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Does a capacitor charges smooth, or in stairs?

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StillTrying:
Are you viewing the open circuit end of the cable rather than the driven end, I don't know why your first step is so high in Reply#49.

RoGeorge:

--- Quote from: rhb on June 10, 2020, 06:50:07 pm ---OK  These are with a Tek 11801 & 20 GHz SD-24 sampling head.  I fed the coax stub through a 150 ohm resistor.

10-12 ft coax

(Attachment Link)

50 cm



16 cm

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(sorry about the burred image.  I didn't notice it until I posted it)

(Attachment Link)

The 250 mV step has a <20 ps rise time.  The only thing changing is the travel time and the capacitance.  As the coax has approximately the same capacitance per foot, the number of steps stays constant and the only thing that changes is the time delay for each step.  If I expand the vertical scale a lot I can count about 13 steps before the steps fall below the noise and quantization.

Q.E.D.
Quod erat demonstrandum. 
It has been shown.

Have Fun!
Reg

--- End quote ---

Wow, the cleanest stair-steps reflections I have ever seen!   :-+

Can you repeat the experiment with a real life capacitor, too, to see if the stair-steps on a capacitor are as visible as the ones seen on the coax cable, please?

Not sure what type and value of a capacitor will be the most advantageous for the experiment, maybe one with large physical dimensions, and with the plates rolled in a cylinder, rather than a tantalum or a MLCC.

rhb:

--- Quote from: StillTrying on June 10, 2020, 07:35:06 pm ---Are you viewing the open circuit end of the cable rather than the driven end, I don't know why your first step is so high in Reply#49.

--- End quote ---

This is the reflected signal seen at the driven end.  The other end of the cable is open.  So each step is a 2 way trip down the cable and back to the source end.  Without the resistor it would be two big steps. This is the corner of the 2nd big step produced by an open circuit line.   Take a look at my "Testing RF connectors and cable"  thread.  There are lots of examples of various tests there.

RoGeorge, Let me think about how to make a test that is not obscured by other artifacts.  As the line length gets short things start getting complicated by parasitic inductance.

If I double the resistance it should double the time constant and the number of steps.  I think that a 1500 ohm resistor and the same piece of RG402 as my last photo would be the best.  That should show >100 steps and still be resolvable.

Have Fun!
Reg

rhb:
I don't think any capacitors are designed to be constant impedance. Certainly rolled foil capacitors cannot be as the diameter is constantly changing.  So both the capacitance and inductance per turn is changing constantly from one end to the other.  In addition there is inductive and capacitive coupling from layer to layer.

The changing impedance is going to produce  a continuous series of small reflection events rather than large discrete events at the ends.    That will tend to make the response look like a piece wise linear approximation to an exponential rather than a stairstep approximation and thus very difficult to show clearly.  The stairstep is the result of the derivative of the impedance being zero except at the ends.

A flat microstrip transmission line of trapezoidal shape would be the simplest way to demonstrate the effect of changing impedance along the transmission line.

The point here is that the exponential is a series of small steps once one takes the finite dimensions of the capacitor into account.  And in the limit as the size becomes infinitesimal, it becomes an exponential.

It's probably easier to calculate the response of a hypothetical capacitor than to measure the effect in a real one.

Reg

T3sl4co1l:
Like I said, the electrical length of a typical film or ceramic capacitor is so short, and the impedance so low, that you'll be lucky to observe anything, even with a ps scale generator and scope.

Tim

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