
20.0 uA
30.0 uA
40.0 uA
50.0 uA
60.0 uA
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10
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0
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CollectorElectronics
Voltage,
Volts
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Drain Current, mA
40
Bound
2.0 V
3.0 V
4.0 V
5.0 V
6.0 V
7.0 V
8.0 V
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30
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20
15
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Drain Voltage, Volts
April 24, 2007
Electronics I for M.E.
Slide 5
Input-Output Voltage Curve
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Called the voltage transfer characteristic curve
A plot of the output voltage versus the input
voltage
The voltage transfer characteristic from load line:
 Draw
the family of transistor v-i curves
 Draw the collector load line
 Find the proper transistor v-i curve from an input
voltage,
 Read the output voltage from the load line
intersection
 Construct a table of input voltages versus output
voltages and plot the table
April 24, 2007
Electronics I for M.E.
Slide 6
The Voltage Transfer
Characteristic From Load Line
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Draw the family of transistor v-i curves
Draw the collector load line
For each of a set of input voltages
 Find
the proper transistor v-i curve for this voltage,
 Read the output voltage from the load line
intersection with the v-i plot, and
 Add the result to a table.

Plot the table
April 24, 2007
Electronics I for M.E.
Slide 7
iC
Saturation line
Load line
iB  500  A
iB  400  A
iB  300  A
iB  200  A
iB  100  A
iB  0  A
April 24, 2007
Cutoff line
Electronics I for M.E.
vCE
Slide 8
Exercise 1: The Diode v-i Curve
Draw a load line for a 6 V source and a 75
Ohm resistor over the diode v-i curve
 Read the voltage and current at the
intersection
 Check the results by using a constant
voltage drop model for the diode, Vf = 0.7
Volts
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April 24, 2007
Electronics I for M.E.
Slide 9
Exercise 2: The BJT v-i Curves
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Draw a load line for a 15 Volt source and a 750
Ohm collector load resistor
For a base series resistance of 1 kOhms and Vf
equal to 0.7 Volts:
 Find
the base current for input voltages of 1.7 Volts,
2.7 Volts, etc. and
 Find the output voltages from the intersections of the
proper v-i curves with the load line and put them in a
table
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Plot the table
April 24, 2007
Electronics I for M.E.
Slide 10
Exercise 3: The MOSFET v-i
Curves
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Draw a load line for a 20 Volt source and a 400
Ohm drain load resistor
For a threshold voltage VTR of 2 Volts:
 Find
the drain current for input voltages of 2 Volts, 3
Volts, etc. and
 Find the output voltages from the intersections of the
proper v-i curves with the load line and put them in a
table

Plot the table
April 24, 2007
Electronics I for M.E.
Slide 11