Here's the question, you don't need to read it all to help me out. I need to find R4.

You are developing a high-tech defense to help the Gator’s secondary. You have built a servo mechanism that can accurately point a 100kW laser to within ±1° of accuracy. Sitting in row 105 in the south end zone, you can sight and track a target which is a thrown football. With this system you are comfortable in the knowledge that you can “shoot down” any aerial missile, including a throw football virtually undetected. Your laser back machine is shown in Figure 4. The difference amplifier, shown in Figure 4, is used to measure the difference between the current pointing angle of the laser back and the angle to target (i.e., the desired angle). Whenever there is a difference between these two angle, the difference amplifier circuit sends a proportional to the angular difference to a DC motor.

Assume that R1=R3=10kΩ. Design the system so that the input-output gain is G=2 where G =Vc/(V2-V1). Explain how the system works. If V2 ∈[-5,5]V, what are the dynamic restrictions on V1? (Don't really need to answer this)

Q: What must be the value of R2 and R4?

I'm given R1 = R3 = 10kOhms and Gain = 2.
Using this, I find that R2 = 20 kOhms and using the forumula G=Vc/(V2-V1) with V2=[-5,5], I find that when V2 = 5V, V1 = 2.5V.

So knowing all this, which is pretty much the entire circuit, how can I find R4? I think I have to convert the voltage amplifier into its voltage-source equivalent with a voltage of A.(V+-V_) where A. = infinity. It's this step that confuses me. Is it even necessary to do this?

 

It looks to me like it's as simple as solving for an expression that equates that output gain of the amplifier to the resistances of the circuit using node analysis. I think you can solve this in two equations. For this, just assume the op amp is ideal - no need to break it down into an equivalent circuit model.

-MasterSnow