# How should I make the gain outside the bandwith of this low pass filter less than -50dB? [closed]

I want to block all frequencies higher than 12kHz coming from diffrent sources. The required filter should have the fastest response possible without inducing any ripple and the gain inside the bandwidth should be higher than +20dB and outside it should be less than -50dB.

My question is how should I design it to have the gain outside less than -50dB.

I'm new to non linear electronics so I don't have much experience.

I know exactly the steps to do for a Sallen Key design but it's just that this outside gain that is confusing me. Does this mean that I should use a 3rd order low pass filter with a Chebyshev 3dB type? Because if a 1st order LPF gives an amplitude of -20dB/decade this means that I need a 3rd order LPF.

• 1. Why is this tagged non-linear? That sounds like the opposite of what you want! Dec 12, 2020 at 12:29
• I suggest that you do some studying on how to specify a filter. For example, "gain ... outside it should be less than -50dB". That's not a proper specification. A first order 1 kHz lowpass filter will not have more than 50 dB rejection at 1.1 kHz. So specify at what frequency (or relative frequency like 10 x $f_c$) you need 50 dB rejection (actually 70 dB rejection as you want a +20 dB in the passband). If you don't study how to do this then you will get in a mess. Dec 12, 2020 at 12:29
• You cannot expect 70dB attenuation immediately outside the passband. That would be what is called a "brick wall" filter which is physically unrealisable. You need to define the centre frequency, the width of the passband AND the (larger) width of the stopband. e.g. 1 kHz passband (each side of the centre frequency, total width 2 kHz), 10 kHz stopband. Then use standard filter design techniques (or online calcs) to design a filter meeting that spec. The calc will tell you the required filter order. Dec 12, 2020 at 12:29
• 2. 70 dB difference between pass and stop band isn't impossible (with a non-zero transition width between the two), but it's challenging, and it requires you to take into account phenomena that are different for different frequencies. So, the answer to this depends very much on whether this is for 1 to 1.5 Hz, or 100 to 150 kHz, or 100 to 150 MHz, or 4 to 6 GHz. Specify your filter! Dec 12, 2020 at 12:30
• Passband to 12 kHz, stopband from 12 kHz, is physically unrealisable. Think again. Dec 12, 2020 at 14:18

The filter 'difficulty' increases roughly as $$\\frac{stopband dB}{transition band width}\$$