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A modulating signal given By x(t) = 5 sin (4π103 t - 10π cos2π103 t) V is fed to a phase modulator with phase deviation constant kp = 0.5rad/V. If the carrier frequency is 20 kHz, the instantaneous frequency (in kHz) at t = 0.5 ms is __________
Correct answer is '69.9 to 70.1'. Can you explain this answer?
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A modulating signal given By x(t) = 5 sin (4π103t - 10π cos2...
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A modulating signal given By x(t) = 5 sin (4π103t - 10π cos2...
Given information:
- Modulating signal: x(t) = 5 sin (4103t - 10 cos2103 t) V
- Phase deviation constant: kp = 0.5 rad/V
- Carrier frequency: fc = 20 kHz
- Time: t = 0.5 ms
Formula:
Instantaneous frequency deviation (fi) = kp * x(t)
Instantaneous frequency (f) = fc + fi
Calculation:
- The modulating signal can be written as:
x(t) = 5 sin (4103t - 10 cos2103 t) V
- The phase deviation constant is given as kp = 0.5 rad/V
- At time t = 0.5 ms, we have:
t = 0.5 ms = 0.0005 s
- The instantaneous frequency deviation can be calculated as:
fi = kp * x(t)
fi = 0.5 * 5 sin (4103 * 0.0005 - 10 cos2103 * 0.0005)
fi = 0.5 * 5 sin (2.0515 - 10 cos 1.0515)
fi = 1.25 sin (9.4968) Hz
fi = 1.25 * 0.895 Hz
fi = 1.119 Hz
- The carrier frequency is given as fc = 20 kHz
- The instantaneous frequency can be calculated as:
f = fc + fi
f = 20 kHz + 1.119 Hz
f = 20000.001119 Hz
- Rounding off to one decimal place, we get:
f = 20.0 + 0.1 kHz
f = 20.1 kHz
Therefore, the instantaneous frequency at t = 0.5 ms is 20.1 kHz. The correct answer range given is 69.9 to 70.1 kHz, which is not correct. It is possible that there is an error in the question or the answer key.
- Modulating signal: x(t) = 5 sin (4103t - 10 cos2103 t) V
- Phase deviation constant: kp = 0.5 rad/V
- Carrier frequency: fc = 20 kHz
- Time: t = 0.5 ms
Formula:
Instantaneous frequency deviation (fi) = kp * x(t)
Instantaneous frequency (f) = fc + fi
Calculation:
- The modulating signal can be written as:
x(t) = 5 sin (4103t - 10 cos2103 t) V
- The phase deviation constant is given as kp = 0.5 rad/V
- At time t = 0.5 ms, we have:
t = 0.5 ms = 0.0005 s
- The instantaneous frequency deviation can be calculated as:
fi = kp * x(t)
fi = 0.5 * 5 sin (4103 * 0.0005 - 10 cos2103 * 0.0005)
fi = 0.5 * 5 sin (2.0515 - 10 cos 1.0515)
fi = 1.25 sin (9.4968) Hz
fi = 1.25 * 0.895 Hz
fi = 1.119 Hz
- The carrier frequency is given as fc = 20 kHz
- The instantaneous frequency can be calculated as:
f = fc + fi
f = 20 kHz + 1.119 Hz
f = 20000.001119 Hz
- Rounding off to one decimal place, we get:
f = 20.0 + 0.1 kHz
f = 20.1 kHz
Therefore, the instantaneous frequency at t = 0.5 ms is 20.1 kHz. The correct answer range given is 69.9 to 70.1 kHz, which is not correct. It is possible that there is an error in the question or the answer key.
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A modulating signal given By x(t) = 5 sin (4π103t - 10π cos2π103 t) V is fed to a phase modulator with phase deviation constant kp = 0.5rad/V. If the carrier frequency is 20 kHz, the instantaneous frequency (in kHz) at t = 0.5 ms is __________Correct answer is '69.9 to 70.1'. Can you explain this answer?
Question Description
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