# Resonant Circuit with Bandwidth

Discussion in 'Electronics Resources' started by Alexj1402, Apr 22, 2015.

1. ### Alexj1402 Thread Starter New Member

Jan 24, 2015
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0
Hi There,

I am hoping you guys could give me a hand. I have a 120v at all Frequencies, a Capacitor at 100nF

I have been asked to make a circuit to suit 500Hz Bandwidth and 200Hz Bandwidth.

I am a little stumped and have resorted to asking, can i use any frequency or is there another method of working back. I am in need of a little inspiration

Your help will be much appreciated

2. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
I don't have a clue about what you are trying to do. I seriously doubt that you have 120 volts at 403 GHz. Bandwidth of a circuit is only one of two parameters that you need to specify, the other parameter is the center frequency. Keep in mind, that if this is for a powerline application, direct connection to the mains of any circuit is forbidden here by the TOS. The other thing you need to address is if this is a filter, is it low pass, high pass, band pass, or band reject.

3. ### Alexj1402 Thread Starter New Member

Jan 24, 2015
18
0
Hi Papa,

Thanks for the reply. Those parameters i have given were then ones i was told to use, i am just not sure where to apply them to get a full circuit.

It is to create a circuit which has a bandwidth of 500Hz and can be adjusted to 200Hz. If i had another value then i may be able to calculate it but i don't have that

Thanks Again

4. ### crutschow Expert

Mar 14, 2008
13,529
3,393
You can't design a filter with incomplete requirements and you are missing the filter center frequency and the filter type (high-pass, low-pass, or band-pass).
You also need to know the rolloff rate of the filter outside the bandwidth (Q or filter order).

5. ### Kermit2 AAC Fanatic!

Feb 5, 2010
3,858
968
maybe you can start by figuring what freq creates the smallest impedance with the given capacitor value.

6. ### Alexj1402 Thread Starter New Member

Jan 24, 2015
18
0
Hey Guys,

if i only have 500Hz & 200Hz Bandwidth with a 120v supply @ all frequency and a 30nF capacitor.
My train of though would be to use a frequency that will provide me with a low XC value which means it will make the circuit purely inductive which will then provide me with a higher Q Factor and therefore a higher Bandwidth. Would that be correct? Then i can work out the inductance using XC = XL then get the resistance from there

Sorry to be a pain on you guys, i had to take some time away from studying due to family issues and i am finding it a little difficult to get back on track. It is not an excuse just a bit behind.

7. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
Your approach is essentially meaningless. In engineering and computer programming we have a saying that goes "Garbage In Garbage Out". What you get from incomplete requirements is just plain garbage and there is no sugar coating it or trying to put lipstick on a pig.

The statement "120 V supply @ all frequency" is also a piece of garbage.

I challenge you to come up with a supply that provides 120V @ 403 GHz.

We still haven't addressed the question of whether this circuit is connected to the mains. Is it?

Last edited: Apr 22, 2015
8. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
The answer to that is simple. An infinite frequency creates the smallest impedance in a capacitor for ANY value of capacitance.

9. ### Kermit2 AAC Fanatic!

Feb 5, 2010
3,858
968
my aim was to have the OP look up and inspect the equation defining impedance for capacitance and inductance. without a specified resistance the "assignment" is a non-starter. then you have the added insanity of a bandwidth choice.
why not declare a Q value while we're at it?

10. ### Kermit2 AAC Fanatic!

Feb 5, 2010
3,858
968
try this another way.
I have 100 horsepower and 120 miles of road.
How far can I go if I weigh 200 lbs? 500 lbs?

Alec_t likes this.
11. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
I apologize; your subtlety completely escaped me.

12. ### Alexj1402 Thread Starter New Member

Jan 24, 2015
18
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Hi guys,

Sorry i haven't replied quickly. So what you guys are inferring is that there is not enough detail.
• a sinusoidal supply voltage source which has a constant output of 120 volts at all frequencies, and a 30 nF capacitor.
• Design a Series resonant circuit which has a bandwidth of 500Hz and can be modified for 200Hz
Thanks

13. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
First of all there are no inferences, only the following facts.
1. There is no such thing as a voltage source with a constant output at all frequencies.
2. A series resonant circuit requires more than a single capacitor.
3. A series resonant circuit needs to have a center frequency in addition to a bandwidth.

14. ### Alexj1402 Thread Starter New Member

Jan 24, 2015
18
0
I am sorry, i used the incorrect word there and it may have been taken the wrong way.

I have been told to focus on the Bandwidth 500Hz but for the life of me i cannot see how i can go further without at least one other component.

15. ### Alec_t AAC Fanatic!

Sep 17, 2013
5,980
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You can't. And we can't go further to help you unless you can supply the other info requested .

16. ### Papabravo Expert

Feb 24, 2006
10,340
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No problem, I was just trying to state the facts as I saw them. I believe that your conclusions are the correct ones. If you had another component and that component was an inductor, and we knew it's value, then we could calculate the series resonant (center) frequency and the bandwidth. Does that help you?

17. ### Alexj1402 Thread Starter New Member

Jan 24, 2015
18
0
Thanks Papa, i do get this. I have a good knowledge of it and the only reason i am asking is i may have overlooked something which you guys may be able to assist with.

I really do appreciate your help, all of you.

18. ### Alexj1402 Thread Starter New Member

Jan 24, 2015
18
0
Sorry to revive a slight aged thread.

I have come back with new information.

So:
• 120v @ All Frequencies - This means i can select any Frequency i like since it is a resonant frequency (I will used 800Hz as an example)
• 100nF Capacitor
So XC = 1 / (2 x pi x 800Hz x 100 x10-9) = 1989.436 Ohms
At Resonant XC = XL so L = XL / 2 x pi x 800 = 395.78 mH

Am i right in thinking that at the Upper Cut Off Frequency R = XC?

So XC = 1 / (2 x pi x 1050Hz x 100 x10-9) = 1515.761 Ohms Since the resistor is constant
Q Fact0r = XL / R --> 1989.436 / 1515.761 = 1.312
Bw = Fr / Q --> 800Hz / 1.312 = 609Hz Approx

This gets me very close to where i need to be within the simulation values. If i wanted to get closer would i need to adjust my rounding values?

My Fr on this is equal to 814 Hz
Fh = 540Hz
Fl = 1.173kHz

Am i missing something or am i on the right track?

Thanks again!

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19. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
I did not check all of the calculations but I agree with the center frequency and the bandwidth. You do realize that a circuit with lumped parameters may not behave as the graph shows in the vicinity of 1 GHz. 1 Hz. to 100 kHz. would have been more than sufficient for the horizontal scale. 200 dB is also overkill on the vertical scaling, and 60-80 dB is plenty good enough.

20. ### Alexj1402 Thread Starter New Member

Jan 24, 2015
18
0
Hi Papa,

I used the standard settings just to show you instead of explaining everything that i have done. My aim is to get a 500Hz bandwith and i got a 609Hz bandwidth, Can i just do something as simple as drop the frequency or is there a specific calculation to fin the ideal frequency since this method of "Trial and Error" on the first attempt has come up pretty successful?

With the suggestions given, on the simulation i look much closer to the mark on this time around than i did before.

So on the graph
FR = 800Hz
FH = 554Hz <--- -246Hz
FL = 1.171 kHz <-- + 371Hz

Thanks

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