# High pass filter attenuating frequencies equal to cutoff frequency

I'm developing a HPF to attenuate frequencies below 30KHz.

My input voltage is a sinusoidal voltage from 0V to + 5V with a frequency of 30KHz.

My objective is to attenuate frequencies below 30KHz including the DC component.

In the end I want to have a sinusoidal voltage from -2.5V to +2.5V and with a frequency of 30KHz.

My HPF is a passive RC circuit. C is equal to 10nF and R is 510 Ohms. The cutoff frequency therefore equals 30KHz. I used this site to help me with component values: sim.okawa-denshi.jp/en/CRhikeisan.htm

But in some simulations that I'm doing with Proteus my signal comes out with attenuations:

What happened? What is the correct cutoff frequency and why? Tks!

• Hint: the cutoff frequency of a RC filter is the -3dB point of the filter. Aug 14 '17 at 1:24
• Hint: The filter does not suddenly drop to -3db, the frequency for a filter like this follows a logarithmic curve. Aug 14 '17 at 3:14
• The site you used to calculate the value for your filter has a nice plot showing the frequency response of the filter. Put in your values, and calculate. Then, look at the plot labeled "Bodediagram magnitude." That shows you how much your filter will attenuate which frequencies.
– JRE
Aug 14 '17 at 5:42
• Kelvin-Hz is not a measure of anything meaningful in this question. Aug 14 '17 at 11:00
• Erm. What kind of filter do you need to turn a 30kHz sinus input into a 30kHz sinus output?! Aug 14 '17 at 13:08

A simple high pass RC filter gradually reduces the amplitude of an applies sine wave as it falls in frequency. At the cut-off frequency the amplitude is already reduced by 3 dB. 3 dB is called the half power point and, in voltage terms, the output voltage will have reduced to 70.71%: -

It sounds to me like you should be aiming for a cut-off frequency that only attenuates at 30 kHz a fraction of a decibel. Maybe try 10 kHz and plug it into the fomula above or simulate it.

Alternatively you could use a 2nd order high-pass filter based on passive components that include an inductor like this: -

The beauty about this circuit is that you can vary "R" and get a peaking response like this: -

If you "tune" R to give a $\zeta$ value of 0.7071 you will get the so-called Maximally flat butterworth response. You would still choose a cut-off frequency that is lower than 30 kHz but you would get a flatter response down to 30 kHz and a larger attenuation of frequencies below 30 kHz.

The okawa site you looked at before covers this type of filter.

Your question is a great illustration of why "cut off frequency" is a bad term. The problem is that some people start actually believing it. Use "rolloff frequency".

No filter has a sudden transition from stop band to pass band. There is always a frequency range where the filter transitions. For simple RC filters like you are asking about, the rolloff frequency is in the middle of this transition. For RC filters, this is where the signal is attenuated by a factor of 2 in power, which is sqrt(2) in voltage, and which is -3 dB.

If you plot the asymptotes of the pass band and stop band on a log/log plot, they are straight lines. The pass band is a flat horizontal line at 0 db. The stop band is a line that goes down 20 dB per decade away from the rolloff frequency. The two lines extended meet at the rolloff frequency.

In any case, if you want a sharper transition between pass band and stop band, then use a different type of filter. Before doing that though, carefully spec out what you really need. Perhaps a simple RC can still fulfill the requirements, once you are clear what those really are. For example, perhaps a single RC high pass filter at 15 kHz is good enough. That will attenuate 30 kHz less, but still reduce lower frequencies, and completely block DC.