PLL Output Frequency

fout = fref × N / R

Quick answer

This calculator solves f_out = f_ref × N / R for Output Frequency. With Reference Frequency 22 MHz, Feedback Divider (N) 0.5, Reference Divider (R) 1.1, the result is 10 MHz. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Output Frequency (MHz)
—

Formula

f_out = f_ref × N / R

Description

A phase-locked loop (PLL) generates an output frequency that is a rational multiple of the reference frequency. The reference divider R divides the reference clock down to the phase detector comparison frequency (f_ref/R), and the feedback divider N divides the VCO output to the same frequency. In lock, f_out/N = f_ref/R, giving f_out = f_ref × N/R. By choosing N and R, almost any output frequency can be synthesized from a single reference crystal. PLLs are used in clock generators, frequency synthesizers, and clock recovery circuits.

Variables

  • f_out — PLL output frequency (Hz)
  • f_ref — Reference oscillator frequency (Hz)
  • N — Feedback divider ratio (integer)
  • R — Reference divider ratio (integer)

Practical Notes

The phase detector comparison frequency (f_ref/R = f_out/N) determines the PLL loop bandwidth limit and the channel spacing in frequency synthesizers. Higher comparison frequency allows faster lock time and lower phase noise, but requires larger N for the same output frequency. Fractional-N PLLs allow non-integer N values using delta-sigma modulation, enabling finer frequency resolution without reducing the comparison frequency.

Symbols and units

Symbol Meaning Default unit Accepted units
fout Output Frequency MHz Hz, kHz, MHz, GHz
fref Reference Frequency MHz Hz, kHz, MHz, GHz
N Feedback Divider (N) — —
R Reference Divider (R) — —

Step by step

  1. 1. What you know: Reference Frequency 22 MHz, Feedback Divider (N) 0.5, Reference Divider (R) 1.1
  2. 2. The relation: f_out = f_ref × N / R
  3. 3. Substitute: fref = 22 MHz, N = 0.5, R = 1.1
  4. 4. Result: Output Frequency = 10 MHz

Worked examples

Minimum range

Given: Reference Frequency 0.22 MHz, Feedback Divider (N) 0.025, Reference Divider (R) 0.055

Result: Output Frequency = 100 kHz

Low range

Given: Reference Frequency 2.2 MHz, Feedback Divider (N) 0.25, Reference Divider (R) 0.55

Result: Output Frequency = 1 MHz

Typical

Given: Reference Frequency 22 MHz, Feedback Divider (N) 0.5, Reference Divider (R) 1.1

Result: Output Frequency = 10 MHz

High range

Given: Reference Frequency 0.22 GHz, Feedback Divider (N) 0.8, Reference Divider (R) 1.76

Result: Output Frequency = 100 MHz

Maximum range

Given: Reference Frequency 2.2 GHz, Feedback Divider (N) 8, Reference Divider (R) 17.6

Result: Output Frequency = 1 GHz

Solving for each variable

Solve for Output Frequency

Reference Frequency 0.22 MHz, Feedback Divider (N) 0.025, Reference Divider (R) 0.055 → 100 kHz

Solve for Reference Frequency

Output Frequency 100 kHz, Feedback Divider (N) 0.025, Reference Divider (R) 0.055 → 0.22 MHz

Solve for Feedback Divider (N)

Output Frequency 100 kHz, Reference Frequency 0.22 MHz, Reference Divider (R) 0.055 → 0.025

Solve for Reference Divider (R)

Output Frequency 100 kHz, Reference Frequency 0.22 MHz, Feedback Divider (N) 0.025 → 0.055

How Output Frequency changes with Reference Frequency

Reference Frequency (input) Output Frequency (result)
2.2 MHz 1 MHz
5.5 MHz 2.5 MHz
11 MHz 5 MHz
16.5 MHz 7.5 MHz
22 MHz 10 MHz
33 MHz 15 MHz
44 MHz 20 MHz
88 MHz 40 MHz
154 MHz 70 MHz
0.22 GHz 100 MHz

The same result in other units

Unit Value
kHz 10000
MHz 10
GHz 0.01

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Frequently asked questions

How do you calculate PLL Output Frequency?

Use f_out = f_ref × N / R. With Reference Frequency 22 MHz, Feedback Divider (N) 0.5, Reference Divider (R) 1.1, Output Frequency works out to 10 MHz.

What is the formula for PLL Output Frequency?

The formula is f_out = f_ref × N / R. A phase-locked loop (PLL) generates an output frequency that is a rational multiple of the reference frequency.

How do you find Reference Frequency when you know the other values?

Rearrange for Reference Frequency: with Output Frequency 100 kHz, Feedback Divider (N) 0.025, Reference Divider (R) 0.055, Reference Frequency is 0.22 MHz.

How do you find Feedback Divider (N) when you know the other values?

Rearrange for Feedback Divider (N): with Output Frequency 100 kHz, Reference Frequency 0.22 MHz, Reference Divider (R) 0.055, Feedback Divider (N) is 0.025.

What units does PLL Output Frequency use?

Output Frequency is shown in kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Timing & Oscillators formulas →
555 Timer Astable 555 Timer Monostable Crystal Load Capacitance RC Oscillator Frequency Crystal Frequency Stability PLL Lock Time VCO Tuning Sensitivity PLL Output Frequency

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