# negative feedback closed loop equation

#### pietj1212

Joined Sep 10, 2015
10
I cant figure what Vout/Vin is some help would be great. #### shteii01

Joined Feb 19, 2010
4,644
What is the voltage at the junction of R1 and R2?

#### Russmax

Joined Sep 3, 2015
82
Label the node between R4 and R3 as V'out.
Can you write a gain equation for V'out/Vin?
Can you then write an equation for Vout/V'out?

Regards

• pietj1212

#### Vijay Kumar 1

Joined Sep 11, 2015
1
What is the voltage at the junction of R1 and R2?
Vin(According to virtual ground concept)

#### pietj1212

Joined Sep 10, 2015
10
But how is Vout divided by R3 and R4 since r1 and r2 are parallel connected, same thing with Vin

#### Russmax

Joined Sep 3, 2015
82
R2 has the same current as R1,
I1 = I2 = Vin/R1
With this knowledge, you can find V'out.

R3 has I3 = (I2 + I4) flowing in it. If you knew I3, you could calculate the relationship between V'out and Vout.
You already know I2. Do you have enough information to determine I4, now that you know V'out?

Now rearrange terms, substitute, and do algebra to determine Vout/Vin from the equations you've written to determine your answers so far.

Regards

#### RBR1317

Joined Nov 13, 2010
696
If this problem had numerical values for the resistors, then it would be best to numerically simplify the resistor network. However, with only symbolic values it would be best to write the node equations and solve for the voltages. In this case there are two equations and three variables, so use one equation to eliminate the variable Vd, then solve the other for Vo/Vin. Be sure to use node equations since the object is to solve for the voltages. Once you have the node equations, just let the algebra do all the work. Don't bring current flow or mesh equations into this - just focus on the voltages. It is simpler that way.

#### Attachments

• Russmax

#### Russmax

Joined Sep 3, 2015
82
Node equations and current flow are the same animal. Mesh equations can easily be used, but the solving is unintuitive, compared to just using how the current MUST flow determined by the virtual node connection at the op amp input, and the voltage forced at the R2 R3 R4 node.

#### shteii01

Joined Feb 19, 2010
4,644
But how is Vout divided by R3 and R4 since r1 and r2 are parallel connected, same thing with Vin
I found the problem with my approach.
I think approach shown by RBR1317 is correct.

#### WBahn

Joined Mar 31, 2012
26,519
But how is Vout divided by R3 and R4 since r1 and r2 are parallel connected, same thing with Vin
R1 and R2 are NOT parallel connected!

To be in parallel, they must have the SAME voltage across them. They don't.

Let's call the left side of R2 Node A and the right side of R2 Node B.

Q1) What is the voltage at Node A? (You already answered this one).

Q2) What is the current in R1 (be sure to specify direction on all currents)?

Q3) What is the current in R2?

Q4) What is the voltage at Node B?

Q5) What is the current in R3?

Q6) What is the current in R4?

Q7) What is the voltage at Vout?

Another way of approaching it is to analyze the circuit to find the voltage at Node A in terms of Vout and then solve that equation for Vout in terms of the voltage at Node A and then simply set the voltage at Node A equal to Vin.

#### pietj1212

Joined Sep 10, 2015
10
Ive got the formula finally i did it by defining junction r2,r3,r4 as (r1+r2)/(r2) * Vin. r1 and r2 same current Vr1 defined. And then calculating current r3 and r4

• Russmax

#### pietj1212

Joined Sep 10, 2015
10
i meant (r1+r2)/(r1) * Vin because (r2/r1)*Vin + r1/r1*Vin = (r1+r2)/(r1) * Vin

• Russmax

#### Russmax

Joined Sep 3, 2015
82