Passive Frequency Selective Circuits | Study

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Passive Frequency Selective Circuits
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Passive RC Low Pass Filter
The input impedance of the oscilloscope is usually large (¿ 1 M Ω) to avoid loading the circuit
it is connected to. The impedance of the source, on the other hand, is usually low in the order
of50 Ω.
Rs=50 Ω
RL=1 M Ω
f c=1 kHz
Since the input impedance of the oscilloscope is much larger than the impedance of the
capacitor, the parallel combination of the two impedances will be just the impedance of the
capacitor. Therefore, the impedance of the oscilloscope may be neglected.
The cutoff frequency ωc is given by,
ωc= 1
RC
Taking into account the output resistance of the generator Rs, the frequency becomes,

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ωc= 1
( R+ Rs) C
2 π ( 1000 ) = 1
(R+ Rs )C
If we choose a value of the capacitor as47 nF, the resistances are given by,
( R+ Rs )= 1
( 2 π ( 1000 ) ) ( 47 ×10−9 )
( R+ Rs )=3386.28
But Rs=50, therefore,
R=3386.28−50=3336.28Ω
The closest practical resistor value is,
R=3.3 k
Figure 1: Circuit implemented in LTSpice

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Table 1: Circuit parameters at different frequencies
f V i V o G GdB Phase
10 7.071 7.0466 0.9965 -0.03 -0.57
20 7.071 7.0436 0.9961 -0.03 -1.15
30 7.0544 7.0225 0.9954 -0.04 -1.71
40 7.0575 7.019 0.9945 -0.05 -2.29
50 7.0641 7.0172 0.9934 -0.06 -2.84
60 7.0629 7.0059 0.9919 -0.07 -3.41
70 7.0607 6.9923 0.9903 -0.08 -3.97
80 7.058 6.9777 0.9886 -0.10 -4.55
90 7.0551 6.9613 0.9867 -0.12 -5.12
100 7.0551 6.9613 0.9867 -0.12 -5.69
200 7.0253 6.7541 0.9614 -0.34 -5.70
300 7.0176 6.5537 0.9339 -0.59 -11.25
400 7.0125 6.3332 0.9031 -0.88 -16.65
500 7.0064 6.0848 0.8685 -1.22 -21.80
600 6.9998 5.8117 0.8303 -1.62 -26.44
700 6.9915 5.5272 0.7906 -2.04 -30.75
800 6.9841 5.2661 0.7540 -2.45 -38.54
900 6.9786 4.9947 0.7157 -2.91 -41.73
1000 6.9732 4.7344 0.6789 -3.36 -44.90
1100 6.968 4.4877 0.6425 -3.84 -47.65
1200 6.963 4.2558 0.6112 -4.28 -50.04
1300 6.9577 4.0293 0.5791 -4.74 -52.33