By now I'm assuming you have done the previous tutorials and I really don't have to hold your hand. Some of the "key" information here took me over twenty years to unearth and I still find it a fascinating topic, although it is largely redundent with today's technology of crystal or ceramic filters.
For reasons of clarity, formulas will often be .gif files, when you see the first one you will realise why.
At the outset please understand that the best response you can possibly get from these filters would be a 1% fractional bandwidth and even then you would be pushing it very hard. In the real world I'd suggest you don't even consider looking beyond 2% bandwidth. What that means is this - if I wanted a filter with a bandwidth of say 5 Khz then if that represented 2% which in fact is 1/50th then the IF would be 50 X 5 Khz = 250 Khz.
Disappointed? Sorry that's reality!. Why would you bother?
Check out the latest price for say a 9 Khz wide crystal filter at any IF. One off, for non standard IF's and you're looking at $US 100.00. Standard IF's probably $US 50.00. H'mmm then for my oddball project maybe doing my own IF filter isn't such a bad idea. Read on.
How about we get some pictorial representation of what we are about and then I'll delve into all the bells and whistles.
Now here I've depicted three I.F. transformers sperarated by two stages of amplification which could be valves, transistors or integrated circuits. We will not consider the actual active or amplifier stages here now, just the I.F. transformers and the circuit as a whole.
These a called "synchronously tuned filters" because each stage is coupled by an active device. From earlier filter tutorials you will remember the filter bandwidth determined the required bandpass Q or Qbp. An example we will use throughout this tutorial will be an IF stage from a typical transistor radio at 455 Kz with a bandwidth of 10 Khz.
Why worry you ask, why not use some surplus 455 Khz I.F. transformers and move them up or down in frequency to suit? Indeed why not! You are about to be imparted with my "black art" of I.F. transformer design wherein you will discover that such a casual approach can be quite disasterous! Don't believe me? Read on.
Guess how many technical articles I have read over the years where people have done just that. But don't confuse those with other quite sensible examples of what appears to be casual I.F. design where the author has simply included standard I.F. transformers etc after crystal filters which were followed by wideband amplifiers. The job there was to minimise wideband noise (those amplifiers are wideband).
Here we go, mathematically you can take several approaches to reach the very same end goal. If our IF is 455 Khz and bandwidth is 10 Khz then Qbp = 455 / 10 = 45.5 This is a high number but single filter synchronously tuned stages (as in Fig 1) offer a relaxation on Qbp in accordance with the following formula. Here's why it's a .gif file.
Now if that doesn't frighten you nothing will. Don't worry I'll talk you through it!
The "m" in Fig 2 is for the number of resonators per stage. In Fig 1 there is only one i.e. one coil / capacitor combination. Therefore m + 1 = 1 + 1 = 2. Substituting the number two into the m + 1 position indicates "the square root". If we were using double tuned resonators then m = 2 so M + 1 = 2 + 1 = 3. Substituting 3 in place of m + 1 would indicate the cube root. If we had triple resonators then m + 1 = 4 which is the fourth root or the "square root of the square root".
The "n" indicates the number of stages we have. In fig 1 we have depicted three stages so 1 / n = 1/3 = 0.3333. Now 2 raised to a power of 0.333 = 1.26 (on my calculator the steps are 2 - Yx - 0.333). From the formula were told to subtract 1 which leaves us with 0.26. Because it is a single resonator filter m + 1 = 1 + 1 = 2, so we take the square root of 0.26 which of course = 0.51
That's the hard part over. Earlier I said a 10 Khz wide IF filter at 455 Khz required a Qbp of 455 / 10 = 45.5. This number is NOW multiplied by the 0.51 calculated from Fig 2 which means Qbp = 45.5 X 0.51 = 23.2
If you have done the earlier tutorials on filters you will recall that Z or more correctly R = (2 * pi * Fo * L * Qbp) Typical 455 Khz IF transormers are nominally 680 uH variable inductors resonated by 180 pF capacitors. In this case we get (2 * 3.1416 * 0.455 * 680 uH * 23.2) = 45,101 which is a typical impedance for that kind of transformer.
If the collector load required for the transistor was say 10K then the transformer would be centre-tapped. If the next stage wanted to see 1K then the coupling turns winding would be the square root of 45K / 1K = 6.7 That means the coupling winding or secondary would have 1 / 6.7th number of turns as the primary.
From here on it is a matter of simple algebra to plug in the knowns to derive the unknowns.
An absolutely critical feature, as in all filters, are the terminating impedances.
It is pointless designing a filter which needs to see say 10K, but in fact is terminated in something widely different. You can't argue with the sums above. Don't waste your time.
If you want to experiment with 455 Khz transformers then forget the secondary windings altogether unless you actually do know the turns (pri:sec) ratio. Believe me literally thousands of different types have been produced. Most have yellow cores, some black, some white but for example no two yellow core types with different numbers (if any) on the can will be the same. Typical (but not always) yellow cores had 146 turns centre tapped primary and often 9 turns secondaries, presumably for 2K7 loads or similar. The red cores are most likely oscillator coils of about 90 turns and a nominal inductance of around 120 uH but not for certain. If you're anywhere near serious about filter experimentation and can afford about $100 for an LC Meter Kit then buy Neil's Inductance / Capacitance Meter Kit it's well worth the money believe me. Tell Neil I sent you! No discount, but I'm sure Neil will give you a friendly grin.
Now for a big gotcha!
Remember in earlier tutorials I said the unloaded Q (Qu) should be at least 5 times the loaded Q otherwise insertion losses become prohibitive? Well these IF transformers have Qu's ranging from 80 to 120. That is a limiting factor with experimentation. BTW as an aside when you turn a can upside down and see what looks like a mini coil sunk in the bottom it is in fact the resonating capacitor (probably 180 pF).
Experimentation I think is better done with toroids capable of very high Qu (200T of #15/44 litz wire on a T94-2 core gives Qu of 250 at 450 Khz - 328 uH - as just one example). Generally speaking the larger diameter cores produce the better Qu's and litz wire certainly enhances it but litz wire is very hard to come by in small quantities. Pot cores are another area for experimentation. Manufacturers like Neosid claim very impressive Qu's and variable inductance.
If you are comfortable with maths this is a fascinating topic leading to a whole lot of "what if's" for the serious experimenter. If you do experiment then let me know because I love this topic.
But if you have got this far then send me a courtesy email
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