Lab 7 Operational Amplifier I

The purpose of the lab is to learn using an Operational Amplifier (Op Amp) to amplifier a input voltage to a specific voltage output.

Prelab:
Some criterias and the limitations in our Op Amp circuit:
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 ≤  1 mA.
The power supplied to the the Op Amp is restrainted to at most 30mW for each rail (each rail has it own power supply).

Using the information above,  we will determine the values of the components that will be using in this circuit.

 R_i = 1.0 V/1.0 mA = 1 kΩ.
Since the ratio of our V_out to V_in output is -10 V, the close loop gain is 10.
Thus R_f = 10*R_x = 10 kΩ.

At the same time, we will need to construct a voltage divider for our V_in. Each lab group recieves only two power supply, so we have decided to use the power supply of V_cc to provide also the V_in.

Since our V_cc = 12 V
Assuming we use only half of the power rating of a 1/4 W resistor,
    R_x = (V^2)*8 = (12^2)*8 = 1152 Ω.
According to the voltage divider rule, R_y must be 11 times smaller than R_x,
    R_y = R_x/11 = 104.7 Ω.

To find the Thevenin Equivalents,
R_th = R_x*R_y/(R_x + R_y) = 96 Ω.
with V_th = 1 V.
 
Though, R_th is NOT 20 times under R_i.
So, we calculate for a new R_i that will be 20 times bigger than R_th
The new R_i is ~~> R_i = 20*96 = 1.92 kΩ.
The new R_f is ~~> R_f = 19.2 kΩ.

Procedure:
We first collect and 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

Instead of using the R_x and R_y as calculated, will will be using a potentialmeter that will allow us to get exactly 1V from the voltage divider for the Op Amp was instructed.

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 result successfully reflect the function of an inverted Op Amp. The power supplied to the Op Amp was controlled below 30 mW. In an attempt to reduce the power even further while keep the -10 gain, reducing the resistance of R_i and R_f  is recommanded as long as their ratio of R_f/R_i remains the same as the close loop gain = 10.