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.
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.