# Transfer function of RC circuit

• Engineering
• Jofo
In summary: So my task is to calculate all integrals and derivations myself.Thank You for response,In summary, you are trying to find the transfer function of a circuit using Kirchoffs laws, but you are not able to solve the equations. You have drawn the nodes and the current flow, but are missing the impedances. You also mention that you might be able to find a circuit that is too complicated for you, which means you will need to calculate the integrals and derivations yourself.
Jofo
Hello all,

I need transfer function of this circuit (it is Bandaxall tone stack). Here is the sheme:

Any help would be greatly appreciated.

Jofo said:
Hello all,

I need transfer function of this circuit (it is Bandaxall tone stack). Here is the sheme:

Any help would be greatly appreciated.

What is the context of your question? If it's for schoolwork, I can move the thread to the Homework Help section of the PF. In any case, you will need to show some effort on your question. How would you go about writing some equations to help you get to the transfer function? Would you use KVL or KCL?

Oh, and the transfer function will also depend on the Zout of the previous stage, and the Zin of the next stage. Do you have those?

Thank You for response,

I'm sorry, I probably put it in a bad section :(

I tried to solve it with my basic knowledge of Kirchoff's laws, but I'm not mathematician, I'm an IT student... my task on this project is to simulate this circuit using a C++ library, but to obtain a block scheme I need differential equatins from transfer function.

When I tried to solve it, I ran into 7 equations, of which 4 were current-related (6 unknown currents), and after discussion with my friend I came to conclusion, that I did either something wrong, or the set of those equations cannot be solved (from my point of view - 6 variables, 4 equations), that means I cannot figure out the currents.

The input and output impedances... well I don't have those. (consider it as an ideal circuit?)

Jofo said:
Thank You for response,

I'm sorry, I probably put it in a bad section :(

I tried to solve it with my basic knowledge of Kirchoff's laws, but I'm not mathematician, I'm an IT student... my task on this project is to simulate this circuit using a C++ library, but to obtain a block scheme I need differential equatins from transfer function.

When I tried to solve it, I ran into 7 equations, of which 4 were current-related (6 unknown currents), and after discussion with my friend I came to conclusion, that I did either something wrong, or the set of those equations cannot be solved (from my point of view - 6 variables, 4 equations), that means I cannot figure out the currents.

The input and output impedances... well I don't have those. (consider it as an ideal circuit?)

No worries, I moved the thread. I only see 5 nodes for writing the KCL equations. Could you please show us the equations you have so far?

And you are being required to solve for the transfer function of this circuit for an IT class?

First I substituded RA||C2 and RB||C3 for impedaces ZA=RA/(1+s*RA*C2) and ZB=RB/(1+s*RB*C3):

Here I drew the nodes and the currents. And my equations:

KCL:
I1=I2+I3
I5=I2+I4
I3=I4+I6
I1=I5+I6

KVL:
VIN=R1*I2+ZA*I2+ZB*I5+R3*I5
0=-R1*I2-ZA*I2+(1/(s*C1))*I3+RX*I3+R2*I4
0=-R3*I5-ZB*I5-R2*I4+R4*I6+(1/(s*C4))*I6

And this is my dead end :(

I had to choose a circuit for simulation, but maybe this one is too complicated for me... I simply need a "not basic analog filter".

Last edited:
After deeper studying of that C++ toolkit, I actually don't need transfer function, but only Kirchoffs equations (not in s-domain, but with all integrals and derivations).

## 1. What is a transfer function in an RC circuit?

A transfer function in an RC circuit is a mathematical representation of the relationship between the input and output signals. It describes how the input signal is affected by the circuit components and how the output signal is related to the input signal.

## 2. How is the transfer function of an RC circuit derived?

The transfer function of an RC circuit can be derived using the principles of circuit analysis and Laplace transforms. The circuit is analyzed using Kirchhoff's laws and the Laplace transform is applied to the resulting equations to obtain the transfer function.

## 3. What does the transfer function tell us about an RC circuit?

The transfer function provides valuable information about the behavior of an RC circuit. It can tell us about the frequency response, gain, phase shift, and stability of the circuit. It is also useful for designing and analyzing the circuit's performance.

## 4. How is the transfer function of an RC circuit represented?

The transfer function of an RC circuit is typically represented in the form of a rational function, with the output signal in the numerator and the input signal in the denominator. It can also be represented graphically as a Bode plot, showing the magnitude and phase response of the circuit at different frequencies.

## 5. What are the applications of the transfer function in an RC circuit?

The transfer function of an RC circuit has many practical applications. It is commonly used in electronic filters, amplifiers, and signal processing systems. It is also useful for analyzing and designing control systems, such as in robotics and industrial automation.

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