# Simple Op-Amp Inverting Amplifier

• xWaffle
In summary, the conversation revolved around finding the gain in an inverting amplifier circuit. The speaker had constructed a simulation and was able to determine the gain, but needed to find an analytical expression for it. They were struggling to find the total resistance in a specific part of the circuit, which included three resistors in a strange configuration. The speaker attempted to use the equation V=IR, but the third resistor connected to ground was causing confusion. They asked for help in solving this problem.
xWaffle

## Homework Statement

I need to find an expression for the gain in this circuit. I know it is an interting amplifier, because with the models we were given to look at, this one fits the inverting amlpifier. I've also constructed a simulation in a simple Java applet that I have.

My problem is, I need to do this analytically. It is very late right now and I know I'm just having a brain fart. This is what the simplest inverting amplifier looks like:

It's fairly obvious that, given a little thinking, the gain on this circuit:

$\frac{V_{in}}{R_{in}} = \frac{-V_{out}}{R_{f}} \rightarrow V_{out} = \frac{R_{f}}{R_{in}} V_{in}$

The problem is, with my circuit, Rf isn't just one resistor. It's 3, in a very strange configuration, and I cannot for the life of me figure out how to find the total resistance in that part of the circuit. This is my circuit:

I tried looking at it as sort of a voltage divider, but that third resistor connected to ground is really screwing with my head! Help!

## Homework Equations

V = IR is basically all I think you'd need.

## The Attempt at a Solution

See above description.

R_3 is connected to the ground and R_2 is connected to a point that's at ground potential because of the negative feedback. These are parallel for the purpose of calculating the potential at the point where R2, R3 and R4 meet.

## 1. What is a Simple Op-Amp Inverting Amplifier?

A Simple Op-Amp Inverting Amplifier is a basic electronic circuit that uses an operational amplifier (op-amp) to amplify an input signal. It is called an inverting amplifier because the output signal is the inverse of the input signal.

## 2. How does a Simple Op-Amp Inverting Amplifier work?

The op-amp takes the input signal and amplifies it by a factor determined by the ratio of two resistors in the circuit. The output signal is then inverted and amplified again by a feedback resistor, resulting in an amplified output signal that is the inverse of the input signal.

## 3. What are the advantages of using a Simple Op-Amp Inverting Amplifier?

Some advantages of using a Simple Op-Amp Inverting Amplifier include high gain, low distortion, and high input impedance. It also has a wide range of applications in various electronic circuits such as audio amplifiers, filters, and oscillators.

## 4. What are the limitations of a Simple Op-Amp Inverting Amplifier?

One limitation of a Simple Op-Amp Inverting Amplifier is that it can only amplify signals within a certain range determined by the power supply voltage. It also has a limited bandwidth, meaning it cannot amplify signals with high frequencies. Additionally, op-amps have a small internal resistance which can cause errors in the output signal.

## 5. How can I calculate the gain of a Simple Op-Amp Inverting Amplifier?

The gain of a Simple Op-Amp Inverting Amplifier can be calculated by dividing the feedback resistor by the input resistor. The equation is Gain = - (Rf / Ri) where Rf is the feedback resistor and Ri is the input resistor. The negative sign indicates the inversion of the output signal.

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