Operational Amplifiers I

The purpose of the lab is to learn how to use an Op Amp to condition a signal from a voltage input into a specific voltage output.

Prelab:
We first start by analyzing our conditioning circuit.
We assume that:
V_cc = 12 V.
V_ee = -12 V.
V_in = 0 V to +1 V.
V_out = 0 V to -10 V.
The sensor outputs at most 1 mA.
The op-amp power supplies supply at most 30 mW each.

Using the information we determine that R_i = 1/1 V/mA = 1 kΩ.
Since the output is -10 V, the gain is 10. Thus R_f = 10*R_x = 10 kΩ.

However, the lab is limited to two power supplies so V_cc is also going to provide V_in using the appropriate voltage divider like the circuit below.

V = 12 V because it is the worst case where R_y is zero while using V_cc.
Using half of the power rating of a 1/4 W resistor, R_x = (V^2)*8 = (12^2)*8 = 1152 Ω.
With the voltage divider rule, R_y = R_x/11 = 104.7 Ω.

When finding the Thevenin Equivalents,
R_th = R_x*R_y/(R_x + R_y) = 96 Ω.
V_th = 1 V.
However, R_th is NOT 20 times under R_i.
Thus, the new R_i = 20*96 = 1.92 kΩ.
The new R_f = 19.2 kΩ.

Procedure:
We first measure the parts and build the circuit according to the two schematics.

Component	Nominal Value	Measured Value	Power or Current Rating
R_i	2000 Ω	1957 Ω	1/8 W
R_f	20000 Ω	19760 Ω	1/8 W
R_x	1152 Ω	1786 Ω	1/4 W
R_y	104.7 Ω	7020 Ω	1/4 W
V_1 = V_cc	12 V	12.12 Ω	2 A
V_2 = V_ee	12 V	12.08 Ω	2 A

Using two DMMs, we vary V_in and take measurements based on different V_in values.

V_in	V_out (Measured)	GAIN (Calculated)	V_Ri (Measured)	I_Ri (Calculated)	V_Rf (Measured)
0.0 V	0.00 V	0.00	0.00 V	0.00 A	0.00 V
0.25 V	-2.55 V	-10.20	0.25 V	0.125 mA	2.57 V
0.50 V	-5.07 V	-10.14	0.50 V	0.250 mA	5.11 V
0.75 V	-7.62 V	-10.16	0.75 V	0.375 mA	7.65 V
1.00 V	-10.16 V	-10.06	1.01 V	0.505 mA	10.18 V

I_v1 = 2.31 mA
I_v2 = -1.645 mA

Analysis:
P_v1 = V*I = 28.00 mW
P_v2 = -19.87 mW

I_v1 + I_v2 = 0.665 mA
I_f = 0.509 mA
Error = 30.6%

Conclusion:
The experiment was a success. The power constraint was under 30 mW. To reduce the power even further and keep the -10 gain, it is better to reduce the resistance R_i and R_f as long as their ratio of R_f/R_i = 10.