Download Moving coil meters for DC measurements

Minimum

2nd. lecture
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
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.
direct (method of) measurement method of measurement in which the value of a
measurand is obtained directly, without the necessity for supplementary calculations
based on a functional relationship between the measurand and other quantities
actually measured
indirect (method of) measurement method of measurement in which the value of a
quantity is obtained from measurements made by direct methods of measurement of
other quantities linked to the measurand by a known relationship
3. lecture: 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)
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:
N
1
2
  xi  x 
N  1 i 1
SDdata 
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.
4. lecture: evaluation of data
Find out the connection between 2 physical quantity, like for example voltage and current of a
resistor. Choose one quantity as a parameter of the measurement, change step by step and
measure another. You will get pairs of data. Make a table. Make a graph: horizontal axe is the
parameter, vertical axe is another measured quantity.
Try to fit your data with some analytical function. It means finding a simple function which
gives similar result like your measurement at the same values of the parameters.
How good is the fitting?
least squares method:
x_i measured data at ith value of the parameter.
y_i calculated result using by the analytical function.
at the best fit quantity
N
 2    xi  yi 2
i 1
should has got a minimum. During fitting you are searching for a best fit, by
changing the type of the analytical function or by changing its parameters.
5th lecture:
Propagation of the errors
A little error in the measured quantity can cause big error in the result of the calculation.
If error means error limit:
In the case of multiplication and divison of the quantities the relative error of the result equals
to the sum of the relative errors of the each quantities.
You have 1V 0.5% and 1A 1% (typical) R=U/I, 1,5%
In the case of addition and substraction the absolute erorr of the result is the sum of the
absolute error of the quantities.
You have I_1 1A +- 1mA, I_2 2A, +-1mA in result I_1+I_2 you get +-3mA absolute error.
deviation (scattering)
Addition and subtraction of a number will not change standard deviation.
Multiplication or division by a number will change standard deviaton in the same way.
Addition or subtraction of two quantities (A,B) with certain absolute standard deviations:
SD A B  SD A2  SDB2
In the case of multiplication and division similar formula is true but for relative SD.
Worst case analysis is a general method for taking into account propagation of errors.
Multimeter basics:
More Material

AC – basics
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
usually written as
or
, is therefore
is +1 and the minimum
. The peak-to-peak voltage,
.
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 peakto-peak value
of the 230 V AC is double that, at about 650 V.
Analog oscilloscope
Of the four basic blocks of the oscilloscope, the most visible of these blocks is
the display with its cathode-ray tube (CRT).
The vertical amplifier
Conditions the input signal so that it can be displayed on the CRT.
The vertical amplifier provides controls of volts per division, position, and
coupling, allowing the user to obtain the desired display.
Must have a high enough bandwidth to ensure that all of the significant
frequency components of the input signal reach the CRT.
The trigger is responsible for starting the display at the same point on the input
signal every time the display is refreshed.
The final piece of the simplified block diagram is the time base.
Vertical and horizontal positioning
Phase shift: http://www.youtube.com/watch?v=30J5U0ThRUc
Moving coil meters for DC measurements
The rotation of the coil (and the pointer attached to it) is due to the torque M,
which dependson the flux density B of the magnet, on dimensions d and l of the
coil, on number of turns z of the coil and of course on the measured current I:
M = Bzdl * I Returning torque of the spring k*alfa, where alfa is the angle of
the pointer.
Microammeter, voltmeter, ammeter
A moving coil meter measures directly the small current. (I alfa)
Voltmeter: Ux proportional with I, R_d is high.
Ammeter: R_d is much higher then R_b shunt resistor
How shunt is working?(extending the range n-times)
Moving coil ammeter
I_max=20mA
Desired range: 200 mA
What to do?
R_inner is small, 9
Moving coil ammeter
I_desired, 200mA
R_inner is small, 9
I_ammeter, 20mA
R_shunt is small
R_inner*I_ammeter=I_shunt*R_shunt (parallel branches, U equal)
I_shunt=I_desired-I_ammeter
R_shunt=R_inner/(n-1), where n=I_desired/I_ammeter
HereR_shunt=1 ohm
How serial resistor is working (extending the range n-times)
Inner resistances
Moving coil ammeter
R_inner is 1M
Measured load 10k
U_max=20V=I_max/R_inner
Desired range: 2kV mA
What to do?
Moving coil ammeter
R_inner is 1M, R_serial
Measured load 10k
Apply more resistivity in serial with the inner resistivity of the voltmeter
U_desired=I_max/(R_inner+R_serial)  R_serial=R_inner*(n-1)
8. lecture: Oscilloscope basics
Digital Oscilloscope
Analog to digital conversion basics
The two major components in a high-speed digitizer's analog front end are the
analog input path and the analog-to-digital converter (ADC).
The analog input path attenuates, amplifies, filters, and/or couples the signal to
optimize the digitization by the ADC.
The ADC samples the conditioned waveform and converts the analog input
signal to digital values that represent the conditioned input signal.
Figure 1
Reprezentation of periodic signals in the time and frequency domain
Fourier theorem: Each periodic singnal can be produced by the sum of the sinus
like signals.
sinusoid signal:
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
5
It has amplitude, frequeny, phase-shift.
sum of them:
10
15
20
2
1
0
-1
-2
0
5
10
15
20
time domain: horizontal axe: time, vertical axe: signal
ferquency domain: horizontal axe: the frequency of the sinusoidal components
of the signal, vertical axe: their amplitude
800
600
400
200
0
0
20
40
x10
-3
60
80
100
Bandwidth
Bandwidth describes the frequency range in which the input signal can pass
through the analog front end with minimal amplitude loss - from the tip of the
probe or test fixture to the input of the ADC.
Bandwidth is specified as the frequency at which a sinusoidal input signal
is attenuated to 70.7% of its original amplitude, also known as the -3 dB
point.
The following figure shows the typical input response for a 100 MHz highspeed digitizer.
Figure 2
For example, if you input a 1 V, 100 MHz sine wave into high-speed digitizer
with a bandwidth of 100 MHz, the signal will be attenuated by the digitizer’s
analog input path and the sampled waveform will have an amplitude of
approximately 0.7 V.
Figure 3
It is recommended that the bandwidth of your digitizer be 3 to 5 times the
highest frequency component of interest in the measured signal to capture the
signal with minimal amplitude error (bandwidth required = (3 to 5)*frequency
of interest).
rise time
Another important topic related to bandwidth is rise time. The rise time of an
input signal is the time for a signal to transition from 10% to 90% of the
maximum signal amplitude and is inversely related to bandwidth by the
following formula, based on the one pole model, R-C limited input response.
Figure 5
This means that the rise time of a 100 MHz digitizer input path is 3.5 ns. It is
recommended that the rise time of the digitizer input path be 1/3 to 1/5 the rise
time of the measured signal to capture the signal with minimal rise time error.
The theoretical rise time measured (Trm) can be calculated from the rise time of
the digitizer (Trd) and the actual rise time of the input signal (Trs).
Figure 6
For example, the rise time measurement when measuring a signal with 12 ns rise
time with a 100 MHz digitizer is approximately 12.5 ns.
sample rate
Sample rate is the speed at which the digitizer’s ADC converts the input signal,
after the signal has passed through the analog input path, to digital values that
represent the voltage level. This means that the digitizer will sample the signal
after any attenuation, gain, and/or filtering has been applied by the analog input
path, and convert the resulting waveform to digital representation. The sample
rate of a high-speed digitizer is based on the sample clock that tells the ADC
when to convert the instantaneous analog voltage to the digital values. National
Instruments high-speed digitizers support a variable effective sample rate
derived from the maximum sample rate of the device. For example, the NI
5112 has a maximum sample rate of 100 Megasamples/second (MS/s) and
can be set to rates of (100MS/s)/n, where n = 1,2,3,4,....
Nyquist theorem
Nyquist Theorem:
Sample rate > 2 * highest frequency component (of interest) of the measured
signal
The Nyquist theorem states that a signal must be sampled at a rate greater than
twice the highest frequency component of the signal to accurately reconstruct
the waveform; otherwise, the high-frequency content will alias at a frequency
inside the spectrum of interest (passband). An alias is a false lower frequency
component that appears in sampled data acquired at too low a sampling rate. The
following figure shows a 5 MHz sine wave digitized by a 6 MS/s ADC. The
dotted line indicates the aliased signal recorded by the ADC and is sampled as a
1 MHz signal instead of a 5 MHz signal.
Figure 8: Sine Wave Demonstrating the Nyquist Frequency
The 5 MHz frequency aliases back in the passband, falsely appearing as a 1
MHz sine wave. To prevent aliasing in the passband, you can use a lowpass
filter to limit the frequency of the input signal or increase your sampling rate.
Resolution
The best way to understand the concept of resolution is by comparison with a
yardstick. Divide a 1 meter yardstick into millimeters. What is the resolution?
The smallest “tick” on the yardstick is the resolution. Yes, you might be able to
interpolate between these, but in the absence of this sophisticated guessing
process the resolution is 1 part out of 1000.
The resolution of a n-bit analog-to-digital Converter (ADC) is a function of
how many parts the maximum signal can be divided into. The formula to
calculate resolution is 2^n. For example, a 12 bit ADC has a resolution of
2^12 = 4,096. Therefore, our best resolution is 1 part out of 4,096, or
0.0244% of the full scale.
An ADC takes an analog signal and turns it into a binary number. Thus, each
binary number from the ADC represents a certain voltage level. Resolution is
the smallest input voltage change a digitizer can capture. Resolution can be
expressed in bits (LSB), in proportions, or in percent of full scale.
Resolution limits the precision of a measurement. The higher the resolution
(number of bits), the more precise the measurement. An 8-bit ADC divides the
vertical range of the input amplifier into 256 discrete levels. With a vertical
range of 10 V, the 8-bit ADC cannot ideally resolve voltage differences smaller
than 39 mV. In comparison, a 14-bit ADC with 16,384 discrete levels can
ideally
resolve
voltage
differences
as
small
as
610 µV.
Let us examine how a sine wave would look if it is passed through ADCs with
different resolutions. We will compare a 3-bit ADC and a 16-bit ADC. A 3-bit
ADC can represent 8 discrete voltage levels. A 16-bit ADC can represent 65,536
discrete voltage levels. As you can see, the representation of our sine wave with
3-bit resolution looks more like a step function than a sine wave. However, the
16-bit ADC gives us a clean looking sine wave. Note that if you are using a 3-bit
ADC, minute voltage fluctuations in the incoming signal will not be detected.
Figure 1. A 5 kHz Sine Wave being sampled by a 3-bit versus a 16-bit ADC
Another way to think of resolution is by considering your television screen. The
higher the resolution of the screen, the more pixels you have to show the picture,
so you get a better picture.
Summary
Analog to digital conversion
1. Bandwidth
Bandwidth is specified as the frequency at which a sinusoidal input
signal is attenuated to 70.7% of its original amplitude, also known as
the -3 dB point.
Higher bandwidth gives smaller rise time due to the presens of the
more high frequency components of the measured signal.
2. Sampling rate
How many samples / second, sampling requency, 100 Ms/s
3. Resolution
Number of digital values using for digital conversion and the
maximum value, calculate!
Featuring of DSO
data-storage
Record length refers to the amount of memory dedicated to storing digitized
samples for postprocessing or display for a single acquisition. In a digitizer,
record length limits the maximum duration of a single-shot acquisition.
For example, with a 1,000-sample record and a sample rate of 20 MHz, the
duration of the acquisition is 50 µs (the number of points multiplied by the
acquisition time per sample, or 1,000 x 50 ns). With a 100,000-sample record
and a sample rate of 20 MHz, the duration of acquisition is 5 ms (100,000 x
50 ns).
In many cases, measurement quality depends on the digitizer's ability to take a
sustained acquisition while maintaining high sampling rates. In these cases, the
amount of acquisition memory determines the fidelity of the acquired signal.
High-speed digitizers with deep onboard acquisition memory have the ability to
take enhanced time and frequency-domain measurements.
Vertical range and Offset
Vertical range is the peak-to-peak voltage span that a digitizer can measure
at the input connector. Most digitizers have several choices for vertical range.
Vertical offset is the voltage the vertical range is centered on. Vertical offset
positions a waveform around a DC value. Using this offset allows you to
examine small changes in the input signal, which can improve the accuracy
of your measurement.
For example, imagine that you are acquiring the waveform shown in Figure 1
that outputs 0.75 V to 1.25 V. Without using vertical offset, you would need to
specify a range of 2.5 V (±1.25 V) to capture the waveform. However, with
vertical offset, you would only need to specify a range of 0.5 V (1.25 V - 0.75
V). Exchange the comments for the figure below!
Coupling (AC,DC, Ground)
On many digitizers, you can configure the input channels to be DC coupled, AC
coupled, or GND coupled. DC coupling allows DC and low-frequency
components of a signal to pass through without attenuation. In contrast, AC
coupling removes DC offsets and attenuates low frequency components of a
signal. Activating AC coupling inserts a capacitor in series with the input. This
feature can be exploited to zoom in on AC signals with large DC offsets, such as
switching noise on a 12 V power supply. GND coupling disconnects the input
and internally connects the channel to ground to provide a ground, zero-voltage
reference.
Block diagram of the digital multimeter
http://www.ti.com/solution/digital_multimeter_bench_system
Design Considerations
A Digital Multimeter (DMM) is a precision analog instrument used to measure AC and DC
voltage, AC and DC current, capacitance, and resistance. Five system level blocks are
common to bench DMM designs: Signal Conditioning and A/D conversion of the input
signal, LCD/LED/Keypad, Control and Data Processing, Memory/Peripheral devices, and
Power Management. Implementation specifics will obviously vary depending on the feature
set of the meter.
The common core subsystems are:
Analog Front-End
Signals are initially passed through a signal conditioning subsystem which amplifies or
attenuates the analog signal in preparation for further conditioning, depending on whether the
measurement is AC volts, DC volts, current, or resistance. Precision amplifiers and analog to
digital converters are used to facilitate resolutions from 5 1/2 to 8 1/2 digits on modern
DMMs.
LCD/LED/Keypad
Bench DMMs offer dual, 7 segment displays. The PC is typically used to provide a fullfeatured graphical user interface for bench DMMs.
Control and Data Processing
Executes measuring processes and controls interface with memory and peripheral devices.
The Digital Signal Processor (DSP) is used to linearize data from the ADC and perform
calibration. It also performs real-time analysis of acquired signals such as min/max,
averaging, and conversion to engineering units. Modern DMMs allow users to directly
measure temperature using a variety of sensors.
Memory/Peripheral Devices
Measurement results are stored in EEPROM or FLASH memory and can be uploaded to a PC
via USB, Ethernet, RS-232, or IEEE-488 (GPIB) interfaces.
Power Management and Conversion
Converts the input battery power to run various functional blocks. TI has a wide range of
products like amplifiers, ADCs, Power, Interface, and Processors to meet the requirements of
bench Digital Multimeter designers.
Questions / Topics:
What is measurement? (uncertainity)
SI quantities, SI system of units, some derived quantities
What is the error? (absolute, relative)
Classification of errors
Average of the absolute error, error limit, Standard deviation
Evaluation of simple measurement
Usage of DMM (also in practical)
Usage of oscilloscope (also in practical)
Net resistance for serial and parallel resistors (in practice, measurement and
calculation)
Settings on DC power supply (in practice)
Measuring AC signal with oscilloscope, settings on function generator (in
practice)
Mathematical description of AC signal:
What is:
amplitude, periodic time, frequency, maximum value
RMS: meaning, formula
How moving coil meters are working?
Extending the maximum range of the voltmeter
Extending the maximum range of the ammeter, the sunt resistor
The inner resistance: measuring high and low resistances
Explain the main oscilloscope functions:
time/div; volt/div; vertical shift, trigger, coupling (AC,DC), vertical gain
How CRT is working?
Fourier theorem
Bandwidth
Rise time
Sampling rate/what is sampling
Bit resolution or resolution of ADC
Offset
Nyquist or sampling theorem
Time diagramm and frequency diagramm of the signal.
Block diagramm and main functions of the digital multimeter
Block diagramm and main functions of the Digital Storage Oscilloscope