Calculating RC and understanding the answer.

Discussion in 'General Electronics Chat' started by Fenris, Mar 3, 2011.

  1. Fenris

    Thread Starter Active Member

    Oct 21, 2007
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    Hi Chaps

    I have just built a circuit based on the XR2066 IC. Basically the circuit is a ring modulator. Now currently it's frequency range is from 3Hz to 5kHz. For my needs this range is excessive and the only portion of the scale that is useful is minute.

    What I would Like is a range between 14.5Hz and 42.85Hz. On the data sheet for the chip the math is given as-

    1/RC=Hz

    Now I do struggle a bit with maths but for the past few hours I have used the existing component values to try and understand the answer and have eventually got what seems to be a set of answers that may be correct. Please believe me when I say I am horrific at math

    The capacitor in the circuit is 100nF

    The resistor is 2K2

    The potentiometer in series with the resistor is 2M2

    so the sum for the minimum frequency is -

    1÷((2.2e3)×100e−6) = 4.545454545 or 5kHz?

    For the maximum frequency -

    1÷((2.2×10e6)×100e−6) = 0.000454545 or 5Hz?

    I may be calling the minimum and maximum values the wrong way round. But have I understood and executed the math correctly?

    If I have then I guess I can work out the values required to get the components that will give me the new range of frequencies.

    Thanks for looking

    regards

    Fenris
     
  2. Vahe

    Member

    Mar 3, 2011
    75
    9
    1/(RC) gives you the frequency in radians/second (angular frequency).
    The frequency in Hertz (Hz) is found by f=1/(2∏RC). For example, if
    you choose R=1kΩ and C=1μF, you will get 159.15 Hz.

    Cheers,
    Vahe
     
  3. Ron H

    AAC Fanatic!

    Apr 14, 2005
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    This is true for filter -3dB points. The XR2206 datasheet says F=1/RC for the oscillation frequency of that device.
     
  4. Ron H

    AAC Fanatic!

    Apr 14, 2005
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    100nF is 100e-9, or 1e-7.
    2.2Meg is 2.2e6.

    Minimum frequency is 4.5Hz, maximum is 4.5kHz, as you said (except you swapped max and min).
     
    Last edited: Mar 3, 2011
  5. Fenris

    Thread Starter Active Member

    Oct 21, 2007
    288
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    Hi there

    Phew! I was beginning to panic at the results for a bit there. =)

    OK. It looks like other than swapping my min/max I had the wrong number of 0's. I've done the sums based on the current setup and I get -

    For the maximum, based on the 2K2 resistor and 100nF cap = 4545.4545r

    For the minimum, based on 2M2 pot and the 100nF cap = 4.5454r

    One utterly stupid question. - Is the 4545.4545r the 4.5kHz I just have an issue with understanding the decimal point in this context.

    If I have understood this then the following should give me a range between 14.49Hz - 45.45Hz which if correct would be great -

    For the maximum -

    1÷(220e3×100e−9) = 45.45Hz

    For the minimum -

    1÷((470e3+220e3)×100e−9) = 14.49Hz

    If by some miracle I have this right let me know! Or even if I've got it all wrong =(


    regards

    Fenris
     
    Last edited: Mar 4, 2011
  6. Ron H

    AAC Fanatic!

    Apr 14, 2005
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    4.5kHz means 4.5 kiloHertz. Kilo is the prefix that means x1000. So 4.5kHz=4500Hz, which, after rounding, is the same as 4545.4545. I'm not sure why you are attaching an "r" to the ends of your numbers.:confused:

    Here are the powers of ten prefixes: http://www.knowledgedoor.com/2/units_and_constants_handbook/power_prefixes.html


    Your answers are correct! :D
     
  7. Fenris

    Thread Starter Active Member

    Oct 21, 2007
    288
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    Hi there

    Thank you very much. The r was because the 4545 was re-occurring. I think I may have a handle on it now and as my results are correct...........I fell of my chair at that! Then I am off to buy a 470K potentiometer to get the range sorted.

    Thanks for the link. I have bookmarked it for possible future brain storming.

    I'm seriously chuffed I got there in the end. Albeit with a large prod in the right direction :)

    many thanks again.

    regards

    Fenris
     
  8. bertus

    Administrator

    Apr 5, 2008
    15,648
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    Hello Fenris,

    When you read the datasheet is is better to choose a lower value for the resistor.

    Did you also see the possibility to control the frequency with a voltage?

    Bertus
     
  9. Fenris

    Thread Starter Active Member

    Oct 21, 2007
    288
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    Hi Bertus

    That's a bit of a show stopper then. It's a shame as I chiselled away at it for hours trying to get the math to work or at least get my head to work with it :D

    I 'sort of' saw the alternative method but my brain began to panic, as I do, when I saw the formula.

    EDIT: Just caught your reply at Projectdalek. Of course! Adjust the cap to bring the resistors in into better range. One day I may just 'get it' :D

    regards

    Fenris
     
    Last edited: Mar 4, 2011
  10. SgtWookie

    Expert

    Jul 17, 2007
    22,182
    1,728
    Fenris,
    Please take note of Bertus' suggestion of using a smaller value of resistance in conjunction with a larger capacitor. If your resistors get to be too large (like they are now), then what happens is the capacitor leakage current (particularly with aluminium electrolytic capacitors) comes into play, and really bollixes up your calculations.

    One way to test your capacitors' leakage current is to first discharge it fully (using a low-value resistor or light bulb) and then charge it with a regulated power supply (10v or 12v should be just fine) via a 10k or 100k Ohm resistor in series with the capacitor; let it sit there for a few minutes to stabilize. Measure the voltage across the resistor. Since I=E/R, the voltage across the resistor directly corresponds to the leakage current flow through the capacitor.
     
  11. Fenris

    Thread Starter Active Member

    Oct 21, 2007
    288
    2
    Hi Sgt!

    Indeed I will. I have changed the the resistor and capacitor to more suitable values. As recommended by Bertus. This morning I am off to maplins to get a pot that also compliments the new values which will still give me the 'ideal' range of frequencies.

    The answer was staring me in the face on the data sheet but I just didn't get it. At least I have learnt something though!

    regards

    Fenris
     
  12. Vahe

    Member

    Mar 3, 2011
    75
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    I was not able to find the datasheet for the part. Is the part obsolete?

    I really hate it when formulas are given for approximations and the units don't match. I was just basing my reply on the units only.
     
  13. Ron H

    AAC Fanatic!

    Apr 14, 2005
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    The OP had a typo in the part number. It is XR2206.
     
  14. Vahe

    Member

    Mar 3, 2011
    75
    9
    Thanks Ron. I looked through the datasheet and expressions for frequency. I really don't like to see things like f=1/(RC) - that makes no sense to me. If it was f=1/(2∏RC), I would be happier. Now sometimes based on the characteristics a curve-fit is generated so that one could write something like f=1.44/(R C) or something like that so entering in the R in ohms and C in Farads generates the frequency in Hz. I think this is the case for the 555 timer for example.

    Anyway, I think I should shut up now ... I have seen so many preventable problems based on the 2∏ factor that I should say something.

    Cheers,
    Vahe
     
  15. Ron H

    AAC Fanatic!

    Apr 14, 2005
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    The frequency of almost any RC oscillator is inversely proportional to RC. In this case, the proportionality factor is one. pretty darned handy, I think.:p
    I think you're being anal.:D

    I think I should shut up now...
     
  16. Fenris

    Thread Starter Active Member

    Oct 21, 2007
    288
    2
    Hi there

    Obsolete. Possibly. I have seen one site that says it is no longer recommended as a component to use due to manufacturing having stopped. But it seemed to be news to everyone else when I mentioned this on another forum.

    RS electronics have them in stock though and don't look like they are going to run out any time soon.

    What your saying may be correct but I am afraid it goes over my head. Maths and I just don't get on, much to my ire, but with the help of the gents here I manage to learn something more often than not. The nuances of how and with what are still, and probably always will be, a difficult area for me to navigate.

    Here's a link to to a vid of the unit being tested. This is with the required components to give me the range that is most useful for it's intended use.

    Thanks again chaps. I am in your dept........again! :D

    http://www.youtube.com/watch?v=twMI6mtBtOA

    regards

    Fenris
     
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