Digital measurement technology
The measurement technology can be broken down according to different aspects. One possibility is to differentiate between analog and digital measurement technology. Specific sub-areas of digital measurement technology are its measurement method, information display and device technology.
Basics - Definitions - Comparisons
The measurement is the execution of planned activities for the quantitative comparison of the measured variable with a unit ( DIN 1319-1, No. 2.1). What makes this measurement a digital one should be described by comparing it with analog measurement.
Analog measurement method
Linguistic basis: analog = corresponding.
The measured value is represented by an analog, a similar or corresponding (analog) fact, here by an intermediate value, the value of which can easily be read as a number. ¹)
- Guarantee error limits (a lower value is possible by correcting with a curve of the measurement deviations, which have been determined from the difference to better devices or another benchmark),
- Measurement uncertainty (a lower value is possible due to finer scale divisions, greater experimental experience and repeated measurements).
If one ignores these deviations in order to recognize the essentials, one recognizes as features:
- The output signal (distance or angle) can be resolved as finely as desired .
- It is a clearly reversible measure for the input signal.
Further examples of analog measurement methods:
- Temperature : expansion of the thermometric fluid
- Pressure : deformation of a membrane
- Speed : voltage of a tachometer generator
The measuring device provides the analog, the observer uses it to determine the numerical value and, together with the unit, the measured value.
¹) This sentence is only to be understood as a clear introduction.
Digital measurement method
Linguistic basis: digit (us) = finger, number. ²)
The measured value is shown directly in numerical form. ¹)
- Example tachometer
A device that
- one counter advances by one per revolution and
- allows counting for exactly one minute.
The counter reading provides the measured value in units of revolutions per minute.
Note: The special name revolution is widely used as a unit in the specification for rotating machines instead of the one. Correspondingly, the units of revolution per second or revolution per minute are widely used for rotational speed.
- Example Wheatstone Bridge
Setting of the resistance decades up to the " zero adjustment ", more precisely up to
This is the smallest adjustable voltage step. If is, then after the adjustment the resistance to be measured is equal to the resistance set on the decade switches. The picture shows:
- = whole number times smallest step size = 235 × 1 Ω.
Here, too, deviations from the measuring device must be observed,
- Guarantee error limits through the error limits of the built-in benchmark,
- in the example counter: the time scale,
- in the example bridge: the resistors used,
- Measurement uncertainty due to a digit in the least significant place. This quantization or digitization deviation can always be made insignificantly small as a relative deviation if it is possible to work with large numbers, see below "On the quantization deviation".
If one ignores these deviations in order to recognize the essentials, one recognizes as features:
- The output signal is in a countable number of steps can be subdivided .
- It is a clear statement in itself.
- in the example counter: the value of the speed by the pulse generator,
- in the example of a bridge: the value of the resistance through the step-by-step setting of the reference resistance .
¹) This sentence is only to be understood as a clear introduction.
²) The term digit is not used uniformly in the literature, often in the sense of a digit, occasionally in the sense of a digit.
To the quantization deviation
It is possible to arrive at a large number of the measured value and thus a small relative quantization deviation ,
- in the example counter, if several pulse generators are used, e.g. E.g. 100 pulses per revolution,
- in the example bridge, if you subdivide the adjustable comparison resistance more finely, e.g. B. add resistance decades with increments of 0.1 Ω and 0.01 Ω.
This achieves a higher reading accuracy, in the two examples with 2 additional digits.
With 5 decimal places, the relative quantization deviation = 1/10000… 1/99999 = 10 −4 … 10 −5 . Whether the overall accuracy has thus increased is at least questionable. Due to the unambiguousness of the reading, it is all too easy to forget to pay attention to the other sources of measurement errors. If every resistor in the bridge has the relative error limit of 10 −3 , then the relative error limit of the result is not smaller either, and specifying 5 digits would not be justifiable. In addition, the avoidance of systematic deviations ( terminal resistance , thermal voltages ) would have to be carefully considered when setting up the measurement .
Definition of the analog measuring method from DIN 1319-2:
Measurement method in which the measured value is determined by continuously processing the measurement signal.
Definition of the digital measuring method from DIN 1319-2:
Measurement method in which the measured value is determined by processing the measurement signal in stages.
The decisive characteristic :
At least in the ideal case, the measurement signal is a clearly reversible mapping of the measurement variable.
(Contrast: with the digital measuring method, a conclusion within the width of a digit is uncertain.)
The decisive characteristic :
The measurement signal is a quantized mapping of the measured variable in fixed steps.
(Contrast: with the analog measurement method, the measurement signal can be adjusted as finely as desired.)
Display of the measured values
Scale display, numeric display
But a misinterpretation would be:
- Scale display means analog measurement method.
- Counterexample: time measurement; Station clocks work with scales, but continue to turn gradually in the minute hand.
- Numerical display means digital measuring method.
- Counterexample: energy measurement; Energy meters work with numeric rollers, but continue to rotate at the last digit and have a scale display for even greater resolution.
Band display, bar display
The tape display contains a number of segments (typically 5 ... 200 segments), of which an increasing number is switched on as the measured variable increases. It works digitally and combines digital technology with the advantages of a dial display. With ≥ 100 segments, the gradation is hardly noticeable and one speaks of quasi-analog . The bar display on a screen also corresponds to a scale display, whereby the length of the bar can be so finely graduated with the number of pixels that subjectively the boundary to the continuous setting can be completely blurred.
Advantages and limitations of the scoreboard
|Dial display||Numeric display|
|With the analog measurement method, the display can only be estimated in its subtleties.||With the digital measuring method, the display can be clearly read.|
|The resolution is limited|
|thanks to the readability to 1/2… 1/10 scale division 1… 0.1% of the final value.
||by grading to 1 digit
step ≤0.1% of the final value with at least three-digit display.
|Visual operational monitoring|
|is possible at a glance .||requires conscious reading and evaluating the number.|
|If the measured variable fluctuates rapidly|
|(quickly in relation to the setting or recording time)|
|a medium size can be read.||the indicator is unsuitable.|
|Trend observation or fault detection|
|is based curve (by Schreiber or screen) clearly easy.||is tedious using columns of numbers (using a printer or screen).|
Coding is the representation of a message in an arbitrarily chosen form. Different codings are appropriate depending on the circumstances.
Representation by a sequence of equivalent characters (pulses); with each impulse is to be counted further by one digit.
In the case of non-electrical measured variables, pulses can be generated by optical scanning (e.g. on a reticle) or inductive scanning (e.g. on a gearwheel).
The number of pulses represents the number to be coded itself.
- Number of revolutions of a shaft or, if there are many pulses per revolution, its positioning.
- Volume measurement with oval gear meters or turbine meters .
The number of pulses in a period represents the number to be coded .
with = allocation factor, e.g. B. Number of pulses per revolution if stands for the speed.
If the variable to be measured is to be determined as a frequency-proportional variable by counting, the duration of the counting must be limited.
Counting is suitable for various measuring tasks:
- using the oval gear meter as an example:
- Volume measurement for sales (delivery quantity),
- Flow measurement for operation (delivery rate or flow velocity).
- Depending on the task, the total duration of the loading (which is not important in the end) must be counted or limited according to the time interval.
- using the example of induction loops in the roadway to the football stadium:
- Unlimited count for the utilization of the parking space,
- Temporary count for road performance.
Representation by a sequence of characters that have to be evaluated differently depending on their position in a compound.
Each digit has the significance or the weighting factor of a power of ten.
Example: Decimal number 145 = 5⋅10 0 + 4⋅10 1 + 1⋅10 2
The sub-representation of the decimal digits is
- mechanically no problem, for example with
- electronically difficult.
Binary or dual representation
In the simplest case, which also occurs frequently, each digit has the significance or the weighting factor of a power of two.
Example: binary number / binary number 10010001 = 2 0 + 2 4 + 2 7 = 1 + 16 10 + 128 10 = 145 10
In the case of non-electrical measured quantities, binary digits can be represented using code disks or code rulers, which have as many paths as there are places.
Example: angle encoder
- In the picture, the binary number 111010101 330 ° is scanned with 9 sensors along the drawn radius from the inside to the outside , if light 0 and dark 1 are evaluated.
Due to imperfections in the adjustment, errors occur in the scanning. In the example of a code ruler shown, an 8 is read between 11 and 12 if unshaded 0 and hatched 1 are evaluated. This mistake can be avoided
- by double scanning,
- by scanning a narrow synchronization field in the middle of the field of the finest gradation,
- by using a one-step code ( Gray code in the picture ), in which a value only changes on one track with each transition ; Disadvantage: no significance on the tracks. For information on the evaluation logic and code converter, see the section "Blocks of binary technology" below.
In the case of internal binary representation, it is necessary to recode to a decimal number in order to display measured values to the observing person. To do this, the device must be able to calculate (divide), or it uses the following mixed form of decimal and binary.
Each decimal place is individually binary coded with a BCD code . The minimum effort is 4 binary digits per decimal digit. Since only 10 of the 16 possible bit combinations are needed, there are several common codes. The 8-4-2-1 code maintains significance; on the other hand, the excess 3 code avoids the combinations 0000 and 1111, which can easily occur in the event of errors.
Example in preferred 8-4-2-1 code: 145 10 = 0001 0100 0101.
In automation technology there are a number of " field buses ", e.g. B. Profibus , Interbus , EtherCAT , where the representation of the binary characters, the time sequence, the structure of a telegram, the data backup and much more are defined. However, this cannot be dealt with here.
A section of the electronics is inserted beforehand. It restricts itself to what is absolutely necessary to help you understand the sections that follow.
The operational amplifier is simply the workhorse of analog electronics, as it can be used for a wide variety of tasks, depending on the circuitry with passive components. The key formula for his behavior is
with = open circuit voltage gain. Almost always the best permissible approximations lead to the "ideal operational amplifier":
- Use without feedback as a comparator
- Without feedback , the output has no effect on the input.
can only have two values:
- positive overdriven
- negatively overdriven.
- Use with feedback to the inverting input
- In the drawing, the inverting input is marked with a minus sign.
- The circuit can be operated using analog technology without overdriving. This must be set because the output is not overdriven .
- Current-voltage converter
- A current-voltage converter is created with ohmic feedback. Because of this , the entire input current flows through the feedback resistor. With a positive input current, the amplifier generates a negative output voltage just large enough that becomes. This applies
- An integrator is created through capacitive feedback.
- If the voltage is switched to the input at the time , and
- if the voltage is present at the output at the time ,
- then is for
- If = const
- This results in a straight line with the rise
Building blocks of binary technology
Counters are stored; they have a number of stable states. Each impulse changes the memory content by one digit.
With limited counting, counters work with averaging over the duration of the count.
Mechanical counters have storage elements with ten stable states.
Electronic meters have storage elements with two stable states. In decimal counters, a memory element is made up of four toggle elements.
For counting over several decimal places, the carry output Ü in the circuit diagram shown can be connected to the clock input T of another counting stage for the next higher place.
Counter structure and additional equipment
The four-digit decimal counter shown has a few additional features:
- Counting pulses only reach the counter as long as there is a 1 at the lower input.
- This allows the counter to be set to 0.
- If all decimal places match the preselection setting, a preselection message is output. This can be used to control other events, e.g. B.
- Stop counting,
- Reset counter and continue counting from 0.
There are also up / down counters. These contain a further control input for the counting direction and require a message about the direction of a change. Such counters are used, for example
- for position measurement using an incremental encoder , if both directions of movement are permitted,
- when measuring the voltage using a follow-up converter when the voltage rises or falls.
In a slightly different circuit, the counter input Z and the start-stop input S react to the transition from 1 to 0 of the input signal. Various applications are explained using the table. Then some additions follow.
- Example with the assumption of a reference frequency = 1 kHz with a period duration = 1 ms:
- Pulses were counted between start and stop . Then ms have passed between start and stop .
- Frequency divider
- Frequency divider for a frequency to be measured
- Example with 5 decimal places:
- At the carry output Ü reduction ratio 100,000: 1.
- Example with a number that can be set on preselection switches and with automatic reset:
- At the pre-selection output V reduction : 1.
- Timers using reference frequency with the same assumptions as before:
- A pulse appears at Ü every 100 s.
- A pulse appears at V every ms.
- Period duration measurement
- If the measurement results in a counter reading that is too small, the counting time must be extended with an auxiliary counter for .
- Example: With = 1 kHz and = 50 Hz, the counter reading is 20 ± 1,
- With a pre-coater for 1000: 1, the counter reading is 20,000 ± 1.
- Note: A coaster 4000: 1 with a numerator result of 80,000 ± 1 would further reduce the relative measurement uncertainty, but is not appropriate. The conversion of the display to the measured value usually only takes place in whole powers of ten (no numerical calculation, only decimal point shift);
- in the example: counter reading 20,000 results in = 20,000 ms.
- Frequency ratio measurement
- Application example: fuel consumption measurement in vehicles
- The not directly measurable quantity (in l / 100 km) can be calculated by dividing by . Since both quantities can easily be represented by frequency-proportional signals,
- (Flow) and (speed)
- division is possible by forming the frequency ratio.
The variety shown in the table above can be implemented in a single device. This is needed
- Counter for the value to be displayed,
- Counter as auxiliary coaster,
- Precision frequency generator ( quartz crystal ),
- Switch to different combinations of the assemblies.
Error limits using the example of time measurement
Guarantee error limits
Crystals have deviations in their frequency
For counters over 5 decades ( i.e. count <10 5 ) using a quartz time base, the reference frequency applies due to these typical error limits
The effort with regard to the error limits of the quartz is optimally chosen for the given meter; it is not worthwhile to push the guarantee error limits below a quantization step.
For the measurement uncertainty due to counting, the example of a time to be measured applies
The digitally displayed time differs from the correct time by the measurement error
Since this difference can be positive or negative, but the amount remains smaller than , the known fact applies
If it succeeds in special cases,
- to synchronize the clock with the beginning of the process to be measured or
- start the process synchronously with the clock,
this halves the width of the possible deviation, and depending on the version, this is between
You can see this in the next picture with narrow pulses - depending on whether the circuit reacts to falling or rising edges.
With a frequency reduction from a continuous clock, there is synchronization both at the beginning and at the end of the generated period, so that the frequency ratio is always exact.
Digital-to-analog converter (DAU)
DAU in measurement technology
There are only a few physical quantities for which a quantization is known. Since even this quantized nature is practically not recognizable, there is no need for a DAC as a measuring device. (Who measures an electric current by counting electrons, except when it is below 10 −16 A?) Since the DAU is part of some measuring devices and simply a counterpart to the ADC, it will be dealt with here.
Strictly speaking, a digital-to-analog converter is something nonsensical: something stepped cannot be turned into something stepless. Rather, the DAU should be understood as follows: It converts digitally coded information into a form that an analog device can understand.
Of the numerous developments, three are explained here.
DAU with weighted resistances
The circuit shows a DAC with voltage summing by weighted resistors in BCD representation. Here the voltage is created by specifying two decimal digits in 8-4-2-1 code and the reference voltage .
can be set by opening switches between 0 and 99% of in increments of 1%. If necessary for a finer resolution, further decades can be added, as long as this is responsible for the quality of the resistors and switches. (Because undesirable properties of switches and resistors sometimes influence the inaccuracy of the output variable.)
- because of ( virtual mass ); regardless of the switch positions.
Each binary one of the binary coded -digit decimal number opens the associated switch and thus the relevant resistor is looped into the chain of resistors.
DAU with resistance chain ladder
The circuit shows a DAC with current summation through resistor chain conductors ( R-2R network ) in binary representation. There are only two resistance values regardless of the significance of the respective digit. The voltage is created here by specifying binary digits.
- for .
Each one of the binary number places the associated switch to the left, and the current flowing through it is switched to the busbar from . This total current flows on through the feedback resistor to the output of the operational amplifier.
General: are required for the two versions shown so far
- Precision voltage source,
- Precision resistors,
- Semiconductor switches that block or conduct as ideally as possible.
DAU with pulse width modulation
A counter that is initially set to zero records a clock frequency and compares its counter reading with two pre-selected numbers. When the first number is reached (after a period of time ) an SR flip-flop is set to A = 1. When the second number is reached (after a certain period of time ) the flip-flop is set to A = 0 and the counter is also reset to zero. As long as A = 0, a reference voltage is applied to a low-pass filter or a mean value image; zero potential is applied for the remainder of the period. The arithmetic mean of this voltage is
The advantage of this circuit is the lack of precision resistors and many switches, the disadvantage is its slow response due to the low pass.
With you determine the fineness of the graduation and the period duration. With you set the tension, where is. If the smallest step size is allowed to be 0.4% of the final value, then ≈ 250 is selected, for which an 8-bit counter is sufficient. At = 1 MHz = ¼ ms is required for this . Microprocessor circuits offer counters with 16 bits; This means that the resolution is much finer, but then in the maximum case = 65 ms, and the response time is ≫ 200 ms, depending on the smoothing requirements.
Analog-to-digital converter (ADC)
Measuring devices for process variables
Various analog-digital converters have already been dealt with in the previous sections
- Frequency measurement (speed, flow measurement)
- Volume measurement
- Angle and length measurement
Electrical voltage meters
Depending on the measuring task, there is a wide range of devices to choose from according to the following criteria:
|Measured value output|
|with computer connection||with display|
|Measured value display and resolution|
|in pure binary code
with 8… 14 (… 28) digits
|in BCD format
with 2000… 100,000 points
or "3½-digit"… 5-digit (… 8½-)
smallest resolvable voltage:
|Fast with instantaneous value quantization - for rapidly changing measured variables or if a larger number of measuring points is to be queried using a switch (multiplexer).||Slow with averaging (integration) - to suppress mains hum ( mains- synchronous interfering AC voltage) or interfering pulses (from switching processes).|
|Integration attenuates the interference. Integration over an integer multiple of the period of the interference signal completely suppresses it; the constant component or mean value contained in the voltage is retained.|
Of the numerous developments, four are explained here, two rapid and two integrative.
The voltage to be measured is compared with all possible quantization levels at the same time. To obtain a -digit binary number one needs comparators.
For operation on the example with :
- There are four voltages formed by the voltage divider , , , simultaneously compared. This converter, which is very roughly graded for reasons of clarity, can only deliver 4 different measured values. The fourth comparator for the highest level of the characteristic provides a fifth value: Exceeding the measuring range .
Parallel converters are extremely fast ("flash converters") and extremely complex. Versions with ≥ 6 bits work in the top class with a conversion time ≤ 1 ns (conversion rate ≥ 1 GHz). Integrated converters with 10 bits (1023 comparators) are also on the market.
The pipeline converters are a further development . They are made up of several independent stages in a pipeline architecture . Their stages usually consist of parallel converters over a few bits. A rough quantization is carried out in each pipeline stage, this value is converted into an analog signal with a DAC and subtracted from the buffered input signal. The residual value is amplified and passed on to the next stage. The advantages lie in the greatly reduced number of comparators (60 for four four-bit converter stages) and in the higher possible resolution of up to 16 bits. The latency time increases with each step , but the sampling rate only decreases because of the longer settling time with higher resolution.
The voltage to be measured is compared with a voltage generated at the DAC . One after the other is changed in several steps and approximated as closely as possible. There are several strategies for doing this; here the successive approximation with the weighing or compensation method is explained.
|Adoption:||> 0 and > 0|
|Step 1a:||A comparison voltage is generated by setting the most significant bit to 1 and all others to 0.
|Step 1b:||If so, the bit is reset to 0.
If so , then the bit is left at 1.
|Step 2a:||A 1 on the next least significant bit is added.|
|Step 2b:||Like step 1b|
To obtain a -digit binary number one needs comparisons. Finally is . This is the smallest voltage jump that can be set on the DAU.
- Example of this:
- 4-bit DAC with = 1 V at = 6.5 V.
- According to the signal-time diagram, the measured value = 0110 B ⋅ = 6 V.
The input signal of the DAU set at the end is regarded as the result of the ADC (binary or BCD graded).
Measurement of instantaneous values; however, must not change during the setting of . A sample-and-hold circuit is often used for this, which temporarily stores analog data during the conversion. Typical conversion time 1… 100 μs.
ADU with the intermediate size of time
The process is explained using the two-ramp or dual-slope process.
The voltage to be measured charges the capacitor of an integrator for a limited period of time (see above in the section on operational amplifiers ). The capacitor is then discharged again in a controlled manner. Both processes run ramp-shaped ( linear ) with DC voltage plotted over time .
|Step 1:||Integration (charging of the capacitor) with for a fixed duration, e.g. B. = 20 ms.
|Step 2:||Downintegration with a fixed end value .
Both times are determined by counting. Is shown
Is used for the integration period
- regardless of .
stands for the value of the voltage to be measured averaged over the duration of the integration; effective interference suppression of 50 Hz signals if ; with , integer. Then
Typical integration time 1… 300 ms. Devices with offer good suppression of network coupling worldwide, both in 50 Hz and 60 Hz networks.
ADU with the intermediate size frequency
The process is explained using the charge balance or charge balancing process.
The voltage to be measured charges the capacitor in an integrator. It is constantly discharged again by short current surges in the opposite direction; on average, the charge balance is balanced.
|further:||> 2 ⋅ maximum value of|
|Step 1:||Loading with for a fixed short duration ,
where ≪ 20 ms
|Step 2:||Unloading with a fixed end value|
|Step 3:||like step 1|
The upper part of the signal-time diagram shows the voltage at the output of the integrator for a DC voltage to be measured . The charge balance is balanced along the thicker sawtooth line after a period.
- (Intermediate size)
The measurement of leads by counting for the duration on the counter reading that is displayed.
As a timer for the frequency is counted up to the count ;
The order of magnitude: = a few 100 ms.
The thinner sawtooth line in the picture differs from the thicker one in two ways:
- The voltage is greater by a factor of 5/2 and generates a number of charging cycles that is greater by the same factor.
- The message from the comparator does not start the timer immediately.
In the circuit shown here, the timing element precisely generates the duration from one rising edge to the next. This synchronization of the timing element to the clock frequency not only runs to the zero line, but continues until the point in time of synchronization. The associated deviation, however, is less than a digit increment - over an arbitrarily long counting period. The three square wave signals in the picture explain the process for the course of the thinner line of
- upper signal for the T akt (So ),
- average signal for the output of the K omparators,
- lower signal for the output of the Z eitgliedes.
The current flows continuously during the counting period . In addition, the current is switched on briefly so that the capacitor does not charge on average.
- only dependent on the reference voltage and a resistance ratio, regardless of .
In terms of its metrological quality, this procedure is similar to the two-ramp procedure, but is still somewhat superior to it (it is switched on continuously).
- resulting from the comparison value (and possibly other multiplicative causes included in the result) and
- resulting from zero point and digitization (and possibly other additional causes).
Important influencing variables that can cause measurement errors and that are not included in the device error limits come into question
- Current consumption of the input terminals,
as well as due to the properties of the applied voltage
- Curve shape,
- superimposed interference voltage,
- Series interference voltage, which can be suppressed in integrating processes z. B. by a factor of 10 −3 at 50 and 60 Hz,
- Common-mode interference voltage that can be suppressed in integrating processes, e.g. B. by a factor of 10 −5 at 0… 10 kHz.
- DIN 1319-1, Fundamentals of measurement technology - Part 1: Basic terms . 1995
- DIN EN ISO 80000-3: 2013-08 Sizes and units - space and time , No. 3-15
- DIN 1319-2, Basics of measuring technology - Part 2: Terms for measuring equipment . 2005
- Tutorial Precision Frequency Generation Utilizing OCXO and Rubidium Atomic Standards with Applications for Commercial, Space, Military, and Challenging Environments IEEE Long Island Chapter March 18, 2004 (PDF; 4.2 MB) Retrieved June 7, 2012.