Answer:
Output voltage equation is [tex]V_{out} (t) = 2.72 \cos (2\pi (57000)t +18.3)[/tex]
Explanation:
Given:
dc gain [tex]A = 23.6[/tex] dB
Input signal [tex]V_{in} (t) = 0.18 \cos (2\pi (57000)t +18.3)[/tex]
Now convert gain,
[tex]A = 10^{\frac{23.6}{20} } = 15.13[/tex]
DC gain at frequency [tex]f = 0[/tex] is given by,
[tex]A = \frac{V_{out} }{V_{in} }[/tex]
[tex]V_{out} =AV_{in}[/tex]
[tex]V_{out} = 15.13 \times 0.18 \cos (2\pi (57000)t +18.3)[/tex]
At zero frequency above equation is written as,
[tex]V_{out} = 2.72 \times \cos 18.3[/tex]
[tex]V_{out} = 2.72[/tex]
Now we write output voltage as input voltage,
[tex]V_{out} (t) = 2.72 \cos (2\pi (57000)t +18.3)[/tex]
Therefore, output voltage equation is [tex]V_{out} (t) = 2.72 \cos (2\pi (57000)t +18.3)[/tex]
