Summing Amplifier & Difference Amplifier

Last week we learned how operational amplifier can be used to perform multiplication. We are able to use it for addition and subtraction also. By connecting multiple voltage inputs in parallel to the same input, we can obtain the sum of two input voltages with a gain factor on the output voltage. By connecting voltage inputs to different input, we can obtain the difference of two input voltages with a gain factor on the output voltage.

Summing Amplifier
Here is a schematic of the circuit

The completed circuit in shown in the following picture 

 After we finished the circuit, we measured the output voltage when both input voltages are 5V

The output turns out to be the negative sum of the two input voltages. It's the sum of two voltages without any gain because R3 is the same as R1 and R2. The output is negative because the two voltages are connected to inverted input.

Then we keep Vb as constant and try different values for Va. The percent error of each value is relatively small except for the ones at saturation or undefined.

Va (V)	Vb (V)	Experimental Vout (V)	Theoretical Vout (V)	Percent Error
-4	1	2.99	3	0.33%
-2		0.99	1	1.00%
-1		0	0	N/A
0		-0.96	-1	4.00%
1		-1.96	-2	2.00%
2		-2.96	-3	1.33%
3		-3.48	-4	Saturated
5		-3.47	-6	Saturated

Difference Amplifier

We determine that Vout = 2(Vb-Va) since the Vb is connected to non-inverting input and Va is connected to inverting input. The gain factor is 2 because R2 and R4 have 2 times the resistances of R1 and R3

Here is the schematic of the lab. We chose R1 = R3 = 10kΩ, R2 = R4 = 20kΩ.

Here is the setup of the completed circuit

We set Vb to 5V and Va to -5V. The output voltage turns out to be 19.86V, which matches our assumption.

We set Vb = 1V and test Va with different voltages.

V1 (V)	V2 (V)	Vin=V2-V1 (V)	Experimental Vout (V)	Theoretical Vout (V)	Percent Error
-4	1	5	4.29	10	Saturated
-2		3	4.29	6	Saturated
-1		2	3.96	4	1.00%
0		1	1.98	2	1.00%
1		0	0.00	0	N/A
3		-2	-3.50	-4	Saturated
5		-4	-3.49	-8	Saturated

Then we set Vb = -1V and test Va with different voltages.

V1 (V)	V2 (V)	Vin=V2-V1 (V)	Experimental Vout (V)	Theoretical Vout (V)	Percent Error
-4	-1	3	4.29	6	Saturated
-2		1	1.99	2	0.50%
-1		0	0.00	0	N/A
0		-1	-1.97	-2	1.50%
1		-2	-3.52	-4	Saturated
3		-4	-3.5	-8	Saturated
5		-6	-3.5	-12	Saturated

The percent error of each value is relatively small except for the ones at saturation or undefined.

Summary: Summing Amplifiers and Difference Amplifiers are ways to connect operational amplifiers in order to perform addition and subtraction. Both of them are scaled by the ratio of the voltages as regular operational amplifier circuits. For Summing Amplifiers, the voltage inputs are connected to parallel. If they all go to the inverting input, the output voltage would be negative. For Difference Amplifiers, we connect to voltage inputs to both inverting input and non-inverting input. The ones that are connected to the non-inverting inputs will be subtracted by the ones connected to the inverting input when we calculate the output voltage. The output voltage always follows the pattern of addition and subtraction until they reach saturation.

Inverting Voltage Amplifier

We are introduced to a new element, operational amplifier. Operational amplifier is a kind of voltage controlled voltage source. Operational amplifiers are commonly used in circuits to implement mathematical operations. Today's lab shows one of the ways to use the operational amplifier, multiplication by a negative constant.

We went over some problems involving operational amplifier.

Inverting

Non-Inverting

The conclusion is that Rout = -R2/R1 * Rin

We did an experiment on inverting amplifier. Here is the setup:

We measured the resistance of the two resistors

The output voltage turns out to be approximately two times of the input voltage. The voltage is negative because the operational amplifier is connected to inverting voltage.

We applied different input voltages to get different output voltages. Here is a table of all the data we collected:

VIn (V)	Vout (V)
-3	4.21
-2.5	4.21
-2	4.22
-1.5	3.17
-1	2.11
-0.5	1.05
0	0
0.5	-1.04
1	-2.1
1.5	-3.16
2	-3.44
2.5	-3.44
3	-3.43
3.5	-3.43
4	-3.43

It saturates at -2V and 2V. There is a linear relation between the input voltage and output voltage between -2V and 2V.

We calculated the percent error of resistance and gain.

	Experimental	Theoretical	Percent Error
R1 (kΩ)	2.17	2.20	1.36%
R2 (kΩ)	4.64	4.70	1.28%
Gain	-2.11	-2.14	1.37%

Summary: Operational Amplifier works as a voltage controlled voltage source. When it is connected to inverting voltage, the output voltage has the opposite sign. By applying different resistance values, the ratio of input voltage and output voltage is different.