# Transfer Function Of A 2nd Order Circuit

• Engineering
• Mitchy190
In summary: You know ##V_i## in terms of ##V_o##, so you can solve for the transfer function.In summary, solving for a transfer function in a 2nd order RC circuit involves treating the circuit as one unit and writing KCL equations to find the ratio of output voltage to input voltage. Attempting to split the circuit into two parts can lead to incorrect answers due to the interaction between the sections and the assumption of no loading effects. The use of buffering amplifiers with low output impedance can eliminate this issue.
Mitchy190
I'm trying to work out the Transfer function for the 2nd order RC circuit in the attachment below: I can't seem to get the right answer :(

circuit:

Please see attachment for my attempt and the relevant information:

View attachment f.pdf

Last edited:
When you solve for a transfer function, the assumption is that you effectively drive it with an ideal source (Vi) that has zero source impedance, and "measure" the output (Vo) with a "meter" that has infinite input impedance (no loading).

Your problem stems from splitting the circuit into two parts and assuming that the two sections did not interact. In fact, the first section is loaded by the input impedance of the second, and the second "sees" the output impedance of the first. This interaction is lost when you divided the sections.

Mitchy190 said:
I'm trying to work out the Transfer function for the 2nd order RC circuit in the attachment below: I can't seem to get the right answer :(

circuit:

View attachment 54818

View attachment 54819

Please see attachment for my attempt and the relevant information:

View attachment 54814

I don't think you can split and cascade the circuit like that. I think you could only treat it as two cascaded circuits if there were a buffer amp in between them (with infinite input impedance and zero output impedance).

Try treating it as one circuit, and write the KCL equations to solve for the transfer function. Does that get you closer to the book's answer?

EDIT -- dangit! Beat to the punch again

Last edited:
Okay thank you, i just assumed that as when you have two transfer functions connected in series you multiply them together to get the overall function.

What does this analogy actually represent then? Does it represent two circuits connected in series and assumes no loading effect? Or something else?

This is what I mean:

Mitchy190 said:
Okay thank you, i just assumed that as when you have two transfer functions connected in series you multiply them together to get the overall function.

What does this analogy actually represent then? Does it represent two circuits connected in series and assumes no loading effect? Or something else?

Yup. It means no loading effects. And it works fine if, as Berkeman suggested, you buffer them with a suitable isolation stage.

When designing separate stages for cascading its possible to design them with a standard input impedance and assumed standard load (usually the same as the input impedance), so that the resulting transfer functions can be cascaded by multiplication (which is why you often see gear with input impedance specified, and output impedance specified). The simple solution, though, is to provide buffering amplifiers with very, very low output impedance so that loading isn't an issue.

Thanks a lot man (:

I'm still struggling with this question :( I don't know where to start, now I have worked out the KCL equation and KVL, I don't know what to do with them?

You're looking to find the ratio ##V_o/V_i##.

## What is a transfer function of a 2nd order circuit?

A transfer function of a 2nd order circuit is a mathematical representation of how the output of a circuit changes in response to a specific input. It describes the relationship between the input and output signals of the circuit and can be used to analyze the behavior of the circuit.

## How is the transfer function of a 2nd order circuit calculated?

The transfer function of a 2nd order circuit is calculated using the Laplace transform. The circuit is first represented in the s-domain, where s is a complex variable. Then, using Kirchhoff's laws and the impedance of the circuit elements, the transfer function can be derived.

## What information does the transfer function of a 2nd order circuit provide?

The transfer function of a 2nd order circuit provides information about the frequency response, stability, and damping of the circuit. It can also be used to determine the poles and zeros of the system, which can help in designing and analyzing the circuit.

## How does the transfer function of a 2nd order circuit differ from a 1st order circuit?

The transfer function of a 2nd order circuit includes two poles, while a 1st order circuit only has one pole. This means that a 2nd order circuit has a more complex frequency response and can exhibit oscillatory behavior, while a 1st order circuit has a simpler response with no oscillations.

## How can the transfer function of a 2nd order circuit be used in practical applications?

The transfer function of a 2nd order circuit can be used to design and analyze electronic filters, control systems, and other circuits. It can also be used in signal processing to determine the frequency response of a system and to filter out unwanted frequencies.

• Engineering and Comp Sci Homework Help
Replies
2
Views
1K
• Engineering and Comp Sci Homework Help
Replies
1
Views
688
• Engineering and Comp Sci Homework Help
Replies
16
Views
2K
• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• Engineering and Comp Sci Homework Help
Replies
9
Views
2K
• Engineering and Comp Sci Homework Help
Replies
1
Views
886
• Engineering and Comp Sci Homework Help
Replies
16
Views
1K
• Engineering and Comp Sci Homework Help
Replies
8
Views
1K
• Engineering and Comp Sci Homework Help
Replies
2
Views
1K
• Engineering and Comp Sci Homework Help
Replies
5
Views
2K