# filter whose gain increases from minimum to maximum for frequency 400Hz to 1kHz

I want to design high pass filter whose gain should increase from minimum to maximum ( minimum upto 400 Hz maximum for 1 kHz) linearly or exponentially. It must be an active filter and my input signal is square wave. How do I design the circuit?

• Simplest solution here. – Null Nov 21 '14 at 19:05
• Can you draw a picture showing the frequency-gain characteristic you ideally want. such as this:radio-electronics.com/images/… - don't forget to add on the values of frequency and also give what is minimally accceptable and what is preferred. – Andy aka Nov 21 '14 at 19:27
• Such a high pass filter can rise neither linearly nor exponentially. That`s impossible. A linear shape of the magnitude is possible only for a log. frequency scale and if the magnitude is given in dB. – LvW Nov 21 '14 at 20:55
• Regarding the low frequencies you haven't nailed it by any means. I appreciate you have got a decent answer from someone but you have to realize that showing the gain drop to zero at 400Hz and stay zero all the way down to DC is an impossibility. Try and state how many dB per octave attenuation you need below 1kHz - you need to define these requirements and not expect some magic to take place. – Andy aka Nov 21 '14 at 22:07
• Yes, I understood. – Vivekanand Dhakane Nov 22 '14 at 16:14

The steep response you want will require a multistage filter. The most commonly used active filter configuration is Sallenâ€“Key topology, which provides two stages per amp using just 2 resistors and 2 capacitors. Various filter responses can be created by varying the component values. Here is an LTSpice simulation of a 4 stage Butterworth high-pass filter with 800Hz cutoff frequency.

This filter provides a frequency response close to your requirements, with an almost linear rise above 400Hz reaching a maximum at just over 1kHz. With more stages and a bit of tweaking you could probably improve linearity at the ends - but why bother?

Note that both the amplitude and frequency scales in this graph are linear, not logarithmic.

That curve looks nice and smooth, however the circuit's pulse response isn't so pretty. Here is the transient analysis for a 1Khz square wave.