Let's solve each question step-by-step.

Question 1

An FM transmitter has an 8.6-MHz crystal carrier oscillator and frequency multipliers of 2, 3, and 4. We need to calculate the final output frequency.

1. Starting frequency = $8.6\ \text{MHz}$.
2. Multiplication steps:
   • First multiplier = $2 \Rightarrow 8.6 \times 2 = 17.2\ \text{MHz}$.
   • Second multiplier = $3 \Rightarrow 17.2 \times 3 = 51.6\ \text{MHz}$.
   • Third multiplier = $4 \Rightarrow 51.6 \times 4 = 206.4\ \text{MHz}$.

Answer: The output frequency is $206.4\ \text{MHz}$.

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Question 2

A crystal has a tolerance of 0.003 percent. We need to convert this tolerance to parts per million (ppm).

1. Tolerance in percent = $0.003\%$.
2. Converting percent to ppm:
   • Since 1 percent is equivalent to 10,000 ppm, we have: $0.003\% \times 10,000 = 30\ \text{ppm}$

Answer: The tolerance is $30\ \text{ppm}$.

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Would you like further details on these calculations?

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Related Questions

1. How would the output frequency change if an additional multiplier was added to the FM transmitter?
2. How is frequency stability affected by the tolerance of the crystal oscillator?
3. What applications would benefit from a low ppm tolerance in frequency control?
4. How could a different initial crystal frequency impact the transmitter’s output?
5. What are some ways to minimize frequency drift in FM transmitters?

Tip

In electronics, ppm (parts per million) is often used to specify precision in frequency control, allowing for very fine adjustments in high-stability applications.