Question

A signal m(t) frequency modulates a 100 kHz carrier to produce the following narrowband FM signal: ONBEM (t) = 10 cos (217.105t + 0.0050 sin 216.104t) Generate (block diagram design) the wideband FM signal ONBEM with a carrier frequency of 125 MHz and a peak freaquency deviation of 100 kHz. Assume that the following are available for the design:

- Frequency multipliers of any (integer) value
- A local oscillator whose frequency can be tuned to any value between 50 MHz to 150 MHz
- An ideal bandpass filter with tunable centre frequency and bandwith.
Your block diagram design must clearly specify the carrier frequencies and frequency deviations at all logical points, as well as the centre frequency and bandwidth of the bandpass filter.

Answer 1

To generate a wideband FM signal with a carrier frequency of 125 MHz and a 100 kHz peak frequency deviation, a local oscillator set to 125 MHz, a modulating signal with appropriate frequency deviation, frequency multipliers, and an ideal bandpass filter with a center frequency of 125 MHz and bandwidth sufficient to cover the FM signal range are used. The signal form at the output represents a frequency-modulated signal.

Step-by-step explanation:

Designing a block diagram for generating a wideband FM signal with a carrier frequency of 125 MHz and a peak frequency deviation of 100 kHz, involves the use of frequency multipliers, a local oscillator, and an ideal bandpass filter. The block diagram would include:

• A local oscillator set to the desired carrier frequency of 125 MHz.
• A modulating signal m(t) that frequency modulates the carrier signal. The peak frequency deviation of this modulation should be set to 100 kHz.
• Frequency multipliers as needed to scale the modulated signal up to the required frequency range.
• An ideal bandpass filter tuned to a center frequency of 125 MHz, with a bandwidth that covers the frequency range from 125 MHz ± 100 kHz to allow the FM signal to pass while filtering out undesired frequencies.

At the output, the FM signal will have the following form: 10 cos(2π × 125×106t + β sin(2π×m(t))), where β is the modulation index related to the frequency deviation and the modulating signal. The carrier frequencies and frequency deviations are specified at all logical points for clarity.