Lab 4: AC voltage and current measurements [Metrology - laboratory]
AC voltage and current measurement
1. The aim of the lab
The main aim of this lab is to acquaint students with AC measurement.
2. AC signal values: Vpp, Vp or VMAX, -Vp or VMIN, VRMS, VAVG
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The amplitude of an AC waveform is its height as depicted on a graph over time. An
amplitude measurement can take the form of peak, peak-to-peak, average, or RMS
quantity.
Peak amplitude is the height of an AC waveform as measured from the zero mark to the
highest positive or lowest negative point on a graph. Also known as the crest amplitude
of a wave.
Peak-to-peak amplitude is the total height of an AC waveform as measured from
maximum positive to maximum negative peaks on a graph. Often named as “p-p”.
Average amplitude is the mathematical “mean” of all a waveform’s points over the
period of one cycle. Technically, the average amplitude of any waveform with equalarea portions above and below the “zero” line on a graph is zero. However, as a practical
measure of amplitude, a waveform’s average value is often calculated as the
mathematical mean of all the points’ absolute values (taking all the negative values and
considering them as positive).
“RMS” stands for Root Mean Square, and is a way of expressing an AC quantity of
voltage or current in terms functionally equivalent to DC. For example, 10 volts AC
RMS is the amount of voltage that would produce the same amount of heat dissipation
across a resistor of given value as a 10 volt DC power supply. Also known as the
“equivalent” or “DC equivalent” value of an AC voltage or current. For a sine wave, the
RMS value is approximately 0.707 of its peak value.
Lab 4: AC voltage and current measurements [Metrology - laboratory]
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The crest factor of an AC waveform is the ratio of its peak (crest) to its RMS value.
The form factor of an AC waveform is the ratio of its RMS value to its average value.
Analog, electromechanical meter movements respond proportionally to the average
value of an AC voltage or current. When RMS indication is desired, the meter’s
calibration must be “skewed” accordingly. This means that the accuracy of an
electromechanical meter’s RMS indication is dependent on the purity of the waveform:
whether it is the exact same wave shape as the waveform used in calibrating.
3. AVG (Average) value calculation
General equation for calculate the average (AVG) value of periodic signal V(t):
𝑉𝐴𝑉𝐺
1 𝑇
= ∫ 𝑉(𝑡)𝑑𝑡
𝑇 0
For sinus, we have V(t) = Vp*sin(t) :
𝑉𝐴𝑉𝐺
1 𝑇
1 𝑇
1
= ∫ 𝑉𝑝 sin(𝑡) 𝑑𝑡 = 𝑉𝑝 ∫ sin(𝑡) 𝑑𝑡 = 𝑉𝑝 [− cos(𝑡)]2𝜋
0
𝑇 0
𝑇 0
𝑇
1
1
= 𝑉𝑝 (− cos(2𝜋) − (− cos(0)) = 𝑉𝑝 (−1 − (−1)) = 0
𝑇
𝑇
4. RMS (Root Mean Square) value calculation
General equation for calculate the root-mean-square (RMS) value of periodic signal V(t):
𝑉𝑅𝑀𝑆 = √∫
𝑇
0
1
(𝑉(𝑡))2 𝑑𝑡
𝑇
In case of a periodic sinusoidal voltage V(t) = Vp sin(t) with a period of T. Then we can
calculate the RMS value of a sinusoidal voltage as:
2𝜋
1
1 2𝜋
1
𝑡 1
2
2
√
= √∫ (𝑉𝑝 sin(𝑡)) 𝑑𝑡 = √𝑉𝑝
∫ (sin(𝑡)) 𝑑𝑡 = 𝑉𝑝
[ − sin(2𝑡)]
2𝜋 0
√2𝜋 2 4
0
0 𝑇
𝑇
𝑉𝑅𝑀𝑆
2𝜋 1
0 1
− sin(2 ∗ 2𝜋)) − ( − sin(2 ∗ 0)
2 4
2 4
√2𝜋
𝑉𝑝
1
1
√(𝜋 − 0) − (0 − 0) = 𝑉𝑝
= 𝑉𝑝
≈ 0.7 ∗ 𝑉𝑝
√𝜋 =
√2𝜋
√2𝜋
√2
= 𝑉𝑝
1
√(
Lab 4: AC voltage and current measurements [Metrology - laboratory]
5. Tasks for you
1. From general equations derive the formulas for VAVG, VRMS for two kind of square
signals: first signal - values from 0 to +Vp; second square signal - values from -Vp to
+Vp (draw signals with period T and derive the formulas using the integrals).
2. Derive the formula for VAVG, VRMS for triangle signal - values from -Vp to +Vp (draw
signal with period T and derive the formulas using the integral for two functions: for a
linear rising edge and for a falling edge in the right range).
3. Read signal from oscilloscope, determine +Vp, -Vp, Vpp, VAVG, VRMS.
4. Read signal from oscilloscope, determine +Vp, -Vp, Vpp, VAVG, VRMS
(first derive the formula for VAVG, VRMS for square signal in p.1)
5. Calculate the value Vpp for AC home power supply voltage 240V.
6. Using a digital multimeter Metex M-3850 (DMM) we read the AC voltage value 240V
(at range 400V). What is the measured value of voltage and what is an accuracy
(measurement uncertainty) ?
Lab 4: AC voltage and current measurements [Metrology - laboratory]
If we use a digital meter, accuracy is calculated according to the formula and data provided by
the manufacturer:
𝑎𝑐𝑐𝑢𝑟𝑎𝑐𝑦 = ∓(% 𝑜𝑓 𝑟𝑒𝑎𝑑𝑖𝑛𝑔 + 𝑛 ∗ 𝑑𝑔𝑡)
For example information from data manual for Metex -3850
6. Report
a) make 1-6 of "Tasks for you".