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Electronic instrumentationImportant Analog and Digital Signals in
TD
Lecturer: Dr. Samuel Kosolapov
Items to be discussed
2
• Sin/Cos wave• Pulse Wave (Square Wave). Duty cycle• Sawtooth Wave• Triangle Wave• Heaviside Step Function• Dirac Function• Examples of Medical Signals
Example of ImportantAnalog Voltage Signal: Sine Wave
3
sec/:2
;;1
),,,(
,,
:
sin2sin2sin
0
000
radianFrequencyAnglef
PeriodTT
f
GHzMHzkHzHzFrequencyf
AmplitudeValuePeakV
Parameters
tVT
tVtfVtV
Please do not forget 2 Pi during exam
Mind SI units rules:kHz and not Khz
Example: Sine Wave
4
VoltVV
radf
THertzHzf
ttV
1
secondradian
sec28.62
);second(sec1);(1
12sin1
0
T: Period1 sec
VoPeak ValueAmplitude
VppPeak-to-Peak
Value= 2 Vo
Example: Sine WaveOLD Style analog scope: How to measure Vo and Vpp
5
OLD Analog Scope:it was hard to measure Vo (where is Zero Line ???)it is much easier to measure Vpp (from lower to upper signal level. (use “fingers”)
Vertical signal shift is not important here (explain why) + explain why scope must be calibrated & zeroed before usage if Vo must be measured
Vpp is more “universal” concept than amplitude.It is not always obvious where the “amplitude is”, but Vpp can be easily evaluated
In case of noise: Vpp can be “easily” “evaluated” approximately, by human eye, but this may be good enough
Modern Digital scope: How to measure Vpp
6
Modern digital scopes has a special means (cursors)+ menu for math operations (V1+V2, V1-V2, etc.)
Digital scope store signal as an array.Simple algorithm can find Min and Max values in the relevant time interval automatically.Then Vpp = Max – Min can be presented.
Another (more sophisticated) algorithm can find closest local minimum and local maximum.But this algorithm may fail in case of noise In some cases digital scope “automatic” calculations may be wrong
Example: Sine WaveModern Digital scope: How to measure Vpp. Problems
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Be sure that signal is clean from noise and not distorted when providing automated measurements with digital scopes
“averaging” function can be usedHumans are still better in noise cleaning
than simple “computer algorithms.
Beware of “alias” when “signal frequency is close Nyquist Frequency High quality analog LPF Filter is a must before ADC
You must be professional EE to properly use “simple and automatic” digital scope
Example of Sine WaveEffective (RMS) Value
8
2
oRMS
VV
Heat equivalent
Can be used for pure sine/cosine wave only !!!
Integral must be used for any other signal
WE WILL MOSTLY USE AMPLITUDE Vo (or Peak-to Peak value) Vpp
Practical Examples of Sine WaveAnalog Electronics: Practical Frequency ranges
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Audio – RF - Optics
Name Abbr. Frequency Usage
Extremely low frequency
ELF 3-30 Hz Communication with submarines
Audio (hi-fi) au 20 Hz – 20 kHz High Fidelity Audio: speech & music
Low frequency LF 1.8-2.0 MHz Amateur radio: USA 160 meters
Medium Frequency MF 0.6-3 MHz AM broadcasts
High Frequency HF 3-30 MHz Shortwave broadcasts, RFID
Very high frequency VHF 30-300 MHz FM, TV, aircraft-to-aircraft communication
Ultra high frequency UHF 300-3000 MHz TV, microwave ovens, mobile phones, wireless LAN, Bluetooth, ZigBee, GPS
Super high frequency SHF 3-30 GHz Wireless LAN, radars, communications satellites
Future: … Optics ( ~ 1015 Hz) …Gamma Rays (~1018 Hz)
Practical Examples of Sine WaveAnalog Electronics: Practical Frequency ranges
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Much More detailed tables are practically used:Frequency range is a valued strategic resource today – like oil
Many abbreviations and buzz names
For Exact definitions see LAST official materials
Practical Examples of Sine WaveAnalog Electronics: Practical Frequency ranges
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Polite advice: never “invent” words like Super, Very Hugh, Ultra High etc.In a number of years this will looks funnyExample: SVGA of 1989 : 1024x768
IMPORTANT:Never transmit RF before checking rules and possible punishment(s)
Practical Example of Sine WaveElectronics: Practical Voltage ranges
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For Exact definitions see LAST official materials
The International Electrotechnical Commission (IEC) defines low voltage as any voltage in the range
50–1000 V AC or 120–1500 V DC.
For Electronics those voltages are very High (especially 1500 V)
We will not speak about voltages above ~ 50 V (except limited number of cases)
Typical laboratory signal generator generates voltages in the range1 mV – 50 V
Sometimes signals are smaller ~ 10 uV (mkV, mV)
Dealing with signals smaller then 1 uV (mkV) is very problematicbecause of noise
Arduino UNO R3:Never apply voltage< 0 V and/or >5 V
to Arduino pins
Some Arduino boards uses 3.3 V
Practical Example of Sine WaveElectronics: Practical Sensors Voltage ranges
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In the typical educational Electronics Laboratory practical voltage limit is ~ 10 mV
Do Experiment: while using scope try to position cellular phone near wires and call some other telephone.
What will You see ? What about lamps, motors of air conditioner, etc…
Q1. Why Faraday cage may be useful ?
Q2. Why Shielded wires are used ?
Many analog sensors produces signal < 1 mV filters, amplifiers, and sophisticated algorithms must be used
Example of Sine WaveElectronics: deciBell (dB)
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The DeciBell (dB) originates from methods used to quantify reductions in audio levels in telephone circuits (~1920).
Original definition is for Power.
For Voltages
For example: V1 = 1V, V0 = 100 mV; Then VdB = 20 dB
+3dB ratio means
0
110log10
P
PPdB
R
VPbecause
V
VVdB
2
0
110 ~log20
707.0~2
1~
0
1
V
V
Example of Sine WaveElectronics: deciBell (dB)
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The deciBell is also commonly used as a measure of gain or attenuation
dB units are used when we want to compare (and plot) different Voltagesin case the voltages can vary in a wide scale (say, from uV to V)
Warning: Exact practical definition of dB contains some specific details concerning cable resistanceWe omitted this for now.
Q1: PdB = +10 dB. What Relative Increase of Power is ? A = 10The same for the Voltage ? A= 20
Q2: PdB is 30 dB. ? A = 10* log (10^3) = 10*3 The same for Voltage ? A = 60
Example of Sine WaveElectronics: dBm
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Important unit is dBm: abbreviation for the power ratio in dB when P0 is 1 mW (milliWatt)
Example: 0dBm means Power of 1 mW.+3dBm is ~ 2mW; -3dBm means 0.5 mW
Some additional examples: Typical transmitter of FM radio with 50 km range is ~ 100 kW 80 dBm
Typical thermal radiation emitted by a human body ~ 100W 50 dBm
Maximum output of Class 1 mobile phone ~ 2W 33 dBm(Can You boil popcorn with this ?)
WiFi transmission power in laptops ~ 32 mW 15 dBm
0
110log10
P
PPdB
Example of Sine WaveElectronics: dBm
17
Typical transmitter of FM radio with 50 km range is ~ 100 kW 80 dBm
Typical thermal radiation emitted by a human body ~ 100W 50 dBm
Maximum output of Class 1 mobile phone ~ 2W 33 dBm(Can You boil popcorn with this ?)
WiFi transmission power in laptops ~ 32 mW 15 dBm
0
110log10
P
PPdB
At least remember order of those numbers when non-professionals(which never learned logarithms)
discuss radiation issues. Beware when business or political interests of any kinds are used
in scientific or technological discussion
Demonstrate how EE can prove for uneducated auditoryanything he/she wants: (example of Dog on the Mars weak effect)
Example of ImportantAnalog Voltage Signal: Pulse Wave (Square Wave)(Compare with sin wave)
18
Q1: Can one use RMS with Pulse Wave ?A: Yes, but this is not sqrt(2)
!!!! (Simple) integral must be calculated!!!
Pulse Wave Signal looks like “Digital” signal, but is widely used in Analog Electronics
Example of Important Analog Voltage Signal: Biased (Shifted) Sin and Pulse Wave
19
Concepts:Bias, Offset, DC Shift
Explain DC shift: bias: +DC
Q1. Propose simple circuit havingDC battery, resistors and capacitorsFor DC-Biasing of SIN signal
Arduino Analog pins accepts signals in the range {0..5 V}. Q. How to cope with negative part of the signals ?
Example of ImportantAnalog Voltage Signal: Sawtooth Wave
20
This signal is used in the Analog Electronics
to check linearity(details later)
Digital Version of this signal is used in some ADC designs(details later)
Laboratory Instrument: Laboratory Signal Generator
21
Generates Sin, Pulse, Sawtooth, Triangle + many others useful waves
Bias (Offset) can be set
Generally signal amplitude can be set but can not be measured
It is assumed that amplitude is measured by attached oscilloscope
Summary of Basic Analog Voltage Signals:Sine wave, Square wave, Triangle wave, Sawtooth waveVirtual Laboratory Instrument: Signal Generator
22
Q1: How to evaluate Frequency for presented signals ?Q2: Do You see that p-p
can be easily evaluatedfor any of those signals
whereas amplitudeevaluation is problematic ?
Virtual Laboratory Instruments (simulation): Usage of Oscilloscope & Signal Generator
23
Generates Sin, Pulse, Sawtooth, Triangle + many others useful waves
Explain how Bias (Ofset) can be set, what duty cycle isExplain: Simulation is actually DIGITAL, in some situations simulation can be WRONGEE can not rely on simulation only !!!!!
Analog Signal: MeasurementsLaboratory Instruments: Multimeter, Signal Generator & Oscilloscope
24
Q1: Can you use Multimeter to measure frequency & magnitudes of the signal ?
Example of Important Analog Voltage Signal:qt, H(t), u(t) Heaviside (step) function
25
Maple default definition
Above is “non-electronic”Analog signal must be defined for any t (or x) Black magic must be used:
Problem: Voltage is changedTOO Fast
Which means that electrons must change their speed in 0 time a == infinity Force == infinity
Example of Important Analog Voltage Signal:qt, H(t), u(t) Heaviside (step) functionMore realistic “Analog” definition
26
When s 0 , F1(t) q(t)
S
F1:=proc(t,s) if t < -s/2 then 0
elif t > s/2 then 1else 1/2+t/s
fi end:
plot( 'F1(t,1)', 't'=-2..2);
#1
Example of Important Analog Voltage Signal:qt, H(t), u(t) Heaviside (step) function
27
When s 0 , F1(t) q(t)
This way EE may imagine“real” but very “fast” switch
(Math presentation of an Electric Switch)
Example of Important Theoretical Analog Voltage Signal:Dirac dt function
28
Example of Important Theoretical Analog Voltage Signal:Dirac dt function
29
MAPLE old definition:The Dirac(t) delta function is defined as zero everywhere
except at t = 0 where it has a singularity.It also has the property that Integral(Dirac(t),t = -infinity..infinity) = 1
Looks NON-ALGORITHMIC.
MAPLE new definitions:
In all these formulas epsilon representsa sufficiently small real number.
In practical applications, as soon as epsilon becomes negligible compared to the x values involved in the problem,
it becomes impossible to distinguishbetween these alternative representations
Example of Important Theoretical Analog Voltage Signal:Dirac dt function
30
F2:=proc(t,s)if t < -s/2 then 0
elif t > s/2 then 0else 1/s
fiend:
Area: s*(1/s) = 1;
When s 0 , F2(t) d(t)
Explains and 1/s
Example of Important Theoretical Analog Voltage Signal:Dirac dt function
31
When s 0 , F2(t) d(t)
The way EE may imagine Dirac’s function
Example of Important Theoretical Analog Voltage Signal:Heaviside & Dirac functions: Properties
32
)()()(
)()()(
)(
1)()(
0
0
d
dqq
d
dd
ftdttf
dtdt
tdt
dttdtt
t
The last formula is very important: Value Extraction:
Delta is non zeroonly when t is near .
This region is really small f(t) is ~ constant there f(t) ~ f() Constant out of integral integral of d is 1.
Medical Signals.
33
A umber of Medical Devices (monitors)used to measure signals
produced by a human bodyin order to get important
diagnostic information
Medical Signals. ECGPropose Formula (or algorithm)describing this signal
34
Sorry, this Quiz is for PhD:Math Model of ECG Signal
35
ECG is a clinical diagnostic tool
More examples of medical signals. EEG (ElectroEncefaloGram).electrical activity produced by brain
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EEG is a clinical diagnostic tool
More examples of medical signals. EMG (ElectroMioGram).electrical activity produced by skeletal muscles
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More examples of medical signals. ERG (ElectroRetinoGram).electrical activity produced by eye
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More examples of medical signals. ERG (ElectroRetinoGram).electrical activity produced by eye
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ERG is a clinical diagnostic tool
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