Summing and Difference Amplifier Lab

Objective:
The goal for today's class meeting is to understand buffet, non inverting, summing, and difference amplifiers. The lab will be based on summing and difference operation amplifiers. The equations for some of the operational amplifiers based on type are:
Inverse: -Rf/Ri * Vinput
Summation: Voutput = -Rf(V1/R1 + V2/R2)
Non-inverting: Voutput = (1+Rf/Ri)* Vinput
Difference: Voutput = R2/R1(V2-V1)

Group Practice:
1. The first in class problem that we worked on was based on plotting a block digram that represents the voltage input as seen in Figure 1. We are given two resistors with resistance of 2.5K and 7.5K. We are then told to plot the output voltage which can also be seen in figure 1. We note that the the lower limit is 0 volts so the bottom portion of the output block diagram is erased.

Figure 1. Plotting the input and output voltage. 

2. We are then told that the voltage input is between 0 to 200mv. Using the equation of an inverting operational amplifier where Vout = -(R2/R1)*Vin, we acquire a new voltage output. The plot can be seen in Figure 2. We note that the voltage output can not be below 0. Therefore it voltage output is 0.

Figure 2. Plotting the voltage output when voltage input is from 0 to 200mv.

3. We are given a circuit which can be seen in Figure 3. We are told to solve for voltage output. In order to this, we assume the circuit to be an ideal operational amplifier. Therefore, no currents flow flowing into the inverting or non inverting terminals. We see that voltage difference between is zero, meaning they are equal V1=V2. We then use nodal analysis at two points which can be seen in the figure below and acquire a Vo = -18/11.

Figure 3. Nodal analysis calculations for voltage output in an inverting operation amplifier.

Summing Amplifier Lab Procedures and Results:
1. The pre lab involves designing a summing circuit with two voltage inputs which can be seen in Figure 4. We note that the circuit is an inverting operational amplifier. As we do the calculations using nodal analysis, we acquire an equation Vout = -(R3/R1)(Va+Vb)

Figure 4. Schematic build for op amp

2. The circuit require us to find R3 as seen in figure 5. The way in which we find the resistance of the resistor is to note that Vout = -(R3/R1)(Va+Vb). In order to get R3, we will note that Vo = Va +VB. In order for this to true, then R3 and R1 must be equal. However, we must consider that we may not have this resistor, so we acquire the resistors that are available in class that are at least 1K . We use resistors of R1 = 2.15K+/-.01, R2 =2.17K+/-.01, R3 = 2.17K+/-.01.

Figure 5. Finding a resistance value for R3

3. We are told that input Va will change from -6,-5,-4,-2,-1,0,1,2,3,5V and the Vb will stay at 1V. We measure the first voltage output  of -2.98V+/-.01 when Va = -4, Vb = 1. The actual circuit can be seen in figure 6.

Figure 6. Output voltage measurement

4. We measure the rest of the voltage outputs as we change the the Va. The experimental and theoretical measurements can be seen in Figure 7. Percentage difference between theoretical and experimental is low between the voltage output ranging from 4<Vout<-2.97 based on what was inputed by Va and Vb. There is saturation at above a voltage output above 4 and -3.37V.

Figure 7. Table that includes experimental and theoretical as well as the percent difference.

Difference Lab Procedures and Results:
1. This lab includes the idea of difference operational amplifiers which is a device that amplifies the difference between two inputs but rejects any signals common to the the two inputs. The first step is to derive an equation which we can apply to the difference operational amplifier as seen in Figure 8 based on the schematic as seen in figure 7.

Figure 7. Schematic for a difference operational amplifier.

Figure 8. Calculating the voltage output based on the resistors in the circuit and the voltage inputs delivered to the positive and negative terminal of the operational amplifiers.

2. We draw out the schematic and plan on building our circuit. We acquire Resistors that will be used in the circuit. The resistance of the resistors are R1=9.99K+/-.01, R2=9.87K+/-.01, R3=19.98K+/-.01, R4=19.82K+/-.01.

Figure 9.

3. We measure the voltage output when the Va ranges from -4V to 5V and Vb stays at 1V. The measurements can be seen in figure 10. The difference is low between the theoretical and experimental voltage output.

Figure 10. Measurements for voltage output when Vb is 1 and Va ranges from -4 to 5V

Figure 11. Vout Vs Vin plot when Vb = 1V

4. We then measure the voltage output when the Va ranges from -4v to 5v and the Vb stays at -1V. The measurements can be seen in figure 12. The difference is low between the theoretical and experimental voltage output.

Figure 12. Measurements for voltage output when the Vb is -1 and Va ranges from -4 to 5V.

Figure 13. Vout vs Vin plot when Vb=-1V

Summary of Labs and Learning Outcome:

In the Summing Amplifier Lab, we notice that the operational amplifier is an inverting amplifier since the input voltage is connected to the negative terminal of the amplifier. We can assume that there will be a relationship in the equations when there are multiple voltage inputs connected to the negative terminal of the amplifier. We can use nodal analysis  for the summing amplifier in the first part of lab in order to find the voltage output which we found it to be Vo= -((Rf/R1)V1+(Rf/R2)V2). This is similar to inverting amplifier lab where Vo=-(Rf/R1) *Vin. We built the circuit and measured the resistance of the resistors that we plan to use. The resistors must be the same so that Vout = -(Va+Vb). The resistors in use are R1 = 2.15K+/-.01, R2 =2.17K+/-.01, R3 = 2.17K+/-.01. We measure the voltage output which can be seen in figure 7 and we notice saturation when the voltage output is above 4 and -4 volts. Anything above that, we see a high percent error between the theoretical and experimental voltage out of 20% when Va=-6 and Vb = 1. Anything below the output voltage of -4, the percent error become high as well. 

The difference amplifier works differently in which the device amplifies the difference between two inputs and rejects any signals common to the two inputs. For the lab we, we are require to find the Voltage output equation by using nodal analysis. Thus, we acquire the equation Vo=V2-V1. We measure the resistance of the resistors of R1=9.99K+/-.01, R2=9.87K+/-.01, R3=19.98K+/-.01, R4=19.82K+/-.01. We then measure the output voltage when Va varies from -4 to 5V and Vb stays the same. We can see based on the graphs and measurements in figures 10 and 11 that there is saturation around 4v and below -3.5V. We see that the theoretical and experimental out voltages have small percentage error below 1% between the saturation points. In other words our theoretical equation satisfies with our experimental measurements as long as the voltage output is within the linear region of Vout vs Vinplot. When the Vb is switched to -1V and Va varies from -4v to 5v. The plot is then reversed but the saturation is the same.