How to quantify relatively simple experimental errors

Discussion in 'Homework Help' started by urb-nurd, Feb 9, 2015.

Jul 9, 2014
269
3
For my coursework task, i am to quantify and discuss errors associated with an experimental procedure. This involved a thyristor control unit which allowed the firing angle of two thyristors (in a half controlled bridge rectifier) to be varied with a rotary dial or pot/rheo.

The image above shows the hardware and the connection diagram supplied.
The output of the bridge was measured with a digital voltmeter.
This output voltage was recorded at various firing angles where the angle is determined on an oscilloscope trace.
Theoretical calculations were also carried out from the formulae : Vout = (√2 * Vrms) / π)*(1+cos(α))
Where Vrms is the measured AC input value and alpha corresponds to the firing angle.
These theoretical values are to be plotted over a range of 0-180 degrees on a graph along with the measured values.
I am tasked to quantify the error associated with the procedure and equipment so as to calculate an overall error. The total error is to be represented by error bars on the graph showing theoretical results and measured results.
My question, is what errors can be quantified here?
I know there is an error associated with the volt meter - ± 1/2 of the least significant figure.
This causes an inherent error in my theoretical calculation i believe.
The firing angle of the half controlled bridge is determined on the oscilloscope, introducing a measurement error of ± 1/2 of the lowest resolution on the scale. For my set up, this is ± 4.5 degrees.
The volt meter output also fluctuated quite a-lot when taking readings causing my recorded voltages to be no more than an approximation of the average value, also due to time constraints of the lab - i have been limited to a single set of measurements I believe these to be to be the dominant quantifiable errors - Voltage reading and angle reading that is.

I think i have quantified the errors appropriately:
Voltmeter error = ±0.5V (half the least significant figure of the output)
Firing Angle reading error = ± 4.5 degrees (given that my scope is set to 9 degree per sub unit and 25 per unit on the scale).
If these two errors are agreed to be the dominant and relevant errors associated with the circuit above, how can i display these correctly as error bars?
I know my theoretical calculations have a level of error based on the error of measured voltage value that the formula utilizes. Is it correct to display this as vertical error bars on my theoretical line? (the percentage error is 0.4% in the theoretical calculation)
The measured values also have this voltmeter error along with an error in reading the corresponding firing angle. How can i combine these two to produce a total error? Or do i display these two errors on their relevant axis oriented error bars? given that the error in angle reading can be displayed as a horizontal error bar on the measured values in the graph, and the voltage reading error can be displayed as vertical error bars on the measured values in the graph.

Any information or advice that may help me understand where to go from here is greatly appreciated! I apologize for any inadequacies or errors in my formatting. Thanks !

2. WBahn Moderator

Mar 31, 2012
18,085
4,917
Read the specs on your voltmeter. You will almost certainly find that the error has two components, one of which is a fraction of either the reading or of full scale on that range and the other is the number of least significant digits. Whichever is larger is the one that you need to use. Don't assume that your meter is accurate to the last digit displayed -- it isn't.
The same with your scope -- don't assume a level of accuracy that isn't justified. Read the specs.

Jul 9, 2014
269
3
Thanks for the input.
The type of voltmeter that was used is so old that i cannot find a datasheet.
Additionally, the scope accuracy was investigated - for this circuit, the vertical error of the scope causes no change in results - the Voltage is read from the dedicated meter.
I didn't think there to be an appreciable error in the timebase of the scope.

Thanks again

Last edited: Feb 9, 2015
4. WBahn Moderator

Mar 31, 2012
18,085
4,917
What's the basis for you not thinking there is appreciable error in the time base of a scope that is so old that you can't find any information on it?