# Matlab Bode Plots: 1st Order High Pass & 2nd Order Band Reject

• burns12
In summary, the task is to create bode plots for a first-order high-pass filter with a gain at infinity of 2 and a cutoff frequency of 1 kHz, in series with a second-order band-reject filter with a center frequency of 5000 Hz, a bandwidth of 500 Hz, and a gain at infinity of 1. The relevant transfer functions are given and it is suggested to put them in standard form for easier understanding.
burns12

## Homework Statement

In Matlab create bode plots for a first-order high-pass filter (with G at infinity = 2 and fc= 1 kHz) in series with a second order band-reject filter (with f0= 5000 Hz, B = 500 Hz, and GDC= G at infinity = 1 ).

## Homework Equations

High pass TF = -jwCiRf/1+jwCiRi
Band pass TF = -Rf/Ri(-1/1+jwC1R - jwC2R/1+jwC2R) I think, not sure if this is for 2nd order

## The Attempt at a Solution

I have no idea how to relate the G to the TF's. I'm not sure what values I even need to do this.

I think that if you put your T(s) in standard form, you will easily see how to do this.

What book are you using?

## 1. What is a Bode plot?

A Bode plot is a graphical representation of the frequency response of a system. It shows how the magnitude and phase of the system's output changes as the frequency of the input signal varies. It is commonly used in control systems and signal processing.

## 2. What is a first order high pass filter?

A first order high pass filter is a type of filter that attenuates low frequency signals and allows high frequency signals to pass through. It is characterized by a single pole in its transfer function and has a slope of 20 dB/decade. It is commonly used to remove unwanted low frequency noise from signals.

## 3. What is a second order band reject filter?

A second order band reject filter, also known as a notch filter, is a type of filter that attenuates signals within a specific frequency range and allows signals outside of that range to pass through. It is characterized by two poles in its transfer function and has a slope of 40 dB/decade. It is commonly used to remove specific frequencies from signals, such as 50/60 Hz power line noise.

## 4. How do I interpret a Bode plot?

To interpret a Bode plot, you can look at the magnitude plot to see how the amplitude of the output changes with frequency, and the phase plot to see how the phase of the output changes with frequency. The cutoff frequency, where the magnitude decreases by 3 dB, can also be determined from the plot. Additionally, the slope of the magnitude plot can indicate the order of the filter.

## 5. How can I create a Bode plot in Matlab?

To create a Bode plot in Matlab, you can use the bode function. This function takes in the transfer function of the system as input and plots the magnitude and phase response. You can also customize the plot by specifying the frequency range, adding grid lines, and changing the axes labels and titles.

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