ENGR 12L
Measuring Thevenin / Op-Amp Circuits
Experimenters:
Part 1: Thevenin Equivalent
Equipment:
Laptop
DMM
Lab Kits
Choose: R1 = 330, R2 = 470, R3 = 560 or closest values to these.
STEPS
1) Measure your resistor values with DMM
R1___________________
R2___________________
R3___________________
2) If Vs = 9V, calculate the Thevenin Equivalent Vth______________ and Rth ______________ from your
measured DMM resistor values.
3) Build the Physical Circuit above on your breadboard. Measure the following:
Voc _________________
Isc __________________
Rth = Voc/Isc _______________
4) Compare to your predictions and debug if you are more than 5% in error.
5) Now connect a 100 Ohm resistor across the terminals A-B and measure VL and IL, the voltage and current at the load
resistor. Do the same with a 1K-ohm load resistor. Construct the table with the measurements you have taken in
steps 3 as well. Also, measure the load resistors out of circuit and put the actual values in the table below.
Table 1, V-I measurements of Physical circuit under varying load conditions
Load Resistor RL (nominal)
0 Ohms (short circuit case)
100 Ohms
1000 Ohms
Infinity (open circuit case)
RL measured
0 Ohms
Vmeasured
0
Infinity
I measured
0
6) Now use Matlab to construct an I-V plot of your data. First type in your voltage and current data from Table 1:
v = [ values separated by commas ];
i = [ values separated by commas ];
plot( i,v, i, v, 'x'); title('physical i-v plot'); xlabel('Current, mA'), ylabel('Voltage, V');
7) Copy and paste your plot above this step. Your plot should show very close to a straight line stretching from (0,Voc)
to (Isc,0) with the varying load values arrayed somewhere in between. This is the linear chart that the Thevenin
equivalent reduces the circuit behavior down to. Once the Thevenin equivalent is known, the voltage and current
for any load resistance will fall on the line you have just measured.
Part 2: Inverting Op-Amp Circuit
(Modified from © Bruce Mayer, PE • Chabot College)
Equipment:
Laptop
LM741CN Operational Amplifier (See Appendix 1)
DMM
Lab Kits
Thornton Power Supply
One each 1/4 Watt Resistors with with Nominal Resistances
Ri = 3.3 kΩ
Rf = 10 kΩ (nominal)
RL= 470 Ω, 1 kΩ, 5.1 kΩ (nominal)
STEPS
1) Select and Measure your Resistors with a DMM
Ri___________________
Rf___________________
RL1___________________ RL2___________________ RL3___________________
2) Build the circuit. The following picture shows one possible layout:
3) Here is a more specific schematic drawing of the circuit layout:
4) Complete the table using your resistor measurements from step 1
Table I – Fixed Actual-Values as Measured with the DMM
Value
+Vs
-Vs
Ri
Rf
RL
Nominal
15.00
-15.00
3 kΩ
10 kΩ
1 kΩ
Measured
5) Complete Table II below by varying Vi (Thornton voltage source) from 1 to 6 volts, then reverse the polarity of Vi and
make one more set of measurements
Vi (nominal)
Vi
V-
V+
Vo
1.0
2.0
3.0
4.0
5.0
6.0
-1.0 (rewire
polarity of
Thornton)
6) With the data above we can calculate the gain of our circuit and compare it to theory. We can also observe signs of
"saturation" when the output reaches the Vcc/-Vcc limit and is unable to keep V+ = V-. Complete the table below
by calculating measured and theoretical gain for the inverting op-amp
Table III – MEASURED & THEORETICAL Voltage Gain
Vi (nom)
1.0
2.0
Gainmeas
Gaintheory
Note:
 Gmeas = Vo/Vi
 Gtheory = -Rf/Ri
 % = 100[Gmeas – Gtheory]/Gtheory
3.0
-1.0
7) Finally, we'd like to see if the op-amp meets our desired behavior of maintaining constant voltage across a variety of
load resistances. Using your load resistors you set aside in step 1, measure the effect of lowering loads on the
amplifier gain. Complete Table IV with your measurements
Table IV – LOADING EFFECT Measured Currents and Potentials
(Set Vi as close to 3V as possible)
RL
Nominal
RL
Actual
Vi
Vo
IL
Gain =
Vo/Vi
5.1 kΩ
1 kΩ
470 Ω
8) How does this relate to Thevenin Equivalents? We could model the amplifier circuit in its current setting (Vi = 3V) at
the output terminals Vo to ground. If the amplifier is very independent of output load resistance we would expect
the amplifier circuit to have a low Thevenin Resistance. However, it's risky to measure a short circuit directly on an
active circuit like an op-amp ( the max current that can be sourced by the amplifier is about 25 milliamps). What we
can do is take our data into matlab and estimate the I-V line by fitting a line to our data from Table IV.
9) Start by entering your data into vectors v and i as you did in part I of this lab.
v = [ values separated by commas ];
i = [ values separated by commas
];
then make a plot of your data as before and enter it here. Note that your data only covers a very narrow range of
voltage and current values and does not come close to the v=0, "short circuit current" range. We'll have to do a
calculation to derive these.
10) Next, we'll create a linear fit to our data with matlab's polyfit command:
p = polyfit(i,v,1)
the result of this command is a vector with two values, representing the equation of the line that defines the
same I-V curve that Thevenin models. The first value will be negative but that will represent the slope of the line,
or - Voc/Isc or – Rth. The units of Rth will be in k-Ohms if your i values are entered in milliAmps.
The second value in the polyfit result will be Voc or the Thevenin voltage. What would the short circuit current
be if the device could source that much? That would be Voc/Rth.
List your Thevenin values here from your matlab analysis:
Vth = _________________
Rth = _________________
Isc = __________________
Part 3 OPTIONAL:
IF you have time you can experiment with a Non-Inverting Op-Amp:
Directions
1. Rewire the circuit you created in Part 2 so the input Vi has been shifted to the (+) non-inverting op-amp pin 3 and
the input resistor Ri now connects the (-) inverting input to ground. Redo the measurements from above.
Value
+Vs
-Vs
Ri
Rf
RL
Nominal
15.00
15.00
3 kΩ
10 kΩ
1 kΩ
Measured
Vi
(nominal)
Vi
V-
1.0
2.0
3.0
4.0
5.0
Vi (nom)
1.0
2.0
3.0
Gainmeas
Gaintheory
V+
Vo