ME 365
To:
From:
Re:
Date:
POST-LAB EXERCISE FOR LABORATORY 1
FALL 2014
ME365 Student
Andy Dufresne, Ellis Corp.
Digital Multimeters
August 18, 2014
1. RMS value of a sine wave with DC offset
As we discussed briefly on the phone, we are having some difficulty understanding
readings from a DMM. First, we couldn’t figure out how a DMM calculates RMS value of a sine
wave with DC offset. When we applied an input of x(t )  3  5sin 100 t  , our DMM
displayed the RMS value of 4.6368 V. However, when we calculated the RMS value of the input
signal by summing the RMS value of the DC component (3 V) and the RMS value of the AC
component (5 2 = 3.5355 V), we obtained 6.5355 V. Is our DMM evaluating RMS value
accurately or am I making some calculation mistake? To verify the results, we tried to calculate
the RMS value of the signal by using the following formula:
VRMS 
 2
 T
, where x(t )  A0  A sin 
1 T
2
x(t ) dt


T 0

t  and T is time period ( A0 is the DC offset).

2
2 

t )   A sin( t )  , we couldn’t finish
T
T 

integration due to the squared sine term. Can you finish the derivation by hand and tell us the
accurate RMS value for the input signal? Your derivation should start form the general form of
After expanding x(t ) as A0 2  2  A0  A sin(
2
 2
x(t )  A0  A sin 
 T
2

t  . After you finish the derivation, plug the numbers to see which result

is right. (HINT: Use a trigonometric identity to get rid of the squared sine term.) Please show us
details of your calculations in a separate attachment.
2. New purchase of DMM
We are currently considering a new purchase of DMM. Our limited budget only allows
us to buy one of two DMM models available in the market today: MEC–2001 and HAN–2010. I
have included their technical specifications in Table 1. Normally, we would have automatically
chosen the more accurate HAN–2010, but we were persuaded by the makers of the MEC–2001 to
test-drive their product with the assurance that it was better suited to our needs. We are going to
use these multimeters to measure DC voltages and RMS values of AC voltages in the range of a
few volts.
1
ME 365
POST-LAB EXERCISE FOR LABORATORY 1
FALL 2014
We first looked at the performance of the DMMs in measuring DC voltages by setting up
in a circuit shown in Figure 1. When we measured the voltage across R2 using HAN–2010, the
measured voltage was only 20 [V], which was significantly lower than theoretical voltage of
24[V]. The MEC–2001 multimeter seemed to give pretty accurate readings however. Is there
anything in the technical specifications of these DMMs that would explain why the HAN–2010
makes such a huge error? Why does the MEC–2001 not make the same error? Please also show
us your calculations explaining how HAN–2010 yielded 20 [V].
Multimeter Model
DC Voltages
Range
Resolution
Accuracy
Input Impedance
AC Voltages*
Range
Resolution
Accuracy
Input Impedance
MEC–2001
HAN–2010
2 mV - 1000V
0.1 mV
± 2% (2 mV-10V)
± 1.8% (up to 1000V)
1100 MΩ
0.1 mV - 600V
0.01 mV
± 0.5% (0.1 mV-10V)
± 0.7% (up to 600V)
200 kΩ
200 mV - 1000V
0.1 mV
± 2% (200 mV-10V)
± 1.8% (up to 1000V)
1100 MΩ
1 mV - 600V
0.01 mV
± 0.5% (1 mV-10V)
± 0.7% (up to 600V)
100 kΩ
* True RMS values
Table 1: Technical specifications of DMMs being investigated
R1
500 kΩ
50 kΩ
10 [V]
30[V]
R2
500 kΩ
200 kΩ
VR
2
Fig 1: Circuit diagram with two serially-connected resistors
2