# Write transfer function G(s) of circuit

• Engineering
• Maurizio
In summary, the conversation is about a problem involving writing the transfer function of an electrical circuit with an operational amplifier. The person is having trouble figuring out the problem and asks for suggestions. They also mention wanting to calculate G(s) = U(s) / Y(s) and applying a formula for G(s). The conversation also includes discussing equivalent impedance for Z1 and finding a solution using the Y-Δ transform.
Maurizio

## Homework Statement

The problem ask me to write the transfert function of a electrical circuit witch include an operational amplifier. I've follow some instruction bur I cannot figure out from this problem.
Could you suggest me somethings?

I'd like to calculate G(S) = U(s) / Y(s)

where U(s) is Lasplace transform of u(t) and Y(s) is Lasplace transform of y(t)

The circuit, and solution is in attached file tf.pdf.

I start cualculating the equivalent impedance Z2.

I get: R + 1/SC

How can I write equivalent impedance for Z1.

I'd like to apply the formula:

G(s) = U(s)/Y(s) = -Z2/Z1

Thank you very much!

## The Attempt at a Solution

#### Attachments

• tf.pdf
62.9 KB · Views: 264
Maurizio said:
How can I write equivalent impedance for Z1.

I'd like to apply the formula:

G(s) = U(s)/Y(s) = -Z2/Z1

Keeping in mind that the minus input of the opamp is a virtual ground, you should calculate how much current will flow to ground from the right end of the Z1 network if you apply 1 volt at the input node u. Then take the ratio of the applied voltage (1 volt) and the output current in the rightmost resistor R of the Z1 network, if the right end of that resistor is grounded.

That ratio will be the equivalent impedance of the Z1 network.

Thank you for your answer. I've found that it's possible to solve this kind of problem in simple way applying: Y-Δ transform

The link of a page on wikipedia is the following:
http://en.wikipedia.org/wiki/Y-Δ_transform

I hope that someone could find this post helpful.

Thank you
Bye
Maurizio

## 1. What is a transfer function?

A transfer function is a mathematical representation of how a system responds to an input signal, in the form of a ratio of the output to the input in the frequency domain. It is commonly used in circuit analysis to analyze the behavior of a circuit.

## 2. How is a transfer function written for a circuit?

A transfer function for a circuit is typically written as G(s) = Vout(s)/Vin(s), where Vout(s) is the output voltage in the Laplace domain and Vin(s) is the input voltage in the Laplace domain. This allows for the analysis of the circuit's behavior in the frequency domain.

## 3. What is the importance of transfer functions in circuit analysis?

Transfer functions are important in circuit analysis because they allow for the prediction and analysis of a circuit's behavior without the need for complex calculations. They provide a simplified representation of the circuit and make it easier to understand and manipulate the circuit's response to different inputs.

## 4. How do you find the transfer function of a circuit?

The transfer function of a circuit can be found by applying the Laplace transform to the differential equations that describe the circuit's behavior. This will result in a transfer function in the form of a ratio of polynomials in the s variable, which can then be simplified and analyzed further.

## 5. Can the transfer function of a circuit be modified or altered?

Yes, the transfer function of a circuit can be modified by changing the components or values of the circuit. This can be done by altering the input or output signals, adding or removing components, or adjusting the values of resistors, capacitors, and inductors in the circuit. These changes will result in a different transfer function and will affect the circuit's behavior.

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