Lissajou method of power measurements

[jacekkedzierski]

power measurements with scope

Hi!

Has anybody heard about Lissajou method of power measurements? I have a circuit with a strongly capacitive load and I would like to measure the power coupled. Somebody has advised me to do that by means of Lissajou method. It incorporates an additional capacitor in series with my load. Can anbody explain how it works and how to calculate this additional capacity??

Many thanks.

 

[VVV]

lissajou figure area calcuate

Though I have not used this before, I think this is how it works:

P=V*I*cosφ.

You can easily measure V and I, but how do you measure φ ?

To measure φ, the phase angle between voltage and current, you use Lissajous figures. So I would say you need to insert a low resistor in series with your load and the voltage across it will be the current information. So the resistance has to be low enough compared to the load impedance, but high enough so you can get a reasonable voltage across it.
Apply that to one of the scope inputs, preferably Y, since you can adjust ist amplitude more easily (depends on the scope). The voltage across the load is the other signal for deflection, say X.
Then, from the Lissajous figure you determine the phase angle, φ.

With that and the voltage and current measuered accurately, you get the power.

But you have to calibrate your scope first, to make sure that the measurement is accurate. The apparent amplitude of the two signals should be equal. So first apply only the voltage to the scope and record the amplitude, as accurately as you can. If you can adjust it to a certain number of divisions, that is best, if not just record it as accurately as possible. If your scope uses the X amplifier, usually you can only adjust the amplitude in a few steps. Then display only the current and adjust the amplidute (using the steps attenuator and the variable one) to exactly match the voltage amplitude you measured previously.
Then apply both the voltage and current, since you know their relative amplitudes are the same and determine the phase angle from the Lissajous figure.

 

[jacekkedzierski]

phase shift measurements by lissajous figures

Thx for the advise, but this is not what I meant. I'll try to be more accurate.

I have a load which is namely a kind of a capacitor (in deed it is a plasma source) working at high voltages (several kV) and middle frequcies (approx. 10kHz). I need a method to quickly (preferabley "in situ") and accurately measure the power coupled. I have a high voltage probe, Rogowski coil for current measurements, TDS684A scope and some additional equipment.

The method I have found in the literature ("Electrical diagnostics of a macroscopic rf plasma display panel cell" B.Caillier, Ph. Guillot, J.Galy....) comprises a capacitor in series with a load. Than you meassure voltages on both capacities and put on the scope as Lissajou figure. The area inside the figure is proportional to the power coupled. I don't have anything more... How to calculate the power? How to choose this additional capacitor? I don't understand how it is possible to meassure the power on a simple voltage divider.

I would appreciate if you or anybody else could help.

Best regards.

 

[VVV]

I believe the method with the capacitor is basically the same, except the voltage across the extra cap lags the current by 90°. The resistor I was suggesting will have 0° of phase shift and its impedance is not affected by the frequency.

Measuring the power is really measuring the voltage, the current and the phase angle and multiplying them:
P=V*I*cosφ

And I believe the Lissajous figure is used just to measure the phase angle, φ.

Since you have the HV probe and the current probe, why don't you try to do a Lissajous figure using the outputs from those probes, and see if what I said makes sense. The current probe will give you the info you would have read across the resistor. The HV probe will be the other input, for the voltage.
Just try it.

 

[jacekkedzierski]

I got some help from the Electrotechnical chair at my University about this method.

From the voltage over the additional capacitor I get an information about a charge (current - timely resolved) flowing through the system. Having the voltage drop over my load and the charge information in one period (that's why Lissajou figures are used) I can calculate the power. I'll try this today. I'll keep you informed how it works.

Thanks for help

Jacek