How can R1 and R3 be expressed in terms of R2 and R4 in an op-amp circuit?

In summary, In the circuit, compute the values of R1 and R3 in terms of R2 and R4, such that vo is always equal to v1 - 5v2.
  • #1
ichabodgrant
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In the following circuit, compute the values of R1 and R3 in terms of R2 and R4, such that vo is always equal to v1 - 5v2.I have marked 3 nodes, A, B and C. v+ = v- as assumption for the op-amp.
Consider node A.
v- = v+ = v1 × (R2 / (R1+R2))

Consider node B and C.

(v- - v2) / R3 = (vo - v-) / R4

I now stick at here...
I can write R1 in terms of R2, but there exist v- and v1.
And for R3, the same problem exists.

First, is there anything wrong in my above computations?
Second, can I express R1 and R3 in terms of R2 and R4 without using other unknowns?
 

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  • #2
The two given expressions (formulas) are correct. However, I would use another approach.
Do you know the gain formulas for (a) non-inverting and (b) inverting opamp circuits?
Your circuit is a combination of both and the most simple solution uses the above mentioned formulas. This is allowed because of the superposition theorem.
That means: The output voltage is Vo = V1- 5V2 = V1*k*gain1 - V2*gain2.
It shouldn`t be a problem to solve the system (starting with gain2).
 
  • #3
LvW said:
The two given expressions (formulas) are correct. However, I would use another approach.
Do you know the gain formulas for (a) non-inverting and (b) inverting opamp circuits?
Your circuit is a combination of both and the most simple solution uses the above mentioned formulas. This is allowed because of the superposition theorem.
That means: The output voltage is Vo = V1- 5V2 = V1*k*gain1 - V2*gain2.
It shouldn`t be a problem to solve the system (starting with gain2).

That's good stuff and all, but how do you get R1 and R3 in terms of R2 and R4?

This is a tough one!
 
  • #4
"...compute the values of R1 and R3 in terms of R2 and R4,"

I think the task is not well formulated. For all opamp amplifiers it is only the ratio of resistors that matters.
Therefore, we have - in theory - an infinite number of resistor values which all fulfill the required ratios.
The answer can only be R2/R1=C*R4/R3 and we can select - as one possible solution - R1=R3 and R2=C*R4.
 
  • #5
ichabodgrant said:
In the following circuit, compute the values of R1 and R3 in terms of R2 and R4, such that vo is always equal to v1 - 5v2.I have marked 3 nodes, A, B and C. v+ = v- as assumption for the op-amp.
Consider node A.
v- = v+ = v1 × (R2 / (R1+R2))

Consider node B and C.

(v- - v2) / R3 = (vo - v-) / R4

I now stick at here...
I can write R1 in terms of R2, but there exist v- and v1.
And for R3, the same problem exists.

First, is there anything wrong in my above computations?
Second, can I express R1 and R3 in terms of R2 and R4 without using other unknowns?

You have 2 equations. both equations have extra variables (V+ and V-). so plug one equation into the other getting rid of V+ and V-. Then solve for Vo.

The equation will then look like this

Vo=XV1-YV2

you know X=1 and Y=5

so solve for the two equations and you will get the relationship between all the resistors in the form of two equations. take it one step further and solve in the form of

R1=Z and R3=T
 
  • #6
LvW said:
"...compute the values of R1 and R3 in terms of R2 and R4,"

I think the task is not well formulated. For all opamp amplifiers it is only the ratio of resistors that matters.
Therefore, we have - in theory - an infinite number of resistor values which all fulfill the required ratios.
The answer can only be R2/R1=C*R4/R3 and we can select - as one possible solution - R1=R3 and R2=C*R4.
1. In general the goal of the exercise is to find that C value
2. I don't want to just give the answer to the OP, but I do want to point for his/her sake that your solution is incorrect.
 
  • #7
I solve it...
I had never thought of using comparing coefficients... turns out to be not too difficult...Thanks everyone
 
  • #8
Can you tell us your solution?
 
  • #9
R1 = 5R2
R3 = (1/5)R4

there might be some calculation mistakes...
 
  • #10
Yes - is correct. And - as I have expected - no other results than a RATIO only (with infinite alternatives for resistor values9.
 

FAQ: How can R1 and R3 be expressed in terms of R2 and R4 in an op-amp circuit?

What is an op-amp and how does it work?

An op-amp, short for operational amplifier, is an electronic component that amplifies the difference between two input signals. It typically has two inputs, an inverting and non-inverting, and a single output. The output is determined by the difference between the two inputs and the gain of the op-amp. It is designed to have a very high open-loop gain, making it useful for amplification and signal processing.

What are some common applications of op-amps?

Op-amps are used in a wide variety of applications, including audio amplifiers, filters, oscillators, and voltage regulators. They are also commonly used in instrumentation and control systems, such as in sensors and feedback circuits.

How do I analyze an op-amp circuit?

To analyze an op-amp circuit, you will need to use Kirchhoff's laws and the op-amp's ideal characteristics. First, you can assume that no current flows into the op-amp's input terminals. Then, you can use the op-amp's ideal characteristics, such as infinite open-loop gain and zero input current, to simplify the circuit and solve for the output voltage. Finally, you can apply Kirchhoff's laws to the rest of the circuit to determine the input and output currents.

What is negative feedback and how does it affect op-amp circuits?

Negative feedback is a technique used in op-amp circuits to stabilize the output voltage and reduce distortion. It involves feeding a portion of the output voltage back to the inverting input of the op-amp, which helps to cancel out any changes in the input voltage. This results in a more linear and stable output voltage.

How do I choose an appropriate op-amp for my circuit?

When selecting an op-amp for your circuit, there are a few important parameters to consider. These include the input and output voltage ranges, the input and output impedance, the open-loop gain, and the bandwidth. It is also important to consider the power supply requirements and the temperature range of the op-amp. Ultimately, the best op-amp for your circuit will depend on your specific application and design requirements.

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