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15th October 2019, 17:59 #1
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Calculate Capacitance Value from Smith Chart
How do I convert 50.04j77.16 on a 50 Ohm Smith Chart to a capacitance value of 10.1pF?
Using GQM2195C2E100JB12

15th October 2019, 20:19 #2
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Re: Calculate Capacitance Value from Smith Chart

16th October 2019, 03:34 #3

16th October 2019, 03:52 #4
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Re: Calculate Capacitance Value from Smith Chart
The smith chart for that cap shows you that at 205MHz it is 10pF ( 77 ohm ) and 50 ohm resistive ...
Last edited by Easy peasy; 16th October 2019 at 03:58.

16th October 2019, 06:33 #5
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Re: Calculate Capacitance Value from Smith Chart

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16th October 2019, 06:49 #6
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Re: Calculate Capacitance Value from Smith Chart
the Smith chart is for a specific 10pF cap, that is clue #1, it is not explicitly shown on the Smith chart, but the 77 ohm at 205MHz gives you 10pF, presumably at very high freq the series L would reduce this figure ....

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16th October 2019, 07:31 #7
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16th October 2019, 08:31 #8
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Re: Calculate Capacitance Value from Smith Chart
he reactive part is 77.16 ohms, this is the sum of the Xc & XL, at 205MHz it is basically all capacitive so yes = Xc

17th October 2019, 02:39 #9
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17th October 2019, 03:45 #10
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Re: Calculate Capacitance Value from Smith Chart
respectfully  even if there is loads of resistance as there is here  50 ohm in fact  the Smith chart tells you the reactive impedance AND the resistive impedance hence 50j77 ohm ...

17th October 2019, 06:20 #11

17th October 2019, 07:45 #12
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17th October 2019, 16:10 #13

17th October 2019, 18:45 #14
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Re: Calculate Capacitance Value from Smith Chart
chiques, my comment was for BradtheRad and his comment. He missed that you specified the proper complex value.
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18th October 2019, 06:16 #15
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Re: Calculate Capacitance Value from Smith Chart
Here's the second half of my simulation. I increased ohmic resistance to 77 ohms, to see if
capacitive impedance still indicates 77 ohms according to the raw XC formula.
We expect it should create a twin 77/77 divider. We expect it to halve the 1V AC source. It does not. (It appears to be 0.5 multiplied by the square root of 2.)
At right, the upper resistor was adjusted so output amplitudes match. The upper resistor needs to be 32.3 ohms, which tells us that's the effective impedance of the capacitor.
It's not expected when we see that the only variables are Farads and frequency in the XC formula.

18th October 2019, 08:32 #16
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18th October 2019, 14:42 #17
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Re: Calculate Capacitance Value from Smith Chart
Yes, it would all be simpler if I'd seen only the calculator at the 'allaboutcircuits.com' webpage (post #2).
1/(2 ∏ f C)
The XC formula would be sufficient and I'd be happy to leave it at that.
In addition however is a formula which complicates things: √(R^2 + XC^2). This is where the phasor diagrams (parallelogram angles) come in. And the capacitive impedance appears to take on a new value.
Example, this site (with screenshot):
http://www.electronicstutorials.ws/...pacitance.html

18th October 2019, 15:04 #18
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Re: Calculate Capacitance Value from Smith Chart

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18th October 2019, 20:50 #19
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Converting Real+Imaginary to Z from Smith Chart
This is related to this post
What is the formula/steps to convert from the (Real + Imaginary) value to the Z?
The complex value is (0.37j.48) and the Z is 50j77.16
   Updated   
Disregard, solved it.

19th October 2019, 04:05 #20
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Re: Calculate Capacitance Value from Smith Chart
Even if I were experienced at calculations with imaginary numbers and complex impedances, it's obvious I would need to learn more in order to account for the results of my Wheatstone bridge experiment (post #15). Isn't there more than meets the eye here?
Your simulation has the calculation of capacitor volts divided by capacitor current, to arrive at an impedance value. It's hard to argue with that. However, can we rely on the XC formula as our only guide? Nomenclature and formulas are a construct which we devise to explain reallife observations. What if we wish to calculate an ordinary RC filter? I think my simulation is hard to argue with too.
Of course we're careful to start with proper specifications for complex impedance and imaginary numbers. I'm not sure we can determine our Farad value exclusively from the XC formula, except if we factor in something else besides.
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