Gain question (Op-amp/capacitors)

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In summary, the equations for an ideal OP-AMP with differential input of zero are i = (v+ - v-)/R1 and i = (Vo - v-)/R2, where R1 and R2 are the resistors in the circuit. By equating these two equations, the i term cancels out and we are left with Vo = (v+ - v-)R2/R1. This shows the relationship between the output voltage (Vo) and the input voltage (v+).
  • #1
CoolDude420
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Homework Statement


3df2cc6f92.png


Homework Equations

The Attempt at a Solution


507c6fd57e.png

[/B]
My approach was to put them into phasor form and do a KVL loop. However I don't see how I'm going to get Vo/Vs in here?

Vs = i(Z1) + i(Z2 parallel Z3) + Vo
 
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  • #2
CoolDude420 said:

Homework Statement


View attachment 211602

Homework Equations

The Attempt at a Solution


View attachment 211603
[/B]
My approach was to put them into phasor form and do a KVL loop. However I don't see how I'm going to get Vo/Vs in here?
Could you type your work into the forum window please? Your images are a bit too fuzzy for me to follow. Also, there is a LaTeX tutorial under INFO at the top of the page under Help/How-To.

It sounds like you are trying to user the correct approach, and I'll download your images to see if I can clean thenm up enought for me to be of some help on your questions...
 
  • #3
berkeman said:
Could you type your work into the forum window please? Your images are a bit too fuzzy for me to follow. Also, there is a LaTeX tutorial under INFO at the top of the page under Help/How-To.

It sounds like you are trying to user the correct approach, and I'll download your images to see if I can clean thenm up enought for me to be of some help on your questions...

My apologies. The final equation I got was this. Where Z1 = resistor impedance, Z2 = other resistor, Z3 = capacitor impedance
Vs = i(Z1) + i(Z2 parallel Z3) + Vo
 
  • #4
An additional equality for an ideal OP-AMP, differential input is zero, i.e., v+ = v

Write a pair of equations having i on their left-hand side, then equate them so the i term disappears, leaving you with an equation relating output voltage to Vs.
 

1. What is an op-amp?

An op-amp, short for operational amplifier, is a type of electronic circuit component that amplifies the difference between two input signals. It is commonly used in analog circuits for amplification, filtering, and signal conditioning.

2. How do op-amps work?

Op-amps typically have two inputs, a non-inverting input and an inverting input, and a single output. The output is determined by the difference between the two input voltages, which is multiplied by a large gain factor. This allows even small differences between the input voltages to be amplified to a much larger output voltage.

3. What is the gain of an op-amp?

The gain of an op-amp is the ratio of the output voltage to the difference between the two input voltages. It is typically a very large number, ranging from hundreds to thousands. The gain can be adjusted by using external resistors in the op-amp circuit.

4. What is the role of capacitors in an op-amp circuit?

Capacitors are often used in op-amp circuits for filtering and frequency response control. They can also be used to stabilize the op-amp and prevent oscillations. In some circuits, capacitors are used to store and release charge, allowing the op-amp to perform mathematical operations such as integration and differentiation.

5. What are some common applications of op-amps?

Op-amps are used in a wide range of electronic applications, including audio amplifiers, instrumentation amplifiers, active filters, and voltage regulators. They are also commonly used in signal processing, automatic gain control circuits, and in feedback loops for control systems.

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