# Resonant Frequency and Transfer Functions

• Apogee
In summary, the conversation discusses the transfer function of a filter and the maximum value of the transfer function. The resonant frequency w0 is mentioned as the frequency at which the impedance seen at the input is purely real, but it is pointed out that this may not always be the same as the frequency at which the transfer function is at its maximum value. The idea of normalizing the transfer function is also mentioned, but it is questioned if this is necessary for such a simple function.
Apogee
Suppose I have some sort of a filter, whose transfer function is given by H(w), where w is the angular frequency of the input signal in radians per second. I want to know the maximum value of the transfer function. If I solve for the resonant frequency w0, which from my understanding is the frequency at which the impedance seen at the input is purely real, is the maximum value of the transfer function given by H_max = H(w0)?

Also, would the normalized transfer function be defined as H(w)/H_max = H(w)/H(w0)?

Hi,

Aren't you mixing up a few things ? Depending on the notation, usually ##\omega_0## and the ##\omega## for which ##|H| ## is maximum, are different.
Read up on simple examples such as harmonic oscillators

Note that the figure right there is much more insightful without your proposed normalization. Why would you want to 'normalize' such a simply defined function ?

## 1. What is resonant frequency?

Resonant frequency is the frequency at which an object vibrates with the greatest amplitude when it is struck or stimulated in some way.

## 2. How is resonant frequency calculated?

Resonant frequency can be calculated using the equation f0 = 1/(2π√(LC)), where f0 is the resonant frequency, L is the inductance, and C is the capacitance.

## 3. What is a transfer function?

A transfer function is a mathematical representation of the relationship between the input and output of a system, such as an electrical circuit, at different frequencies.

## 4. How is a transfer function used in engineering?

A transfer function is used to analyze and design systems, such as filters or amplifiers, in various engineering fields. It helps engineers to understand how a system responds to different input frequencies and to optimize its performance.

## 5. What factors affect the transfer function of a system?

The transfer function of a system is affected by the components used in the system, such as resistors, capacitors, and inductors, as well as the physical properties of the system, such as its size, shape, and material. Environmental factors, such as temperature and humidity, can also affect the transfer function.

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