Designing an LPF with a 17kHz Cut-off Frequency: Question and Guidance

[fran1942]

Hello, I have been asked to:
- design an LPF with a cut off frequency of 17kHz and a roll-off of 40dB Decade. I have attached a picture of the circuit diagram I came up with.
Can someone please confirm if I have this correct ?

The second part of the question was:
- prove both time domain and frequency domain plots for the output waveform for the above filter, if a 5kHz square wave was applied to it.
For this question I am rather lost. Can someone please give me some guidance on how I would display these 2 graphs. I can't find anything in my notes directly explaining how to do this.

Thanks kindly for any help.

 

[NascentOxygen]

Hi fran1942. Were you told to use only R-C passive components in your design? You can achieve a sharper response (i.e., closer to what most would consider the ideal) if you use an active element, e.g., an op-amp with feedback.

Can you simulate this with SPICE to determine its Bode plot?

 

[moogull]

Like Nascent said, SPICE will allow you to simulate a circuit for various input signals that you specify: its free! http://www.5spice.com/

 

[gneill]

Hello, I have been asked to:
- design an LPF with a cut off frequency of 17kHz and a roll-off of 40dB Decade. I have attached a picture of the circuit diagram I came up with.
Can someone please confirm if I have this correct ?

The second part of the question was:
- prove both time domain and frequency domain plots for the output waveform for the above filter, if a 5kHz square wave was applied to it.
For this question I am rather lost. Can someone please give me some guidance on how I would display these 2 graphs. I can't find anything in my notes directly explaining how to do this.

Thanks kindly for any help.

First, perhaps a small problem with your circuit. It looks as though you've simply cascaded two identical low pass filters with a cutoff frequency of about 17.5 kHz. The problem with doing this in this manner is that the two filters will interact and change both of their cutoff frequencies. One way to avoid this is to make the input impedance of the second filter section much higher than that of the output impedance of the first. Make the second resistor about 10x that of the first (adjust the second C accordingly).

For the plots, if you are familiar with Laplace transforms then you can find the response curve using the transform of a square wave to "drive" the transfer function. Working in the time domain you could decompose the square wave into its first few harmonics (until the harmonic frequency is well above the cutoff), find the amplitude of each harmonic at the output of the filter, then sum the resulting waveforms.

 

[DeeNos]

I would like to offer some guidance and suggestions for designing an LPF with a 17kHz cut-off frequency and a roll-off of 40dB decade.

Firstly, it is important to understand the purpose of an LPF and its characteristics. An LPF, or low-pass filter, is designed to allow low-frequency signals to pass through while attenuating high-frequency signals. The cut-off frequency is the point at which the filter starts to attenuate the signal, and the roll-off refers to the rate at which the attenuation occurs.

To design an LPF with a specific cut-off frequency and roll-off, you can use various tools and techniques such as analog or digital filter design software, filter design equations, or circuit analysis methods. It is essential to carefully select the components and their values to achieve the desired cut-off frequency and roll-off.

Regarding the circuit diagram you have attached, it is difficult to confirm its correctness without knowing the specific components and their values. It would be helpful if you could provide more information or a detailed description of your design. Additionally, it is always a good practice to simulate the circuit using a software tool to verify its performance before implementing it in hardware.

Moving on to the second part of the question, to prove the time and frequency domain plots for the output waveform, you can use a signal generator to apply a 5kHz square wave to the LPF and measure the output using an oscilloscope. The time domain plot will show the amplitude of the output signal over time, while the frequency domain plot will show the frequency components present in the output signal. You can also use a spectrum analyzer to display the frequency domain plot.

If you are unable to find information in your notes on how to display these plots, I would suggest researching basic signal analysis techniques such as Fourier transforms or using online resources for guidance. It is also a good idea to consult with your instructor or a more experienced colleague for assistance.

In conclusion, designing an LPF with a specific cut-off frequency and roll-off requires a thorough understanding of its characteristics and careful selection of components. It is also essential to verify its performance through simulation and testing. I hope this guidance helps you in completing your task successfully.