# Construction of a Band reject filter

I'm trying to construct something like the band reject filter on the bode graph below.

I know that I could make this by using four different filters and adding them up (low pass filter + high frequency amplifier + high frequency amplifier + high frequency "reducer"). By adding them up I mean connecting them with buffers.

I read on many webpages that this could be made by just using a high pass filter and a low pass filter like this:

I don't understand how could I make this frequency shift on the high pass filter shown in red so it doesn't "subtract" frequencies below $$\f_L\$$. And how to translate this into an actual circuit.

Any help is appreciated!

EDIT: Sorry I don't have much knowledge on this, but I'm guessing that it could be made with something like this:

$$\G_v(s)=\left(1+\dfrac{s}{a}\right)^{-1}\left(1+\dfrac{s}{b}\right)\left(1+\dfrac{s}{c}\right)\left(1+\dfrac{s}{d}\right)^{-1}\$$

Where the first and last terms are low pass filters with cutoff frequencies of a and d respectively.

How could I make the second and third terms in a way that all are connected in series with dependent volages?

• Take the transfer function, and implement in software. Trust me on this one. – Matt Young May 30 '19 at 3:55
• What order is the slope, and spacing? This looks like the -15 dB cut switch on midrange that I had on my Bogan Stereo tube amp. It worked so well that I thought later amp “loudness” switches were annoying. It’s not hard if you have specs – Tony Stewart Sunnyskyguy EE75 May 30 '19 at 4:03

It sounds like you are looking for what hi-fi designers would call a bass and treble shelving filter. This is made from two parallel circuits sharing the same input source with there outputs summed together: -

Picture taken from this page. Scroll down to the section called 6.1 Shelving Filters with Operational Amplifiers.

There is also this page produced by Elliot Sound Products that describes various filters (including shelving filters) in some detail.

• But if I add them up (I have very basic knowledge on this, just learned bode diagrams) shouldn't I get something like a straight line in this case? – FelipeMedLev May 30 '19 at 12:21
• Make sure you add them in parallel. Then you get a Gmax + Gmin at high and low frequencies and this translates to basically Gmax, when Gmin is quite small. At mid frequencies you get Gmin + Gmin . The two bode diagrams shouldn't be regarded as having same values for f_high or f_low i.e. f_high on the low pass circuit will be less than f_low on the high pass filter. – Andy aka May 30 '19 at 12:55
• Ohhh. I thought that the $f_{LOW}$ and $f_{HIGH}$ was the same for both of them. Thanks!! – FelipeMedLev May 30 '19 at 14:35

It's not quite like you show. The filters are combined in parallel and there is a common plateau in the middle.

In the 70's, I had a 100W Bogan Stereo Tube HiFi. It had this amazing switch called "-15 dB contour" It was very effective for reducing the midrange. Then someone could use the phone in the kitchen, while guests could still enjoy the music. The theory behind this was defined many decades before that, with the Fletcher-Munchen curves for human hearing response.

Here are my design and simulations. You can change the depth of the plateau with the 2k2 part and shift the centre and both edges by scaling both caps by the same amount.

What you showed was a 1st LPF and 1st order HPF which creates a flat response in series and a notch filter in parallel.

What I show has a plateau in each filter by the added series 2k2.

If you have specific asymptotes for f1,f2 and the plateau level, append it to your question.