Q11
a(ii)A sinusoidal carrier wave has frequency 500 kHz and amplitude 6.0 V. It is to be
frequency modulated by a sinusoidal wave of frequency 8 kHz and amplitude 1.5 V.
The frequency deviation of the carrier wave is 20 kHz V^–1
Describe, for the carrier wave, the variation (if any) of
1. the amplitude,
2. the frequency.
Answer:
1. Amplitude does not vary (I got this)
2. Upper limit 530kHz (I assume they got this by using 20kHz/V x 1.5V??)
Lower limit 470kHz
Changes from lower to higer and to lower limit at 8000 per second (I'm not sure how they got 8000/s??)
Please help?
Thankkkkkks :)
The frequency of the wave by which the carrier wave is going to be modulated is 8KHz that's why it'll vary 8000 times per second
L.O interview question about the service delivery protest
To determine the frequency variation of the carrier wave, we need to consider the frequency modulation by the sinusoidal wave of 8 kHz.
1. The amplitude of the carrier wave does not vary. This means that the 6.0 V amplitude will remain constant throughout the modulation process.
2. The upper limit of the frequency deviation can be calculated using the formula:
Upper Limit = Carrier Frequency + (Frequency Deviation x Modulating Signal Amplitude)
Upper Limit = 500 kHz + (20 kHz/V x 1.5 V)
Upper Limit = 500 kHz + 30 kHz
Upper Limit = 530 kHz
Similarly, the lower limit of the frequency deviation can be calculated by subtracting the frequency deviation from the carrier frequency:
Lower Limit = Carrier Frequency - (Frequency Deviation x Modulating Signal Amplitude)
Lower Limit = 500 kHz - (20 kHz/V x 1.5 V)
Lower Limit = 500 kHz - 30 kHz
Lower Limit = 470 kHz
Now, to further describe the frequency variation, we need to consider the frequency of the modulating wave which is 8 kHz.
The frequency of the carrier wave will change from the lower limit to the upper limit and then back to the lower limit at a rate equal to the frequency of the modulating signal, which in this case is 8 kHz.
Hence, the frequency will change from the lower limit of 470 kHz to the upper limit of 530 kHz, and then back to 470 kHz 8000 times per second, resulting in a variation in frequency known as frequency modulation.
I hope this clarifies the steps involved in describing the variation of amplitude and frequency of the carrier wave in this frequency modulation scenario.
To determine the variation of the frequency of the carrier wave when it is frequency modulated, we need to understand how frequency modulation works.
Frequency modulation (FM) involves varying the frequency of a carrier wave in accordance with the instantaneous amplitude of a modulating signal. In this case, the modulating signal is a sinusoidal wave with a frequency of 8 kHz and an amplitude of 1.5 V.
To determine the upper and lower limits of the frequency, as well as the rate of change, we need to consider the frequency deviation of the carrier wave, which is given as 20 kHz V^–1. The frequency deviation indicates the maximum change in frequency that occurs due to the instantaneous amplitude of the modulating signal.
1. Amplitude does not vary:
Frequency modulation does not affect the amplitude of the carrier wave. The amplitude of the carrier wave remains constant at 6.0 V.
2. Upper and lower limits of the frequency:
To determine the upper and lower limits of the frequency, we can use the formula:
Upper limit frequency = Carrier frequency + Frequency deviation x Modulating signal amplitude
Lower limit frequency = Carrier frequency - Frequency deviation x Modulating signal amplitude
Given:
Carrier frequency = 500 kHz
Frequency deviation = 20 kHz V^–1
Modulating signal amplitude = 1.5 V
Calculating the upper limit frequency:
Upper limit frequency = 500 kHz + (20 kHz/V x 1.5 V)
Upper limit frequency = 530 kHz
Calculating the lower limit frequency:
Lower limit frequency = 500 kHz - (20 kHz/V x 1.5 V)
Lower limit frequency = 470 kHz
3. Rate of change:
The rate at which the frequency changes occurs at a rate equal to the frequency of the modulating signal. In this case, the modulating signal has a frequency of 8 kHz. Therefore, the frequency of the carrier wave changes from the lower limit to the upper limit and back to the lower limit at a rate of 8,000 cycles per second (or 8,000 Hz).
Thus, the variation of the carrier wave frequency when it is frequency modulated is from 470 kHz to 530 kHz, with the frequency changing at a rate of 8,000 Hz.