tab. 2. |
Obliczenia powinny być poprzedzone sprawdzeniem równania h(t) dla układu |
bieguny |
ogólnie |
transmitancje + obliczenia |
ogólnie |
2-go rzędu |
stała czasowa z pomiaru |
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0 |
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Ugen [V] = |
1 |
Rgen [Ω] = |
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Odwrotna transformata Laplace'a |
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Pomiary |
Obliczenia |
Uwagi |
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Lp. |
t |
Uwyj=h(t) |
[1-e^(-t/RC)]*Ugen
Uwyj=h(t) |
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stała czasowa ['tau']
τ |
z wykresu (ręcznie) |
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[μs] |
[mV] |
[mV] |
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[μs] |
tn |
to |
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1 |
0 |
0 |
0 |
Układ dolnoprzepustowy |
pomiar |
ręcznie
120 |
[μs] |
[μs] |
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2 |
140 |
48 |
106 |
teoria |
RC
1250 |
1120 |
60 |
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3 |
180 |
96 |
134 |
RC |
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4 |
280 |
144 |
201 |
R [Ω] = |
1000 |
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5 |
340 |
192 |
238 |
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6 |
440 |
256 |
297 |
C [nF] = |
1250 |
wart. Charakterystyczne |
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7 |
500 |
296 |
330 |
s = |
-800 |
Ugen [s.ustalony] |
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8 |
660 |
352 |
410 |
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90% |
0.9 |
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9 |
720 |
408 |
438 |
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50% |
0.5 |
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10 |
840 |
456 |
489 |
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10% |
0.1 |
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11 |
960 |
512 |
536 |
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12 |
1100 |
552 |
585 |
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fg [Hz]= |
1/2πRC
127.32395 |
800 |
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13 |
1200 |
600 |
617 |
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tn [μs]= |
tn = (035 <>0,45)/fg
2748.89 |
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14 |
1400 |
648 |
674 |
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to [μs]= |
0,1/fg
źródło: materiały wykładowe
785.40 |
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15 |
1540 |
696 |
708 |
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współczynnik czułości aparatury
Ks = |
przyjąłem 0,1
0.1 |
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16 |
1820 |
744 |
767 |
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0.01 |
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17 |
2040 |
800 |
804 |
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czas trwania stanu nieustalonego
ts = |
przyjąłem tą wartość
2878.23136624256 |
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18 |
2460 |
856 |
860 |
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5756.46273248511 |
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19 |
2920 |
896 |
903 |
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20 |
3940 |
952 |
957 |
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21 |
5560 |
992 |
988 |
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Zwis pom |
Zwis teor |
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0.0 |
0.0 |
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7.5 |
12.0 |
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12.2 |
16.1 |
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16.1 |
20.1 |
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21.6 |
25.0 |
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25.5 |
30.8 |
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30.2 |
35.1 |
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36.5 |
40.1 |
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41.2 |
45.6 |
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45.9 |
49.7 |
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63.017 |
50.6 |
55.8 |
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tab. 3. |
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56.9 |
60.5 |
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Ugen [V] = |
1 |
Rgen [Ω] = |
0 |
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60.0 |
64.1 |
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Pomiary |
Obliczenia |
Uwagi |
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65.5 |
69.9 |
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Lp. |
t |
Uwyj=h(t) |
[e^(-12500t)]*Ugen
Uwyj=h(t) |
|
stała czasowa ['tau']
τ |
|
69.4 |
73.1 |
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|
[μs] |
[mV] |
[mV] |
|
[μs] |
|
76.5 |
78.1 |
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1 |
0 |
1020 |
1000 |
Układ górnoprzepustowy |
|
pomiar |
ręcznie
118 |
|
81.2 |
83.3 |
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2 |
160 |
944 |
880 |
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teoria |
L/R
1250 |
|
85.1 |
87.9 |
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3 |
220 |
896 |
839 |
RL |
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4 |
280 |
856 |
799 |
R [Ω] = |
1000 |
Z(t6) = |
ze skryptu:
z(t) = h(t)|max - h(t)
0.132 |
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5 |
360 |
800 |
750 |
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z%(t6) |
Z%(t)=[ (h(0) - h(t) ) / h(0) ] * 100%
1.79 |
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6 |
460 |
760 |
692 |
L [mH] = |
1250 |
współczynnik czułości aparatury
Ks = |
przyjąłem 0,1
0.1 |
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7 |
540 |
712 |
649 |
s = |
-800 |
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0.01 |
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8 |
640 |
648 |
599 |
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czas trwania stanu nieustalonego
ts = |
przyjąłem tą wartość
2878.23136624256 |
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9 |
760 |
600 |
544 |
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5756.46273248511 |
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10 |
860 |
552 |
503 |
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11 |
1020 |
504 |
442 |
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12 |
1160 |
440 |
395 |
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13 |
1280 |
408 |
359 |
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14 |
1500 |
352 |
301 |
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15 |
1640 |
312 |
269 |
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16 |
1900 |
240 |
219 |
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17 |
2240 |
192 |
167 |
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18 |
2640 |
152 |
121 |
Rl [Ω] = |
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3300 |
96 |
71 |
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5560 |
40 |
12 |
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tab. 4. |
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Pomiary |
Obliczenia teoretyczne |
Uwagi |
pomocnicze |
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Lp. |
R |
L |
C |
2*√(L/C)
2√(L/C) |
Bieguny |
współczynnik tłumienia:
σ = α = R/2L
σ |
pulsacja drgań swobodnych:
ω = 1/√LC
ω |
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--------- |
Ω |
mH |
nF |
Ω |
s = σ ± jω
s1 |
s2 |
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[rad/s] |
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1 |
100000 |
40 |
40 |
2000.0 |
-1250000 + j 25000 |
-1250000 - j 25000 |
brak oscylacji |
-1250000 |
25000 |
-12.5 |
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2 |
1590 |
40 |
40 |
2000.0 |
-19875 + j 25000 |
-19875 - j 25000 |
na granicy oscylacji |
-19875 |
25000 |
-0.19875 |
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3 |
0 |
40 |
40 |
2000.0 |
0 + j 25000 |
0 - j 25000 |
oscylacje tłumione |
0 |
25000 |
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WOLFRAM ALPHA - obliczanie odwrotnej transformaty Laplace'a |
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potrzebne do wykreślenia wykresu ->
-25000 |
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tab. 5. |
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-25000 |
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Ugen [V] = |
3.52 |
Rgen [Ω] = |
0 |
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-25000 |
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Pomiary |
Obliczenia |
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Lp |
Um1 |
Um2 |
Ts |
N |
R |
C |
L |
Dobroć układu:
Q = π/Ln(Δ)
dekrement tłumienia:
Δ = Um1 / Um2
Q |
współczynnik tłumienia drgań swobodnych układu:
α = -(Ln(Δ)/Ts)
dekrement tłumienia:
Δ = Um1/Um2
α |
Nie wiem, co oznacza C2, więc liczę dla C
to równanie wygląda na okres oscylacji
2π√(LC2) |
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--- |
V |
V |
μs |
- |
kΩ |
nF |
mH |
- |
Np. |
μs |
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1 |
1.04 |
0.1 |
256 |
2 |
0.6 |
40 |
40 |
1.34 |
-9147.68 |
251.33 |
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2 |
1.56 |
0.36 |
256 |
3 |
0.4 |
40 |
40 |
2.14 |
-5727.88 |
251.33 |
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3 |
1.82 |
0.52 |
256 |
4 |
0.3 |
40 |
40 |
2.51 |
-4893.61 |
251.33 |
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4 |
2 |
7 |
256 |
5 |
0.29 |
40 |
40 |
-2.51 |
4893.61 |
251.33 |
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