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Q&A Design high -pass filter with 2 points of the bode plot

Filter design 101 given hypothetical high-pass (HPF) filter -3dB gain HPF at fc attenuation of -8dB at fc/2 Assumptions gain = 0 dB at f>> fc Ripple between -3dB and 0 dB...

posted 2y ago by TonyStewart‭  ·  edited 2y ago by TonyStewart‭

Answer
#2: Post edited by user avatar TonyStewart‭ · 2022-08-13T18:04:31Z (over 2 years ago)
  • Filter design 101
  • -
  • 1. given hypothetical high-pass (HPF) filter -3dB gain HPF at fc
  • 2. attenuation of -8dB at fc/2
  • 3. Assumptions gain = 0 dB at f>> fc
  • 4. Ripple between -3dB and 0 dB is unknown but assume 0dB max for simpler case.
  • 5. steepness of skirts << fc is unknown but we know 1st order slope is 6 dB/octave maximum
  • 6. the attenuation at fc on a 1st order filter at fc/2= -7 dB which almost satisfies -8dB so is slightly greater than 1st order, which means a 2nd order filter that results in -1dB at fc/2 may be added to solve this problem. That frequency may be computed from impedance ratios to obtain the final transfer function, but I can tell you -1dB is about 2xfc.
  • 7. There are also an infinite number of other solutions if the assumptions change above.
  • The breakpoint is defined as the half-power point where the voltage drop is 0.707 or -3dB approx.
  • Using my assumptions in 6. above I declare the 2nd order HPF transfer function is;
  • $$H(s)=\dfrac{s^2}{(s+\omega_0)(s+2\omega_0)}$$
  • See if that suits your specs.
  • Filter design 101
  • -
  • 1. given hypothetical high-pass (HPF) filter -3dB gain HPF at fc
  • 2. attenuation of -8dB at fc/2
  • 3. Assumptions gain = 0 dB at f>> fc
  • 4. Ripple between -3dB and 0 dB is unknown but assume 0dB max for simpler case.
  • 5. steepness of skirts << fc is unknown but we know 1st order slope is 6 dB/octave maximum
  • 6. the attenuation at fc on a 1st order filter at fc/2= -7 dB which almost satisfies -8dB so is slightly greater than 1st order, which means another 1st order filter that results in -1dB at fc/2 may be added to solve this problem. That frequency might be computed from impedance ratios to obtain the final transfer function, but I can tell you -1dB is about 2xfc.
  • 7. There are also an infinite number of other solutions if the assumptions change above.
  • The breakpoint is defined as the half-power point where the voltage drop is 0.707 or -3dB approx.
  • Using my assumptions in 6. above I declare the 2nd order HPF transfer function is;
  • $$H(s)=\dfrac{s^2}{(s+\omega_0)(s+2\omega_0)}$$
  • See if that suits your specs.
#1: Initial revision by user avatar TonyStewart‭ · 2022-08-13T18:02:00Z (over 2 years ago)
Filter design 101
-

1. given hypothetical high-pass (HPF) filter -3dB gain HPF at fc 
2.  attenuation of  -8dB at fc/2 
3. Assumptions gain = 0 dB at f>> fc
4. Ripple between -3dB and 0 dB is unknown but assume 0dB max for simpler case.  
5. steepness of skirts << fc is unknown but we know 1st order slope is 6 dB/octave maximum
6. the attenuation at fc on a 1st order filter at fc/2= -7 dB which almost satisfies -8dB so is slightly greater than 1st order, which means a 2nd order filter that results in -1dB at fc/2 may be added to solve this problem. That frequency may be computed from impedance ratios to obtain the final transfer function, but I can tell you -1dB is about 2xfc.
7. There are also an infinite number of other solutions if the assumptions change above.


   The breakpoint is defined as the half-power point where the voltage drop is 0.707 or -3dB approx. 

Using my assumptions in 6. above I declare the 2nd order HPF transfer function is;

$$H(s)=\dfrac{s^2}{(s+\omega_0)(s+2\omega_0)}$$

See if that suits your specs.