# Creating resonance

Discussion in 'Wireless & RF Design' started by Matjelo Naleli, Oct 7, 2015.

1. ### Matjelo Naleli Thread Starter Member

Oct 7, 2015
42
0
Hi guys

I am new in this forum so I'll probably make mistakes of posting where I am not supposed to.

Anyway I have a few questions, with regard to resonant circuits, which I will outline below:

I want to build a resonant circuit with resonance frequency of about 15MHz and a quality factor as high as 1000 or more. The transfer function of the circuit relating input voltage to output voltage can be that of a low pass or band pass or high pass, it doesn't really matter. It can also be of higher orders than 2nd order.

1) With Passive Components:
The series RLC circuit is one way of building a resonant circuit which can achieve resonance frequency of 15MHz. However the Quality factor of this 2nd order resonant circuit is inversely proportional to the resistivity in the circuit. Since inductors or wires in general have parasitic resistivity then it becomes very difficult to obtain quality factor values as high as 1000.

One way to improve the quality factor would be to have a cascade of two or more resonant circuits, each with resonance frequency of 15MHz. In such a configuration the overall quality factor would be the product of the individual quality factors contributed by each resonant circuit. Unfortunately I haven't been able to synthesize the cascade/ladder of even just two resonant circuits with a condition that their resonance frequencies are equivalent. I tried to build a two-stage ladder network with arbitrary impedences and then enforce the contraint of equal resonance frequencies, but the result was either the entire transfer function self-destructs or imaginary values of R,L,C are required. So if anyone has an idea as to how to go about building cascaded resonant filters please point me in the right direction.

2) Active Components
My approach in this case is based on pole placement in root locus. So I resolve my spec into poles and zeros of a desired transfer function which gives the resonance frequency of 15MHz and quality factor of 1000. I then start with some open loop transfer function and determine the root locus gain necessary to move closed poles to the desired positions. After that I then try to realize the open loop transfer function in terms of op amps and passive components, which is quite easy in principle, and implement the feedback.

In most cases the active filters are build mainly with op amps + resistors + capacitors combination. I don't remember seeing an active filter with an inductor connected to the op amp. Of course resistors and capacitors are sufficient to build any transfer function. However the problem comes when one has to design for higher frequencies, given that most op amps that I know gets overloaded by resistances smaller than a few kiloOhms in their output. It becomes very difficult to get resonance frequencies in the order of tens of MHz since avoiding op amp overloading leads to terribly small (or even unrealizable) capacitances which aren't available in standard capacitors.

Mathematically, including the inductors when building these circuits would solve this poblem. However I am not certain of the main reasons why the inductor is never used with the op amp and I need help with that from any one who may have some ideas. I know inductors dissipate a lot more than capacitors but there might be a more stronger reason.

I would also appreciate any general suggestions and links for high Q resonator design including helical resonator design (which I have little knowledge of).

Thank you.

2. ### Wendy Moderator

Mar 24, 2008
21,413
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Welcome to AAC!

A thread belongs to the OP (original poster). Trying to take over someone elses thread is called hijacking, which is not allowed at All About Circuits. I have therefore given you a thread of your very own.

Apr 5, 2008
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4. ### Matjelo Naleli Thread Starter Member

Oct 7, 2015
42
0
My apologies for hijacking someone else's thread.

Oct 7, 2015
42
0
6. ### KL7AJ AAC Fanatic!

Nov 4, 2008
2,181
410
If you cascade tuned circuits, you MUST use very loose coupling between them, or the circuit will be "double humped." Actually the Q of multiple resonant circuits is only multiplied IF they are totally isolated from one another....but you can approach the multiplication principle with a very low coupling factor.

7. ### alfacliff Well-Known Member

Dec 13, 2013
2,449
432
for that high a Q facor, use a quartz crystal. it will be dificult to get an LC circuit that high without silverplating the coil ( use large diameter wire) and knowing how to compensate for everything around it.

8. ### sjgallagher2 Active Member

Feb 6, 2013
128
12
Coupling resonant networks is a very tricky business, if you need proof just look at coupled oscillators in physics! I do not knDow if this is obvious, but there are ways to actively and passively couple resonant circuits- using a capacitor, an inductor or transformer, and of course using active circuitry like BJTs. I think it should be straightforward to find an online resource for coupling resonators. Again, I don't know if you're beyond this, you obviously know your way around filters, but it came to mind! All in all though, a passive network is not really the way to go. A side note, people don't use inductors in active amplifiers because capacitors are simply easy to get a hold of in so many values. If the design calls for an inductor, it not a bad idea to use one (as far as I have ever seen). A crystal would most likely be perfect and inexpensive so that is one suggestion. Other than that, I don't know! Hope I stirred your mind a little bit or helped in some way. Good luck!

Sam Gallagher

9. ### ronsoy2 Member

Sep 25, 2013
67
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You will not be able to get a passive filter working with a Q of more than a few hundred at that frequency. Even a few hundred would require ge specially made inductors. To get the Q you desire you will have to have individual tuned circuits isolated by buffer circuits like an FET follower, so the interaction between the individual circuits is minimized. It may take two or more buffer stages to get to where you can adequately tune the individual circuits to exactly the same frequency. You also will need to contain the circuit in a temperature regulated oven enclosure since temperature variation will cause drift enough to ruin you 1000 Q. It is much better to use different techniques to get that much effective Q than doing it directly. Radio receivers convert the frequency to a lower frequency where a high Q is easy to get.