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# Bandpass filter, take 2

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#### Gandledorf

##### New Member
Ok, I've been reviewing some bits on bandpass filters, and wanted to repost the design suggested by this helpful board, with a few changes, and questions.

I've changed the variable 1uH inductor to a fixed 470uH inductor, as I couldn't find any variable inductors. Also, I've changed the 8nF capacitor to a variable 8.5 - 120pF capacitor. This ought to give the device a frequency range from 21.192kHz to 79.627kHz, allowing me to play with the frequencey a bit during calibration (target frequency is going to be between 38kHz and 56kHz).

In addition, I was wondering, what is the purpose of the voltage follower at the end of the system? Also what major effect does Q have on the system? I still don't 100% understand the effect of Q.

EDIT: In addition, if I want to pass this into the ADC of an ATMega8, do I need to demodulate it? It seems that I do, but I am unsure how to do this...

I think you need to take another hack at the equation for resonant frequency.

L*C=1/((2*pi*fc)^2)

Solve for LC, pick a value for one then solve for the other. You probably should keep XL=XC=(2*pi*fc*L) in the range 300<X<3000 ohms. I pulled this range out of my hat, so it's not a hard and fast rule. If you try to use a large L value in order to be able to use a variable capacitor, the self-capacitance of the inductor may be too large.

The voltage follower is there because the impedance looking back into the tank circuit at resonance is the value of the series resistors (the tank circuit itself has very high impedance). You don't want to load it with the next stage. If the next stage has very high input impedance at 56 kHz, then you don't need the voltage follower.

Q is a measure of the bandwidth of the bandpass filter. The higher the Q, the lower the bandwidth.

Ron H said:
I think you need to take another hack at the equation for resonant frequency.

L*C=1/((2*pi*fc)^2)

Solve for LC, pick a value for one then solve for the other. You probably should keep XL=XC=(2*pi*fc*L) in the range 300<X<3000 ohms. I pulled this range out of my hat, so it's not a hard and fast rule. If you try to use a large L value in order to be able to use a variable capacitor, the self-capacitance of the inductor may be too large.

Ack! You're right, I was writing uH, but calculating with mH, didn't check my units. So my calculations were off by 3 orders of magnitude.

One thing I don't understand is this: Why would a large inductor fail to work? I am not used to using inductors at all, and so I am very unfamiliar with their characteristics.

Ok then... doing a bit more searching, I found some HiQ tunable coils but they are each near 1uH, instead of 1mH. How would these changes go:

Tunable coil: .450uH - .550uH
Capacitor: 16uF

This would tune from 53.651kHz - 59.313kHz, a bit narrower than I wanted. Is there a way to increase this range?

The other problem is the fact that I can only find 8uF capacitors in 10% meaning we push ourselves out of frequency if each is 8.8uF, and nearly so if each is 7.6uF, this seems like a bad result to me.

Digikey has some here: **broken link removed** but I don't see the range of each in the listings. Ideally I'd love to have one that tunes over .3uH - 1.5uH.

The voltage follower is there because the impedance looking back into the tank circuit at resonance is the value of the series resistors (the tank circuit itself has very high impedance). You don't want to load it with the next stage. If the next stage has very high input impedance at 56 kHz, then you don't need the voltage follower.

Q is a measure of the bandwidth of the bandpass filter. The higher the Q, the lower the bandwidth.

Gotcha, both of those make sense to me, except, what are the units on Q?

Checking, I can find tunable coils up to the 1mH range, but if I am reading correctly, they only have a 10% tuning range. This seems awfully narrow. Is there a way to make this better? Do they sell variable capacitors with larger values?

You don't really want to be messing about with coils at all, op-amp based bandpass filters are far better for the ultrasonic audio frequencies in question. I realise the MicroChip filter design package I mentioned only runs under Windows (but so does much of the worlds software), if you can't find something similar under your operating system, perhaps it's time to change to something more useful?.

The MicroChip package isn't the only such package available for Windows, the basic details are also available in books - so you could always write your own.

The problem with large capacitors/small inductors is that, in order to get moderate Q values (~2-10), you need tiny resistors, because Q=R/XL. For signal content that is off resonance (the stuff you're trying to get rid of), the input impedance of your filter becomes very low, and so is difficult to drive.
If you will check back to one of my previous posts, I commented on the narrow tuning range of 1mH inductors.
What you really need (I think) is a switched-capacitor filter. They are made by various companies - do a Google search. They are very versatile, but I have never used them, and while I'm sure I could figure out how to use them, teaching you is probably beyond my capabilities. Maybe some of the other trolls have experience with them. Or, if you have time to play with them and post your results and questions here, you could probably get help here.

Nigel Goodwin said:
You don't really want to be messing about with coils at all, op-amp based bandpass filters are far better for the ultrasonic audio frequencies in question. I realise the MicroChip filter design package I mentioned only runs under Windows (but so does much of the worlds software), if you can't find something similar under your operating system, perhaps it's time to change to something more useful?.

The MicroChip package isn't the only such package available for Windows, the basic details are also available in books - so you could always write your own.
I agree with you, Nigel. It's pretty obvious that Gandledorf would like to have knobs on center frequency and Q (and gain, but that's easy). That's the only reason I posted the LC circuit. Perhaps a state-variable filter would allow non-interacting controls. I haven't looked at the software you're referring to.

Nigel Goodwin said:
You don't really want to be messing about with coils at all, op-amp based bandpass filters are far better for the ultrasonic audio frequencies in question. I realise the MicroChip filter design package I mentioned only runs under Windows (but so does much of the worlds software), if you can't find something similar under your operating system, perhaps it's time to change to something more useful?.

LOL, trust me I am using the most useful system. I couldn't do 99% of my work on Windows, and run all of my machines with Linux.

The MicroChip package isn't the only such package available for Windows, the basic details are also available in books - so you could always write your own.

I'm waiting on a copy of "The Art of Electronics", so I may do just that.

I agree with you, Nigel. It's pretty obvious that Gandledorf would like to have knobs on center frequency and Q (and gain, but that's easy). That's the only reason I posted the LC circuit. Perhaps a state-variable filter would allow non-interacting controls. I haven't looked at the software you're referring to.

Truthfully the cf and Q knobs would really just be icing on the cake, they aren't truly needed, I just would like the option of dynamically playing with the value of Q, as I am not sure what an appropriate value would be, and cf for the testing phase.

Thanks again for the help, I'm going to wait on my book before I proceed further.

Band Pass Filter

Ron H said:
The problem with large capacitors/small inductors is that, in order to get moderate Q values (~2-10), you need tiny resistors, because Q=R/XL.]

If the R is in series with the inductor then actually Q=XL/R and as Ron said, R needs to be as small as possible. If it is in parallel, R needs to be as high as possible.

You need Q to be as high as possible in order to reject other frequencies.

But as I said in a PM and others have also said, why use an LC filter?

I was only using an LC filter because it is what I am familiar with, and I am still waiting on my books, without which, I can't do much in the way of other designs, as the internet sites I've found tend to be a little "light on the material".

Re: Band Pass Filter

ljcox said:
You need Q to be as high as possible in order to reject other frequencies.
Not true. High Q can wipe out the modulation, which appears as sidebands on either side of the carrier frequency. The bandwidth (Q) required depends on the modulation scheme.

Re: Band Pass Filter

Ron H said:
ljcox said:
You need Q to be as high as possible in order to reject other frequencies.
Not true. High Q can wipe out the modulation, which appears as sidebands on either side of the carrier frequency. The bandwidth (Q) required depends on the modulation scheme.

I agree re the Bandwidth, but my point stands. Low Q means a wider bandwidth, but it also means lower selectivity, ie. unwanted frequencies may intrude.

If he really wants to use an LC filter, he should design a tuned amp like the IF amp in a radio receiver, ie. 2 or more parallel tuned circuits stagger tuned to increase BW and isolated by Trans Conductance amps. Then it will be possible to combine high Q and adequate bandwidth.

I still feel that an Active Filter would be easier.

Well my books arrived last night, and I've been reading the active filter sections. I think I have found a design that will work. It's composed of four op-amps, but has separately adjustable G, Q, and cf.

Looks like a winner, I'll post more this evening when I finish reading.

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