# calculate the Q factor of LC bandpass

Discussion in 'Electronic Design' started by power boy, Mar 9, 2013.

1. ### power boyGuest

Hi:

Anybody knows how to calculate Q factor for LC bandpass?
checked many online pdfs and books but got nothing.

the circuits is

----------Ls---Cs------------
| |
Lp Cp
| |
--------------------------------

We know there are too many types but I just want to know if all values
are given,
how to calculate the Q or BW. f0 is easy to calculate but I forget how
to calculate Q.

Thanks.

2. ### rickmanGuest

The Q relates to the resistance relative to the reactive components. Do
you know the values for your resistances? It will depend also on
whether you model the resistances as parallel or serial to the other
components. Typically the L will have an ESR (equivalent series
resistance). But if you are working at high frequencies such as power
supply distribution, for example, the ESR of the capacitor might be the
significant factor.

I just solved the equations for resonance of this circuit. But I left
out the R values to simplify the math. With typical Q values the R does
not change the resonance significantly.

What formula do you use for f0?

3. ### Phil AllisonGuest

"power boy"

** You sure about that schem?

..... Phil

4. ### Guest

In order to calculate the Q for the individual section, you still
would have to know the parasitic components, usually the series
resistance of the inductor. From there calculate separately the Q for
the series LC as well as separately for the parallel LC.

5. ### LeeGuest

I omitted the series source resistor Rs and load resistor RL in the
schematic. As I said, there are many types of LC bandpass. When you do
a design:
1. you can convert LC bandpass from LC low pass.
2. you can get a book, they tell you a chart, you calculate the
attenuation, and ladder # to get a bandpass type, sometimes you have
to convert based on LpCp=LsCs the fundamental equation. (chebychev,
butterworth, elliptical, linear phase, bessel, gaussian, constant-K,
etc), then convert from basic topology to final circuit.

But if all values a given, you simulate and find this is a bandpass,
you want to calculate the Q or Bw. How can you do? I couldn't find a
formula to do this.
I can find RLC series bandpass formula and RLC parallel(resonance)
formula.

6. ### power boyGuest

I omitted the series source resistor Rs and load resistor RL in the
schematic. As I said, there are many types of LC bandpass. When you do
a design:
1. you can convert LC bandpass from LC lowpass.
2. you can get a book, they tell you a chart, you calculate the
attenuation, inband ripple, and ladder # to get a bandpass type, sometimes you have to convert based on LpCp=LsCs the fundamental equation. (then find type like chebychev,
butterworth, elliptical, linear phase, bessel, gaussian, constant-K,
etc), then convert from basic topology to final circuit.

But if all values are given, you simulate and find this is a bandpass,
you want to calculate the Q or Bw. How can you do? I couldn't find a
formula to do this.
I can find RLC series bandpass formula and RLC parallel(resonance)
formula.

7. ### rickmanGuest

I'm no expert on filters, but my undestanding is that each of the two
sections, series and parallel, are resonant at some frequency with
bandwidths defined by the resistances in the circuits. When you connect
the two with the input across the two terminals on the left of your
diagram and the output across the parallel cap and inductor on the right
of the diagram, you get two peaks of resonance defined by all four
components. The Q of each peak is again defined by the resistance. To
the best of my knowledge this is *not* a band pass circuit. I wrote the
equation for this circuit in by treating it as a voltage divider using
the impedances of the parallel and series circuit. When you solve the
equations you get two roots, so two resonances. I only did this with
the reactive components and ignored the resistance. The resistance
makes the math a lot more complex. Feel like solving some very messy
equations?

Vout/Vin = Zp/(Zp+Zs) I'm sure you can find the equations for Zp and
Zs. If not I can provide them. Radiotron Designer's Handbook, very
old, but science doesn't change much. Download this and go to page
number 193 in the PDF (labeled 152 in book), section E. Z1 and Z2 are
Zs and Zp. Construct the formula above and find the roots... simple
right? Well, actually that gives you the resonances, but not the Q. I
don't actually know how to figure the Q in this circuit. That's another
section of this book I haven't read completely...

Neither of these sets of components are low pass filters, so I don't
know why you refer to converting from a low pass to a band pass. I
guess if you drop Cs and Lp you get a low pass...

As someone else said, are you sure you have the schematic right? Move Cp
to the point between Ls and Cs and you get a band pass... or a band
reject... But then they wouldn't be named with s and p for series and
parallel, would they?

If this is a band pass with Q not defined in terms of the resistance, I
don't get it.

BTW, try simulating this. I'm pretty sure you will get two peaks.

8. ### rickmanGuest

I *did* the math. This circuit has two peaks in response. This morning
I went back to the equations to see if/when the two peaks could overlap
to form one peak. The discriminant can't be zero with positive values
of inductance and capacitance, so the circuit will *always* have two
peaks and is never a simple band pass.

The width of each of the two peaks is defined by the resistances in the
circuit.

The amazing thing is that all this algebra is giving me flashbacks to
high school math class. I keep hearing, "What's a zero and who cares
about finding them?" I wonder who was saying that...

9. ### rickmanGuest

I can show my work if I have to. I flunked my first physics test at UMD
because I didn't show my work. I was not a happy camper.

10. ### josephkkGuest

I can usually do 1 pole in my head. Two poles to 4 poles i can do with
pencil and paper. Beyond that i don't bother, i use table based design or
software. Never had to go past 8 poles, but that was a bitch to tune with
10% parts.

11. ### josephkkGuest

A single peak is possible in theory. It is not likely to be realizable in
production quantities. Doing it one off may be reasonably achievable.
(How close do the peaks have to be before you cannot tell then apart? /
How good is your measurement gear?)

?-)

12. ### o pere oGuest

It is easy, at least if you are not too stringent on the fractional
bandwidth of the bandpass filter. If you want a narrow filter, with this
approach you end up with unrealistic component values, and have to
resort to the coupled-resonator approach.

Pere

13. ### josephkkGuest

I'll bet you even still remember all the neat tracks that you can do with
a complex Riemann sphere.
My favorite filter system is inverse Chebychev.

14. ### Fred AbseGuest

If it has, pleas tell me how. I'm pissed off with having to use Berkeley
Spice 3f to do PZ analysis.

15. ### josephkkGuest

I would literally try the same file in LTSpice. It may work. And you
should get some possibly helpful diagnostic messages if it doesn't. This
should work best from CL.

?-)

16. ### josephkkGuest

Gosh, you mean you didn't learn about interesting transforms of the
complex frequency plane (rotations of the complex Reimann sphere before
transforming back)? It can be handy for understanding going between s and
z transforms.
Well my favorite trick is placing the maximum attenuation notches just
where i want the to block narrowband interfering signals. Like harmonics
of power line frequencies. Then if needed another filter could restore
much of the pass response in the stop band (initial design has to be low
minimum stop band loss. They are also fairly good at approximating a
brick wall filter with high minimum stop band loss. I think the phase is
well behaved in the pass band as well.

I would have to find my book of tables to setup some spice examples.

?-)

17. ### Fred AbseGuest

I did. It didn't.

18. ### rickmanGuest

I can see I'm going to have to separate Phil and Jim, but this isn't
even *your* discussion! You will just have to stay after class in
detention.

Rick

19. ### josephkkGuest

Oh well. If it is not secret perhaps you could send me a copy of the file
and let me tinker it a bit. I might figure it out.

?-)

20. ### josephkkGuest

For what it is worth, i remember it as rickman claiming only two peaks is
possible. Please recheck the thread.

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