# Bode Plot Method For a Transfer Function

• jendrix
In summary, the conversation discusses the interpretation of a transfer function with s replaced by jw and divided by 10. It is noted that the first term in dB form uses 20log10 and the 100 in the numerator may be a typo. The reason for standardizing the form (jω/N + 1) is also mentioned. There is a discrepancy in the use of 10‧log |(jω)2 + 1| and the correct expression involves 20‧log. However, due to the form of the frequency-dependent expression, it is possible to combine the 20 and √ and write it as 10 without the √. Overall, the conversation is a bit confusing and it is
jendrix
Hi ,

I was hoping you could look at this link and let me know if I have interpreted the method correctly

http://i.imgur.com/5axTiBN.jpg

As I understand it the transfer function has had s replaced by jw but also the top and bottom are divided by 10 -
This is so that the brackets on the bottom fit a first order lag? Though it looks like they forgot to divide the top by 10.

When it gets put into dB form 20log10 is used for the first term though?

Is that correct and the 100 in the numerator is a typo?Thanks

Yes, they factorized the denominator from (jω + 10) to 10(jω/10 + 1) but accidently lost that first 10.

The reason for standardising on the form (jω/N + 1) is so that for ω<<N this term contributes a value of approx unity to the T.F. so can be "ignored" until ω→N.

I don't like their use of 10‧log |(jω)2 + 1|
I think the j should not be included like that; we don't want to square the j.

The full expression for the amplitude of each term does correctly involve 20‧log
but because each frequency-dependent expression is of the form,
e.g., 20‧log √((1/10)2 + 12)
the rules of mathematics allow them to combine the 20 and the √ and write it as 10 without the √.

you should satisfy yourself of the validity of this.

A little confusing! [emoji84]

## What is the Bode Plot method for a transfer function?

The Bode Plot method is a graphical method used to analyze and visualize the frequency response of a system described by a transfer function. It consists of plotting the magnitude and phase of the transfer function against the frequency on a logarithmic scale.

## What is the purpose of using the Bode Plot method?

The Bode Plot method allows for a quick and intuitive understanding of the frequency response of a system. It can also help identify the key characteristics of a system, such as stability, bandwidth, and resonant frequencies.

## How is the Bode Plot constructed?

The Bode Plot is constructed by first converting the transfer function into its magnitude and phase components. The magnitude is plotted on a logarithmic scale against frequency, and the phase is plotted on a linear scale against frequency. Both plots are typically shown on the same graph, with the magnitude plot above the phase plot.

## What information can be obtained from a Bode Plot?

A Bode Plot can provide information about the overall gain and phase shift of a system at different frequencies. It can also show the location of poles and zeros, which can give insight into the stability and frequency response of the system.

## What are the limitations of the Bode Plot method?

The Bode Plot method assumes that the system is linear and time-invariant, which may not always be the case in real-world systems. It also does not take into account the effects of non-linearities, noise, and disturbances on the system's response. Additionally, the Bode Plot may not accurately represent the system's behavior at very high or very low frequencies.

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