A PLL frequency synthesizer has a reference frequency of 25 kHz. The frequency divider is set to a factor of 345. What is the output frequency?
The correct answer and explanation is :
To find the output frequency of a PLL (Phase-Locked Loop) frequency synthesizer, we use the basic formula:
$$
f_{\text{out}} = N \cdot f_{\text{ref}}
$$
Where:
- $f_{\text{out}}$ = Output frequency
- $f_{\text{ref}}$ = Reference frequency
- $N$ = Frequency divider (or multiplication) factor
Given:
- Reference frequency, $f_{\text{ref}} = 25\ \text{kHz}$
- Divider factor, $N = 345$
$$
f_{\text{out}} = 345 \times 25\ \text{kHz} = 8,625\ \text{kHz} = \boxed{8.625\ \text{MHz}}
$$
Explanation (Approx. 300 words):
A PLL (Phase-Locked Loop) frequency synthesizer is an electronic system used to generate a range of frequencies from a fixed reference frequency. It is widely used in radio, telecommunications, and clock generation in digital systems due to its ability to provide stable and programmable output frequencies.
At the heart of the PLL is a phase detector, a low-pass filter, a voltage-controlled oscillator (VCO), and a feedback divider. The system locks the VCO’s output frequency in phase and frequency with the reference signal. This is achieved by comparing the phase of the reference frequency $f_{\text{ref}}$ with a divided version of the output signal $f_{\text{out}}$, typically divided by an integer factor $N$.
When locked, the output frequency of the VCO is:
$$
f_{\text{out}} = N \cdot f_{\text{ref}}
$$
In this case, the PLL uses a reference frequency of 25 kHz. The feedback divider is set to 345, meaning the VCO output must be 345 times higher than the reference frequency for the loop to be in lock.
Thus, the output frequency becomes:
$$
f_{\text{out}} = 25,000\ \text{Hz} \times 345 = 8,625,000\ \text{Hz} = \boxed{8.625\ \text{MHz}}
$$
This principle allows PLLs to generate high frequencies from low-frequency stable references (such as a crystal oscillator), with fine control over the output by simply adjusting the divider factor $N$. It’s particularly valuable for generating clock signals in digital circuits or carrier signals in RF systems.