1. Mérések régen
Many devices, without connection around the place of the measurement, in presense of the researcher.

2. Modern mérőrendszerek
Szenzorok: (hall, fotocella, termisztor stb)
DSP: digital signal processing
Lásd jegyzet

3. Lengő tekercses mikroamper-mérő
0,1%

4. Elektromágneses V/A DC

6. How shunt is working?(extending the range n-times)
Moving coil ammeter
R_inner is small, 9
I_max=20mA
Desired range: 200 mA
What to do?

7. R_inner*I_ammeter=I_shunt*R_shunt (parallel branches, U equal)
Moving coil ammeter
R_inner is small, 9
R_shunt is small
I_ammeter, 20mA
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

8. Moving coil ammeter
R_inner is 1M
U_max=20V=I_max/R_inner
Desired range: 2kV mA
What to do?
Measured load 10k

9. 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)
Measured load 10k

11. Ballisztikus galvanométer nullindikátor

12. AC, elektrodinamikus
0,2%
2kHz

13. Electrostatic voltmeter and quadrant electrometer
The balance position of the moving plate is proportional to the square of the applied voltage,

14. Kvadráns elektrométer
Four fixed plates realize four quadrants and surround a movable vane suspended by a torsion fiber at the center of the system.

15. Fogyasztásmérő

16. Elektronikus mérőműszerek
Electronic meters process the input signal by means of semiconductor devices in order to extract the information related to the required measurement.
An electronic meter can be basically represented as a three-port element
The input signal port is an input port characterized by high impedance, so that the signal source has very little load.
The measurement result port is an output port that provides the measurement result (in either an analog or digital form, depending on the way the input signal is processed) along with the power needed to energize the device used to display the measurement result.
The power supply port is an input port which the electric power required to energize the meter internal devices and the display device flows through.

17. Elektronikus, analóg DC – meter: 1% fullscale
AC – meter with half wave rectifier

18. Elektronikus DC analóg voltméter
Műveleti erősítő +
Milliampermérő

19. AC mérő félhullám egyenirányítóval

20. RMS vagy effektív érték
Ha a váltakozó áram effektív vagy RMS értéke I_eff, akkor a tekintett áram Dt idő alatt R terhelésen I_eff2*Dt*R hőt fejleszt.

21. True RMS analóg voltméter

22. Digitális műszerek The main factors that characterize DVMs:
Speed (reading/sec)
Automatic operation
Programmability.
They presently offer the best combination of speed and accuracy
Capability of automatic operations and programmability
A typical application field is therefore that of automatically operated systems.

23. The basic measurement ranges of most DVMs are either 1 V or 10 V
The basic measurement ranges of most DVMs are either 1 V or 10 V. It is however possible, with an appropriate preamplifier stage, to obtain full-scale values as low as 0.1 V.
If an appropriate voltage divider is used, it is also possible to obtain full-scale values as high as 1000 V.
Presently, a six-digit DVM can feature an uncertainty range, for short periods of time in controlled environments, as low as the % of reading or % of full range.
The speed of a DVM can be as high as 1000 readings per second.

24. Digitális műszerek

25. Dual-Slope

26. Dual Slope képlet

28. Transzformátor
Ideális esetben

29. A teljesítmény nem változik-Power transformers

35. Kapacitív feszültségmérés
Capacitive sensors detect voltage by different methods:
1. Electrostatic force (or torque)
2. Kerr or Pockels effect
3. Josephson effect
4. Transparency through a liquid crystal device
5. Change in refractive index of the optic fiber or in light pipe

36. Elektrosztatikus erő

37. Polarizáció

38. Nagyfeszültség mérése

39. Árammérés: Hall szenzor

40. Áram – feszültség átalakító

41. Áram feszültség átalakító

42. Oscilloscope
Cathode Ray Tube
LCD display
Analogue
Digital

43. Principle of displaying
Horizontal movement

44. The main function of the oscilloscope is to somehow stop the picture on the screen.
If the period of oscillation of the sawtooth signal is the same or multiple as the period of investigated signal the successive pictures appear to be the same.
This creates the illusion that the picture is standing still.
We say that the investigated signal is synchronized with the sweep signal.

46. The electron beam from the cathode is passing through the acceleration anode and focusing area. This beam strikes the phosphor coating on the screen causing the light.
Usually the system of deflection of the electron beam consists
of two pairs of plates: horizontal and vertical ones.
Recently, the cathode ray tube is often substituted by the liquid crystal display LCD (Sarma 2004), especially in hand held oscilloscopes.

47. Folyadékkristályos kijelző / LCD display

48. Synchronisation
The sawtooth voltage is initiated by the pulse from triggering system.

49. Triggering modes
In the simplest case of the automatic trigger mode this start can occur for the zero value of signal
Of course it is possible to set manually the moment of triggering – for example for defined value or for rising or falling slope.
The triggering mode can be periodical or a single sweep mode

50. Volt/div
Channel
At high frequencies
Time Base: Sec/div

51. Alternate or Chopper mode

52. X-Y operation

53. Analóg oszcilloszkóp

54. Coupling AC DC
Ground

57. Measuring a function: Something depends on something
20 4.9
268 64
First col: measured I (mA)
Second col: measured U (mV)
Error of DMM: 1% in current, 0.5% in voltage
U-I graph means: U as a funcion of variable I so
I has been varied and the consequent changes in U were measured.

58. X-Y type graph
Labels
Units
Measured points

59. Error bars
+-5% error - bars

60. Error boxes real DMM

61. Fitting Measured points: U_i, I_i
n – number of data points
p – number of parameters (R so 1)
Measured points: U_i, I_i
Probe function: Up_i=R*I_i, where R is constant
Change R until good fit reached.
Sometime probe function is also subject to change!

62. IGOR v. Excel v. Root v. SciLab v. MatLab v. Origin

63. DMM and Digital Oscilloscope

64. DMM
Symbols
Automatic range
True RMS

65. Fluke specifications

69. FLUKE 8845a-DMM

70. Precision and versatility for bench or systems applications
6.5 digit resolution
Basic V dc accuracy of up to %
Dual display
100 μA to 10 A current range, with up to 100 pA resolution
Wide ohms range from 10 Ω to 1 GΩ with up to 10 μΩ resolution
2 x 4 ohms 4-wire measurement technique
Both models measure frequency and period
8846A also measures capacitance and temperature
USB memory drive port (8846A)
Fluke 45 and Agilent 34401A emulation
Graphical display
Trendplot™ paperless recorder mode, statistics, histogram
CAT I 1000 V, CAT II 600 V

71. Ranges:
 8845A: 100 mV to 750 V
 8846A: 100 mV to 1000 V
Max. Resolution:
 100 nV
Accuracy:
 8845A:
 8846A:
Frequency:
 3 Hz to 300 KHz

72. Ranges:
 8845A: 10 mA to 10 A
 8846A: 100 mA to 10 A
Max. Resolution:
 8845A: 10 nA
 8846A: 100 pA
Accuracy:  
Frequency:
 3 Hz to 10 kHz

73. 2x4 Wire:
 Yes
Ranges:
 8845A: 100 Ω to 100 MΩ
 8846A: 10 Ω to 1 GΩ
Max. Resolution:
 8845A: 100 μΩ
 8846A: 10 μΩ
Accuracy:
 8845A:
 8846A:

74. Accuracy is often expressed as: (% Reading) + Offset or
Pontosság / accuracy
Accuracy essentially represents the possible difference between the measured and the real value of the inquired quantity.
Accuracy is often expressed as:
(% Reading) + Offset or
(% Reading) + (% Range)
±(ppm of reading + ppm of range)

75. Note: Refer to the specifications included with your DMM to determine which method is used.
For example, assume a DMM set to the 10 V range is operating 90 days after calibration at 23 ºC ±5 ºC and is expecting a 7V signal. The accuracy specifications for these conditions state ±(20 ppm of reading + 6 ppm of range). To determine accuracy of the DMM under these conditions, use the following formula:
Accuracy = ±(ppm of reading + ppm of range) Accuracy = ±(20 ppm of 7 V + 6 ppm of 10 V) Accuracy = ±((7 V(20/1,000,000) + (10 V(6/1,000,000)) Accuracy = 200 µV
Therefore, the reading should be within 200 µV of the actual input voltage.

76. Absolute unit of resolution = 20.0 V/200,000 = 100 µV
For a noise-free DMM, resolution is the smallest change in an input signal that produces, on average, a change in the output signal. Resolution can be expressed in terms of bits, digits, or absolute units, which can be related to each other.
For example, a noise-free DMM set to the 10 V range (20 V total span) with 200,000 available counts has an absolute unit of resolution of:
Absolute unit of resolution = 20.0 V/200,000 = 100 µV
The readout of this noise-free DMM displays six digits. A change of the last digit indicates a change of 100 µV of the input signal.

77. Noise
Noise in a measurement can originate from the instrument taking the measurement or from an interfering signal passing through the instrument and causing measurement instability. When considering noise, you need to know the measurement bandwidth because it sets the bounds for how you can manage the noise. You can decrease the measurement bandwidth by increasing the aperture of the measurement or by averaging the measurement.

78. A commonly overlooked source of noise in precision instrumentation is the source noise resistance (ohms), as shown in the following figure.

79. If the DMM is digitizing at a 1 kS/s, the measurement bandwidth is 1 kHz and the effective noise is:
en = 4 nV x 316 en = 1.26 µVrms or 8.3 µVp-p
Thus, the source resistance (ohms) limits the noise floor of the measurement over a 1 kHz bandwidth to 8.3 µVp-p.

80. EDISON, olcsó, magyar, kézi
EDISON digitális multiméter

94. Belső sönt!

95. Egy belső áramforrás referencia áramot hajt át a mérendő ellenálláson.

98. Measuring RMS Thermal ac-to-dc converters
This older technology for rms measurements uses the equivalent-heatingvalue approach. The ac signal heats a thermocouple, then the dc section of the meter reads the thermocouple output.

99. Peak and Averaging ac-to-dc converters
Inexpensive meters, particularly inexpensive hand-held meters, usually derive rms levels from either peak or average values. They deliver true rms only for pure, undistorted sine waves. If you need true rms measurements on real-world signals, these meters are not a viable option.

100. Analog ac-to-dc converters / true rms
Many mid-range and high-end DMMs use a chain of analog circuits to compute the square, then the mean, then the square root of the mean to deliver true rms for nearly all signal types. Thanks to advances in integrated circuitry, these DMMs are small, accurate, and still relatively inexpensive.

101. ADC

102. Digital Oscilloscope
The two major components in a high-speed digitizer's analog front end are
analog input path
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

104. 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.

105. 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).
The theoretical amplitude error of a measured signal can be calculated from the ratio of the digitizer's bandwidth in relation to the input signal frequency (R).
For example, the error in amplitude when measuring a 50 MHz sinusoidal signal with a 100 MHz high-speed digitizer, which yields a ratio of R=2, is approximately 10.5%.

106. Rise time of the input signal
Rise time of the digitalizer
Rise time of the input signal

107. This means that the rise time of a 100 MHz digitizer input path is 3
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).
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.

108. Sampling 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.
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,....

109. Time and frequency domain: Fourier theorem
Often, you will sample a signal that is not a simple sine or cosine wave
However, Fourier’s theorem states that any waveform in the time domain (that is, one that you can see on an oscilloscope) can be represented by the weighted sum of sines and cosines.
The "sum" waveform below is actually composed of individual sine and cosine waves of varying frequency.
The same "sum" waveform appears in the frequency domain as amplitude and phase values at each component frequency (that is, f0, 2f0, 3f0).

111. The first relationship links the highest frequency that can be analyzed (Fmax) to the sampling frequency (fs) (see discussion of the Nyquist theorem).
                    (8)
The second relationship links the frequency resolution (f) to the total acquisition time (T), which is related to the sampling frequency (fs) and the block size of the FFT (N).
                         (9)
DFT, FFT
Y(t)
Z(1/t)

112. The FFT spectrum output is complex;
Every frequency component has a magnitude and phase.

113. Spektrum analyzers

114. Nyquist theorem
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).

115. Resolution
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 % of the full scale.

116. An ADC takes an analog signal and turns it into a binary number
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.

118. Digital Storage Oscilloscope Record length
Record length refers to the amount of memory dedicated to storing digitized samples for postprocessing or display for a single 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).

119. Vertical range and offset
Change the figs!

120. 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.

121. Probes
Passive probes
The passive probe is the most widely used general-purpose probe. Passive probes are specified by bandwidth (or rise time), attenuation ratio, compensation range, and mechanical design aspects. Probes with attenuation X10, X100, or X1000, have a tunable capacitor that can reduce capacitive effects at the input. The ability to cancel or minimize effective capacitance improves the probe’s bandwidth and rise time. Figure 2 shows a typical X10 probe model.

123. Analog to Digital

124. Bridge Circuits

125. Most accurate devices (till 2003) for the measurement of
Resistance
Impedance
Resistance/Impedance to voltage converter

126. Z is impedance, contains R, L, C components

127. Impedances

128. Power supplies

129. Both modes of working are available by setting the current limit for the measurement.
Real curves are different, depending on the inner resistivity of the power supply.

130. Balanced Bridge:
the bridge circuit is in the balance state when the
products of the opposite impedances are the same.

131. Modes of operation Null type Deflection type
Sensitivity of the bridge: S

132. R3/R4 ratio  range

133. Measuring small resistivity -resistivity of the wires
If R2=R4 the resistivity of the wires is eliminated
Measuring small resistivity
-resistivity of the wires
-contact potencials (change the polarity and repeat the measurement)

134. This condition is relatively easy to achieve by mechanical coupling of the resistors R3 /R3’ and R4/R4’.
condition for balance of the Kelvin bridge is the same as for the Wheatstone bridge.
The Kelvin bridge enables measurement of the resistances in the range – 10 ohm

135. AC bridge circuits

138. How to calculate with impedances?
Complex method

139. RLC bridges

140. Measuring L,C

141. Transformer bridge circuits

144. Unbalanced Bridge Circuits

147. Linearization

149. Bridges with amplifiers

150. Anderson loop

151. Comparison by compensation
The idea of compensation circuits

152. Comparators using compensation