IE1206 Embedded Electronics

Transcription

1 IE06 Embedded Electronics Le Le3 Le4 Le Ex Ex PI-block Documentation, Serial com Pulse sensors I,,, P, series and parallel K LAB Pulse sensors, Menu program Start of programing task Kirchhoffs laws Node analysis Two-terminals AD Le5 Ex3 K LAB Two-terminals, AD, omparator/schmitt Le6 Le8 Ex6 Le3 Ex4 Ex5 Le0 Le7 Le9 Le Le Ex7 Display Written exam K3 LAB3 Transients PWM Step-up, -oscillator Phasor PWM P AP/IND-sensor K4 LAB4 LP-filter Trafo L-osc, D-motor, P PWM Display of programing task Trafo, Ethernet contact

2 A signal from reality Actual signals are difficult to interpret. They are often disturbed by noise and hum. Hum is our 50Hz network induced into the signal lines. Noise is random disturbances from amplifiers (or even resistors).

3 Maybe a slow D Perhaps the signal is a slowly increasing direct voltage from eg. a temperature sensor? In this case, the interference consist of 50 Hz hum and high frequency noise. A LP-filter (=LowPass) filters away the interference and removes the interferences from the signal.

4 Maybe a sine wave Maybe the signal is a sine wave? In this case, the interference consist of the D voltage level slowly changing, offst, and that noise is added. A BP-filter (BandPass) will block the offset and filters out the noise.

5 Maybe rapid variations Perhaps the signal is the rapid variations? In this case, the interference consist of the D voltage level slowly changing, and that hum has been added. A HP-filter (HighPass) removes the interferences from the signal.

6 LP HP BP BS LP lowpass HP highpass BP bandpass BS bandstop BP and BS filters can be seen as different combination of LP and HP filters.

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8 ( L-Filter ) With L and one can build effective filters, and this was formerly one of the most important branches of electronics.

9 Simple Filters Inductors are more complicated to manufacture than capacitors and resistors, therefore, is typically only combination and used. Fast computers can filter signals digitally. alculating a signal s moving average can for example correspond to the LP filter. Nowadays dominates the digital filter technology over the analog. Simple filter are natural parts in most measuring instruments, or are even arising from "itself" when we are linking equipment together. This is the reason that one must know and be able to calculate on simple -links, even though they regarded as filters are very incomplete.

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11 Voltage divider, Transfer function Simple filters are often designed as a voltage dividers.a filter transfer function, H() or H(f), is the ratio between output voltage and input voltage. This ratio we get directly from the voltage divider formula! ) ( Z Z Z H Z Z Z

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13 LP-filter, vectors Phasor diagram: and has the current I in common. Volyage over resistor and voltage over capacitors kondensatorn therefore becomes perpendicular. Pythagorean theorem can be used: 3 arctan 3 4 5

14 LP-filter, arctan arctan 0 ) arg( arg() arg ) (

15 LP-filter, H() H abs H H argh arctan ( ) At the angular frequency when =, will the numerator real part and imaginary part be equal. This is the filter cutoff frequency.

16 LP-magnitude function = k = F fg Hz 6 H G fg ( )

17 LP-Phase function arg H arctan( )

18 Graphs with Mathematica Mathematica has commands for complex absolute value (abs []) and argument (arg [], in radians). r=*0^3; c=*0^-6; uu[f_]:=/(+i**pi*f*r*c); LogLinearPlot[Abs[uu[f]],{f,,0000},Plotange->All,PlotPoints->00]; LogLinearPlot[(80/Pi)*Arg[uu[f]],{f,,0000}, Plotange->All,PlotPoints->00]; Press SHIFT + ENTE to start the calculation and the plot. Amount plot Phase plot [degres] ([rad]80/)

19 Two sides of the same coin G Low cut off frequency G will supresses interference good, but it will also mean that the time constant is long so it takes time until T reaches its final value and can be read.

20 ( AD-converter LP-filter ) It is necessary to compromise! In order to remove noise from the input signal to the AD converter one usually add a capacitor. S must have no bigger value than 0k otherwise you risk losing accuracy because of the leakage current I LEAKAGE. When the sample charge from is taken to sampling capacitor HOLD. should therefore be at least 04 times greater than HOLD (0pF) if you do not want to lose accuracy. S gives the cutoff frequency of how fast signals AD converter can follow.

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22 HP-filter, arctan arctan 90 ) arg( ) arg( arg ) ( = arccot()

23 HP-filter, H() H abs H argh arctan ( ) At the angular frequency when =, will the numerator real part and imaginary part be equal. This is the filter cutoff frequency.

24 HP-magnitude function = k = F f G Hz 6 abs H ( )

25 HP-phase function arg H arctan

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27 Wien bridge (4.5) Was investigated by Max Wien 89 For a certain frequency and frequency? are in phase. What

28 Wien bridge Z Z and are in phase if the transfer function imaginary part is 0!

29 Wien bridge Z Z and are in phase if the transfer function imaginary part is 0!

30 Wien bridge Z Z ) ( ) ( ) ( ) ( and are in phase if the transfer function imaginary part is 0!

31 Wien bridge Z Z ) ( 3 3 = 0 and are in phase if the transfer function imaginary part is 0!

32 Wien bridge 3 ( ) 0 0

33 Wien bridge 0 f0 Magnitude plot Phase plot Wienbridge is a band pass filter.

34 William Hewlett s master thesis Master thesis 930. Wien bridge with lamp!

35 William Hewletts master thesis Hewlett constructed a tone generator. Wien bridge attenuates the signal to /3 so he needed a amplifier with the gain exactly three times. The bulb stabilizes the signal. If the amplitude becomes too large the lamp will glow and then the signal is attenuated in the voltage divider at the amplifier input. Voltage divider < In phase! >3 Lamp will glow Lamp will glow In phase! Stabilized amplitude times = exact one! times

36 The Palo Alto garage the birthplace of Silicon Valley Which global business will you start with your thesis?

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38 When are filters used? One speaker alone can not cope with all frequencies!

39 ross over filter No iron core for audio. The crossover filter split the frequencies between the speakers.

40 Passive/Active speaker Analog crossover filter L Digital crossover filter = computer program When the amplifier is built in the speaker it becomes possible to use digital crossovers. ( XOVE = crossover filter )

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42 ( Digital filter ) Ex. a "rolling" average of the 7 most recent readings. Noisy signal LP-filter t xn6 x n5 x n 4 xn3 x n x n n6 x n n y x n 7 n Low frequencys pass High frequencys are damped Filtered signal There are much better digital filters than this...

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