Download Stochastic error: Its behaviour is random from measurement

1. What means the term “measurement”?
Measurement is the estimation of the quantity of certain value (with known uncertainty) by
comparison with the standard unit.
Main terms:
estimation
measurement
uncertaintity
standard unit
2. Main standard units of SI system:
SI system of units:
7 main units and derived units from them.
All quantities and their units are collected in the ISO (International Standard Organization)
standard.
3. What the term “error” means? Cassification of errors.
Error is the difference between the reading (measured) value and real value.
Sometimes not the difference but its magnitude.
Systematic error: Its behaviour is deterministic, it is present in the same way in every
repeated measurement. Example! (shift)
Stochastic error: Its behaviour is random from measurement to measurement. Example!
(scattering)
4. What means accuracy, giving it in relative and absolute way
The error could be given in two ways:
Absolute way, like: 125 V +-2V
It means that real value more than 123 but less then 127
Relative to the real or to the measured value: 125V+-2%
Meaning of the error could be different:
-
limit or range
average error
standard deviation (appr. 68% probability that real value is within 1 SD, 95% that
within 2 SD, 99,8% within 3 SD)
others
Accuracy: Error of the instrument, when you measure once. It depends on range.
from manual:
0-20V ----- 0.5% +1digit
First term is relative SD of the reading value.
Second term is the error of the last digit seeing on the display.
Example:
Reading value is 15.6V within 0-20V range.
1% 0,156 0,2V
15.6V+-0,2V with 68% prob.
Error of counting: (1/156)*100%=0,6% means app. 0,1V.
Within 1 SD there is no significant difference between the 2 results.
If you repeat the same measurement N-times, you can calculate the result and assume the
error.
Result equals to mathematical mean:
x
1
N
 i 1 xi
N
SD of the measured data:
SDdata 
N
1
2
  xi  x 
N  1 i 1
SD of the result:
SDresult 
SDdata
N
Result should be given as the mean and +- SD_result and should be rounded according to the
magnitude of the error.
6. Multimeter basics:
7. What is the meaning and the importance of
RMS value of an alternating signal?
Alternating Current (AC)
Alternating Current (AC) flows one
way, then the other way,
continually reversing direction.
An AC voltage is continually changing
between positive (+) and negative (-).
AC from a power supply
This shape is called a sine wave.
The rate of changing direction is called
the frequency of the AC and it is
measured in hertz (Hz) which is the
number of forwards-backwards cycles
per second.
Mains electricity in the UK has a
frequency of 50Hz.
This triangular signal is AC because it changes
between positive (+) and negative (-).
An AC supply is suitable for powering
some devices such as lamps and heaters but almost all electronic circuits require a
steady DC supply (see
Properties of electrical signals
An electrical signal is a voltage
or current which conveys
information, usually it means a
voltage. The term can be used
for any voltage or current in a
circuit.
The voltage-time graph on the right
shows various properties of an electrical signal. In addition to the properties labelled
on the graph, there is frequency which is the number of cycles per second.
The diagram shows a sine wave but these properties apply to any signal with a
constant shape.

Amplitude is the maximum voltage reached by the signal.
It is measured in volts, V.




Peak voltage is another name for amplitude.
Peak-peak voltage is twice the peak voltage (amplitude). When
reading an oscilloscope trace it is usual to measure peak-peak
voltage.
Time period is the time taken for the signal to complete one cycle.
It is measured in seconds (s), but time periods tend to be short so
milliseconds (ms) and microseconds (µs) are often used.
1ms = 0.001s and 1µs = 0.000001s.
Frequency is the number of cycles per second.
It is measured in hertz (Hz), but frequencies tend to be high so
kilohertz (kHz) and megahertz (MHz) are often used.
1kHz = 1000Hz and 1MHz = 1000000Hz.
frequency =

1
time period
and
time period =
1
frequency
Mains electricity in the UK has a frequency of 50Hz,
so it has a time period of 1/50 = 0.02s = 20ms.
Alternating currents are accompanied (or caused) by alternating voltages. An AC voltage v
can be described mathematically as a function of time by the following equation:
,
where



is the peak voltage (unit: volt),
is the angular frequency (unit: radians per second)
o The angular frequency is related to the physical frequency, (unit =
hertz), which represents the number of cycles per second, by the
equation
.
is the time (unit: second).
The peak-to-peak value of an AC voltage is defined as the difference between its positive
peak and its negative peak. Since the maximum value of
value is −1, an AC voltage swings between
and
voltage, usually written as
or
is +1 and the minimum
. The peak-to-peak
, is therefore
The relationship between voltage and the power delivered is
where
represents a load resistance.
.
Rather than using instantaneous power,
, it is more practical to use a time averaged
power (where the averaging is performed over any integer number of cycles). Therefore, AC
voltage is often expressed as a root mean square (RMS) value, written as
, because
For a sinusoidal voltage:
The factor
is called the crest factor, which varies for different waveforms.

For a triangle waveform centered about zero

For a square waveform centered about zero

For an arbitrary periodic waveform
of period
:
Example
To illustrate these concepts, consider a 230 V AC mains supply used in many countries
around the world. It is so called because its root mean square value is 230 V. This means that
the time-averaged power delivered is equivalent to the power delivered by a DC voltage of
230 V. To determine the peak voltage (amplitude), we can rearrange the above equation to:
For 230 V AC, the peak voltage
is therefore
, which is about 325 V. The
peak-to-peak value
of the 230 V AC is double that, at about 650 V.
8. Oscilloscope
What is the function of Trigger?
What is the function of Coupling?
What means Y-T mode, X-Y mode?
What means and how to set horizontal and vertical resolution?
How to measure time period, frequency, voltage (rms, peak) with the
oscilloscope?
How to connect oscilloscope into the circuit?