(a) Design a first-order passive high-pass filter with a cutoff frequency of 1000 rad/sec.
1 answer:
Answer:
See the attachment
Verification shown in explanation
Explanation:
wc= 1/(RC)
The value of R and C shown in the attachment can be calculated as follows:
R=100 ohms
1000= 1/(100×C)
C= 10 microfarads
Gain= R/√(R²+Xc²)
at f=500, wc= 3142.59 rad/s
Xc= 1/(2πfC)
Xc=31.83
Gain= 100/√(100²+31.83²)
Gain= 0.953
at fc= 100, wc= 628.32 rad/s
Xc= 159.15
gain= 100/√(100²+ 159.15²)
gain= 0.532
As see form calculations that gain at low frequencies is smaller and gain at very high frequencies is near to 1. This means that at high frequencies Vin≈ Vout
Hence this filter allows high frequencies to pass but blocks low frequencies by lowering the gai
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