Hi, i am studying parallel resonant circuits in school now and am having some trouble with some of the results from a lab I was assigned. The assignment was that given a 2.2mH inductor, calculate the capacitor required for the resonant frequency to equal 10KHz.
The inductor that I used measured 2.197mH and and had a DC resistance of 4 ohms. The value of C that I calculated was approx 115nf. The actual value of C that I used was 112.76nf. These values calulated to give a resonant frequency of 10.1118KHz.
The circuit was constructed using a 4.7K hm: resistor in series with the LC circuit. The source had a 50hm: output impedance. When I measured the maximum voltage across the LC using a DMM and an oscilliscope, I came up with a frequency of 10.83KHz. Why is there such a large difference in frequency? Without using a network analyzer, what is the best way to measure the resonant frequency? Thanks for your help.

 

I wouldn't say that 712Hz is large difference in frequency at 10.11kHz, it's only +7.03% which is pretty good considering the components probably have a tollerance of 10%.

When was the oscilloscope and meter last calibrated?

Does the oscilloscope have a frequency counting function or did you work out the frequency manually?

The multimeter probably wouldn't give an acurate voltage reading as unless it's very expensive, it's only calibrated for 50/60Hz.

Does the meter have a frequency counting function? If so did you use it.

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Thanks for the response. The component values were measured using a GenRad digibridge at school. I made the measurements on the circuit at our lab at work(I work in a calibration lab) using an Agilent 33250A for a source, a 3458A for the DMM and a Tektronix DPO7104 for the scope. I guess that I should probably recheck the measured values of the components to see if they are off from the measurements that I took at school. Is being off by 7% not that much?

 

In Addition to the Possible % Tollerance of the Inductor, There is Also an Internal Capacitance in ALL Inductors.
(Wire to Wire, Internal Capacitance.)

Both these errors will affect your test results.

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I understand that will be some capacitance, but the tolerance of the inductor should not matter, as I measured the value before calculating the resonant frequency. When I get a chance I will remeasure the values at work and redo the calulations. Thanks

 

hi,
Where on the circuit did you connect the DMM and the scope.?

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The Vout was measured across the parallel LC. I remeasured the cap and inductor using a digibridge at work set to 10KHz and after recalculating came up with an error of about 150Hz, which seems more like what I should be getting. The bridge at school is fixed at 1KHz. The reading that I got at work for the inductor at 10KHz was 1.84879mH. Is that because of the capacitance in the inductor?

 

hi,
Whats the effect on the resonant frequency of the tuned circuit due to scope and DMM lead capacitance, while you are measuring..???

EDIT:
Is this link any help.?
http://www.users.cloud9.net/~stark/ctappb.pdf

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Yes, that link helped out. The book that we are using does not go into detail about the real world application and measurements. It would seem that the lead capicitance would lower the resonant frequency a little bit, which is what I experienced here. Thanks all for the help.

 

The issue of cap and inductor tolerances is moot: the guy measured them using a decent LC meter.

The issue of inductor capacitance is most likely moot: the C in his circuit is 115 nF (over a tenth of a microfarad for those in the U.S. not familiar with nanofarads) and it's not likely that the inductor capacitance will affect the circuit's resonant frequency to that extent.

If a 10X probe is being used, I doubt that more than 100 pF will be added to the mix. That's not enough to mess things around. Even a 1X probe will add maybe 500pF.

Here's the real kicker: the guy originally calculated 10.118KHz and the actual circuit resonated at 10.83KHz. ADDING all that supposed capacitance (from the coil and scope system) will LOWER the measured frequency, not increase it.

The next step he took was to remeasure the component values using other equipment (I would have also double-checked using the original equipment just for curiosity's sake) with a more-appropriate test signal. That was the best check he could have made. Things improved a lot.

I'd say that the Agilent DMM will have good frequency response. I don't know the frequency measuring characteristics of the Tek scope in use, but if nothing else, it probably has an output that is a sample of the vertical preamp and that could be fed to a frequency counter for a good cross-check there. With a 150Hz error, you can possibly take some test equipment accuracy specs into account, although that's getting harder and harder to do these days with all this fantastic Agilent and Tektronix equipment available -- and in a school, no less!

I'm just thankful that we have a school that's making the students use real test equipment and having them breadboard real components. Too many schools, even high-end ones, are reverting to Electronics Workbench and all the other similar programs that are laced with errors and problems and give the student absolutely NO experience with real equipment and components.

Dean

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well I have seen all your posts but what is this 4.7k resistor. If you have a schematic please put it on the post.
Really Nice work from a worthy student of so Nice an school.
Congratulations for for applying your self so much to the practical work.

All the best to you.

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It's tough to make measurements on a parallel RC circuit directly connected to the output of a 50 ohm generator. By putting a resistor in series with the parallel RC connection (I'd have probably used a much lower value), you can more-easily measure the tank voltage and see the peak. You can also measure across the resistor and measure a voltage that is proportional to the tank current.

A really-high Q tank circuit operating at a higher frequency would be affected by the insertion of the test leads, and by sticking with measuring across the resistor, you can get a decent measurement of the resonant frequency without affecting the circuit, especially if the resistor is placed in the grounded end.

Dean

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R.I.P.

 

Thanks Dean. Rather forgot after 4 decades of academic education

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Sarma.

 

Well, the equipment like the 3458A and the Tek scope are where I work, although the equipment at the school is not too bad. Our professor prefers that we design our circuits using real components as opposed to using Multisim, so that we can get a better idea of the problems encountered in a real world application. I just wanted to understand where the error was coming from. I will try measuring the resistor and see what happens there. Thanks again.

 

Of course, the resistor will have zero effect on the resonant frequency as long as it's non-inductive.

Dean

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Contributing Editor emeritus, "Q & A", of the former "Poptronics" magazine (formerly "Popular Electronics" and "Electronics Now" magazines).

R.I.P.