(a) The system transfer function is given as
The DC gain of the system is
So -3 dB bandwidth is when
Or,
Or,
But here it is given that
So,
Or,
Or,
Or,
So -3 dB bandwidth is given as
(b) Input pressure is given by
Since input has frequency = 150kHz, we need to evaluate the
transfer function H(s) at s = j*2*pi*150*103 so that we
get
Or,
Or,
Or,
Or,
When angle is expressed in radian, we get
So output voltage is given by
Or,
Hie) Vout(s) – Kl_ W Pin(s) 52 +2Ewns + WA
Hs = 0) = K
K = (دز = H ( s | هند + بیع 2 + 2-
ਕ - ਪੰਕ
عدد 4 + کند * ارد * 2 دی + ب = 2
{= 0.707 =
لاند * *4 + 2 * حد * 2 - انت + ب = 2
ابی + ب = 2
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م = اس
f = fn = 100 kHz
Pin(t) = 5 sin(2 * 7 * 150 * 10% *t) psi
H(j2*150*103) = 10-3 (2 * 7 * 105) -(2* 7 * 150 * 103)2 + j2 * 0.707* (2* 7 * 105) * (2* 7 * 150 * 103) + (2* 7 * 105)
H(j27*150*103) = 10-3 (105) -(150 * 103)2 + j2*0.707 * (105) * (150 * 103) + (105)2
1010 H(j27 * 150 * 103) = 10-3 -1.25 * 1010+ 2.12 * 1010
H(j27 * 150 * 103) = 10-3 1-1.25 + 12.12)
H(27 * 150 * 10%) = 4.06 * 10-42 - 120°
H(27 * 150 * 10%) = 4.06 * 10-42 - 2.094 rad
Vout (t) = 5 * 4.06 * 10-4 sin(2 * 7 * 150 * 10% *t - 2.094) V
Vout (t) = 2.03 sin(2 * 7 * 150 * 10% *t - 2.094) mV