Download Chapter 4 Digital meters

Chapter 4
Digital meters
Note: This handout is to be read together with the handouts on DMMs and ADCs.
It makes reference to the diagrams contained therein.
• The last lectures have focussed on analog meters
• Advantages include:
• Observing trends
• obtaining an indication of the value of a reading rather then its absolute value visual queues
• The ability to measure large signals by using ammeter shunts for example
• Disadvantages included:
• Reading errors - parallax
• limited resolution
• limited accuracy
• loading due to low meter resistance.
• Most if not all of the disadvantages can be eliminated using digital meters
• Recall our earlier lecture:
• Analog meters - display continuous amplitude changes
• digital meters - display numbers corresponding to discrete amplitude changes
• Digital meters include:
• Voltmeters
• Ammeters
• Ohmmeters; and
• Multimeters (DMMs) which do all of the above functions
The following is a diagram of a typical digital multimeters: Refer to and study Figure
7-21 in handout
• The heart of the DMM is the Analog to digital converter or ADC.
• The input to the meter is an analog signal. The ADC’s function is to convert this into
a number which accurately represents the analog input.
• The conversion is a 2-step process
• sampling - getting a ‘snapshot’ of the input
• quantizing - converting it to a number
Refer to and study Figure 6-21(a) in section 6-5 handout
• The typical sequence of steps followed are
• The input is amplified or attenuated to bring it into a standard range for example ±
5V, ± 12V
• The signal is sampled
• The amplitude of the sample is compared to some internal reference
• the numerical value closest to the sampled value is obtained
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• this is quantization and is an approximation
• The numerical value is presented to the user.
• The internal numerical values used by the ADC are binary numbers, or base-2
• in contrast, we normally deal in decimal or base-10
• Base 2 uses the digits 0 and 1 to represent numerical values
• base 10 uses the digits 0 to 9
• The base-2 digits are called bits
• thus 8 bits means 8 binary digits like 10001110 for example.
• In the base-10 or decimal system a number such as 356 really represents:
356  3 102  5 101  6 100
• that is, we are dealing in powers of 10
• In the binary system, the numbers 1011 therefore represent:
1011B  1 23  0  2 2  1 21  1 2 0  11D
• that is, we are dealing in powers of 2
• Therefore if our ADC uses a ±5V reference and 8-bits:
8 bits  28 levels  256
10V
each level 
 39mV
256
• The following table represents the levels for each binary number
Binary Decimal Voltage
00000000
0
-5.000
00000001
1
-4.961
00000010
2
-4.922
00000011
3
-4.883
00000100
4
-4.844
00000101
5
-4.805
….
….
…
….
….
..
11111100
252
4.883
11111101
253
4.922
11111110
254
4.961
11111111
255
5.000
• The topic of ADC is beyond the scope of this course, however, be aware of the
following conversion methods
• Staircase
• Successive approximation
• Dual slope
• Voltage-to-frequency
• parallel or flash
• The handouts give a readable explanation of these forms of ADC
• READ!!
• Of concern to us are the accuracy, precision and resolution of the ADC
• The number of bits used to encode the sampled data is finite
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• therefore the quantized value is an approximation
• The difference between the true analog value and the quantized value is called the
•
•
•
•
•
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quantization error.
• This error is always present in digital meters
The ideal transfer curve for an ADC is as shown in the following figure. Refer to and
study Figure 6-21(b) in handout
Note the step changes in the characteristic.
• We only have exact values at one point per input
• for example 1.3 has no binary equivalent
Here a value <0.5 is interpreted as 0, .5 to 1.5 as 1, 1.5 to 2.5 as 2 etc.
If we designate the step size as V, then the maximum quantization error is:
V
error  
2
This follows form our example. A ‘1’ lies between 0.5 and 1.5 which can be
expressed as 1  0.5. Our step size is 1 so that the error was  ½ or 0.5.
V is determined by the number of bits. Thus for n bits:
n bits  2 n levels
8 bits  28  256 levels
voltage span
V 
2n
• Note the 256 levels are numbered from 0-255
• Both the precision and accuracy of the ADC are determined by the number of bits
• the greater the number of bits, the smaller is the step size, hence the better the
resolution.
• The accuracy of the ADC is determined by the cumulative effect of three errors
• the gain error
• the offset error; and
• the linearity error.
Gain Error: Refer to and study Figure 6-22(b) in handout
• The input/output relationship for the ADC should be 1:1.
• X volts in should be converted to the binary equivalent of X
• If the ADC exhibits gain error, then the input is modified so that the 1:1 relationship
no longer exists.
Offset error: Refer to and study Figure 6-22(a) in handout
• A zero input is supposed to represent zero output
• If a zero input produces a non-zero output, the ADC is exhibiting an offset error
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Linearity error. Refer to and study Figure 6-22(c) in handout
• Equal changes in input are supposed to result in equal changes in the digital output
• If this does not occur then the ADC is exhibiting a linearity error (sometimes called
non-linearity error)
DMM specifications
• Most manufacturers specify their DMMs as 3 1/2 digit, 4 1/2 digit etc. but what is
meant by the ‘1/2 digit’ part of the specification?
• The display of a digital readout normally displays the digits 0 to 9
• The 1/2 digit refers to a display that is capable of indicating only 0 or 1.
• To examine the usefulness of this consider the following:
• What is the range of values that can be displayed by a 3-digit display?
• 000 to 999
• If we add at the MSB (Most Significant Bit or the leftmost bit) position a display
indicating only 0 or 1, what is the range of values now possible?
• We can now indicate 0000 to 1999
• We have in fact doubled the range by adding the 1/2 digit
• To appreciate the usefulness of this consider the following:
• What would be displayed on a 3-digit voltmeter on its 1-volt range if the input was
1.856V?
• Since the maximum displayed value is .999, this is going to be indicated
• What would be displayed on a 3 1/2-digit voltmeter on its 1-volt range if the input was
1.856V?
• Because of the 1/2 digit, the meter can in fact display 1.856V
• The 1/2 digit acts as an overrange indicator allowing the DMM to display a value up
to 100% over the range being used.
• What is the resolution of a 3 1/2 digit DMM?
• 1 reading in 2000
• What is the resolution of a 8 1/2 digit DMM?
• 1 reading in 2 108
• What is the resolution of the above 3 1/2 digit DMM on the 2 volt range?
• It can display 0.000 to 1.999, hence the resolution is 0.001V
• Some meters now have a ‘¾ digit’ specification, (like the Fluke 10 which is a 3 ¾ digit
DMM) where the MSB can display 0, 1, 2, 3 or 4. We will not examine this here, but
the same and even better resolution advantages apply here too.
Accuracy Specifications of DMMs
• The accuracy of a DMM is usually expressed as:
Accuracy   x % range  y % reading  z digits
• ± x% range - the constant error, since it is a function of the range being used
• ± y% reading - the proportional error, since it is a function of the magnitude of the
reading
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• ± z digits - refers to the value of the least significant digit (the rightmost bit) being
displayed.
Example:
For a 3 1/2 digit DMM whose accuracy is given by:
Accuracy  0.01% range  0.1% reading
 2 digits
What would be displayed and what is the error for a 5V reading taken on the 20V range?
Solution:
A 3 1/2 digit DMM would display 00.00 to 19.99 on the 20V range.
• What is the value of 1 digit?
• 1 digit represents the LSB or 0.01V
• Therefore the accuracy is:
0.01
0.1
Accuracy  
 20 
 5  0.02 
100
 100

Accuracy  0.002  0.005  .02  0.027V
• The displayed value is 5.00V
• The overall answer is 5.00 ± 0.03V to 3 sig. figs.
Additional Features of DMMs
• High input impedance
• Typically >10M
• Less loading for most applications
• Higher accuracy than analog meters
• 0.005% compared to 0.5% for analog instruments
• Multiple ranges like their analog counterparts
• sometimes automatically switched - called auto-ranging
• Over-ranging
• the ability to remain at a lower range setting for some % over the particular range
limits.
We can illustrate this through an example.
Example:
• What happens if 10.17V is presented to a 3 1/2 digit auto-ranging DMM on its 10 Volt
range.
• Normally the meter would switch to the next higher range, say 100V
• displayed value is then 10.2V
• This is a loss of precision
• If the meter had a 20% over-range capability, then up to 12V would be allowed to be
displayed on the 10V range before a range change takes place.
• Displayed answer is 10.17V on 10V range.
• We can theoretically have up to 100% over-range.
Read the chapter 5 handout specially pages 113 and 114 for additional information
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