# Question about Active Bandpass Filter Circuit

#### erickson71

Joined May 13, 2012
6
Hello all. Being more versed in the digital side of electronics than the analog side. I have a specific question about a published application note here:
https://www.maximintegrated.com/en/design/technical-documents/app-notes/4/4622.html

It seems they are using an Infinite Gain Multi Feedback Active Bandpass filter similar to what is described here:
https://www.electronics-tutorials.ws/filter/filter_7.html

A few things bother me about the Max circuit and I wanted to see what other folks thought.

First the formula for obtaining the resonant frequency of the receiver from what I can see is

Frequency = 1/(2*pi*sqrt(C1*C2*R1*R2))

I tried plugging the application note values for C1 C2 and R1 R2, I get in the 9.8khz range and not 10khz. Is this right?

Second, this circuit does not seem to have phase shift adjustment tuning to ensure the sender 10khz wave is synchronized with the receiver clock. I know there are techniques to handle this by ANDing the input with 90 degree phase shifted input as well as others, but this particular circuit does not seem to have any of these. Am I missing something?

Thanks again,
Stephan

#### erickson71

Joined May 13, 2012
6
Ok I worded this question wrong and need to correct: There is no clock on the receiver. The AC coupling filters out the DC component of the signal. So now on the inverting side of the op amp we have a bandpass filter with 10khz (or roughly 9.8khz) resonent frequency. How does this handle phase shift of the ac single? I just seems intuitive to me that a phase shift is needed and am sure someone will have an explanation as to why this circuit should actually work.

#### Papabravo

Joined Feb 24, 2006
16,830
Yeah. Here is the problem. You don't have a continuum of component values. Capacitor value are from the E12 series. That means there are 12 possible values in each decade. Resistors are a bit better because you can select them from the E96 series which has 96 values per decade. Being off by 150 Hz. out of 10,000 Hz. is actually pretty good. You were perhaps expecting something a bit closer to the design value. You can try playing with the values to get closer. I think it is odd that the ratio of R1 to R2 is so large: almost 200:1. IMHO unless there is a good reason for that choice I would try for something a bit closer to 20:1. Maybe there is something going on that I am missing.

In most high-Q bandpass filters there is a dramatic phase shift at the center frequency as you make the transition to the upper stop band. As you can see from the simulation the center frequency is off even more than your calculations -- not surprising. On a logarithmic scale there is not a lot of difference between 9 kHz and 10 kHz. I don't know if that is any comfort to you. There is a radical phase shift at the center frequency as expected. 42 dB (125.9) of gain is quite a bit for a part with a +5V supply biased at 2.5V. ±20 mV on the input is all it would take to hit the rails. It's a good thing you can do things in simulation that you can't do on the bench. Good luck with your rockets.

#### Attachments

• 23.7 KB Views: 5
• 50.2 KB Views: 6
Last edited:

#### erickson71

Joined May 13, 2012
6
Thanks Papabravo. Duh yes of course about the discrete R and C values I should have seen that.

Now about R2 being so high the gain is -R2/2R1 so they want to amplify by 100 here I think. That seems to make sense.

Re dramatic phase shift at the corner thanks for sending me in the right direction. Though not 100% clear yet I will fill in after some research. Still new to the analog side..

#### crutschow

Joined Mar 14, 2008
27,753
I just seems intuitive to me that a phase shift is needed
Intuition is seldom a valid reason to design a function into a circuit.
The circuit after the filter rectifies the AC to give a DC level, which is entirely insensitive to (or affected by) the phase shift of the 10kHz signal.

#### erickson71

Joined May 13, 2012
6
Yeah. Here is the problem. You don't have a continuum of component values. Capacitor value are from the E12 series. That means there are 12 possible values in each decade. Resistors are a bit better because you can select them from the E96 series which has 96 values per decade. Being off by 150 Hz. out of 10,000 Hz. is actually pretty good. You were perhaps expecting something a bit closer to the design value. You can try playing with the values to get closer. I think it is odd that the ratio of R1 to R2 is so large: almost 200:1. IMHO unless there is a good reason for that choice I would try for something a bit closer to 20:1. Maybe there is something going on that I am missing.

In most high-Q bandpass filters there is a dramatic phase shift at the center frequency as you make the transition to the upper stop band. As you can see from the simulation the center frequency is off even more than your calculations -- not surprising. On a logarithmic scale there is not a lot of difference between 9 kHz and 10 kHz. I don't know if that is any comfort to you. There is a radical phase shift at the center frequency as expected. 42 dB (125.9) of gain is quite a bit for a part with a +5V supply biased at 2.5V. ±20 mV on the input is all it would take to hit the rails. It's a good thing you can do things in simulation that you can't do on the bench. Good luck with your rockets.

Thanks! Ok my lesson is time to get one of those simulators. .. It will give me more time to call my mother...
All the best

#### erickson71

Joined May 13, 2012
6
Intuition is seldom a valid reason to design a function into a circuit.
The circuit after the filter rectifies the AC to give a DC level, which is entirely insensitive to (or affected by) the phase shift of the 10kHz signal.
Understood, yet the Peek detector circuit depends on a non zero amplified AC signal and comes after the fact. The AC signal itself was what my question was about. Because there is a 90 degree phase shift at the corner frequency it does not matter if we are off by 45 degrees for example as long as we are close enough to the desired frequency. Otherwise we could have ended up with a dc filtered 'close to zero' volt ac signal just because we were unlucky about the phase of emitted signal. (The simulation provided by papabravo does not include the peek detector circuit)
Thanks again.

#### erickson71

Joined May 13, 2012
6
Ok nevermind my last note, this makes sense: the bandpass filter itself is insensitive to phase shift of input since it always amplifies the full signal at the frequencies which it allows through.

#### Papabravo

Joined Feb 24, 2006
16,830
The historical context for the comedy clip which was made in the early 1960's. Many young engineers were working for NASA, trying to get men into space. Some of those early efforts met with spectacular failures. Early in the skit "Elaine May", the non-technical mother, tells her son, Arthur, that he keeps losing the rockets. Later she relents a bit and wants to wish him good luck with his rockets. I remembered this skit throughout may career as a reminder not to get too arrogant or ahead of myself. I almost succeeded.