This tool converts from crystal oscillator stability in terms of **parts per million** (ppm) or **parts-per-billion** (ppb) to the equivalent **frequency variation** (Hz/kHz/MHz/GHz).

It also calculates the change in period between the max and min frequencies and the frequency error expressed as a percentage.

Enter:

**PPM or PPB value****Center Frequency**with the appropriate units (Hz/kHz/MHz/GHz)

**Formula**

The frequency variation **df** on either side of the center frequency **F** is given by

**df = F*ppm*10 ^{-6}**

The maximum and minimum frequency are given by

**Fmax = F + df**

**Fmin = F – df**

The change in period between these two frequencies is given by the formula

**1/Fmin -1/Fmax**

*Note: 1 ppm = 1000 ppb*

The frequency error is expressed as a percentage and is given by the formula

**Frequency error (%) = (ppm/10 ^{6})*100**

**Example Calculation**

The 32 MHz oscillator has a frequency stability of +/- 25 PPM.

The oscillator can be used as a reference clock with a phase locked loop to generate a frequency of 1 GHz.

Enter these numbers into the calculator above to calculate a frequency variation of **+/- 25 kHz**. The minimum and maximum frequencies generated are **999.975 MHz** and **1000.025 MHz**, respectively.

The corresponding change in period is **50 ns**.

Note the crystal oscillator above is missing a key specification – that of **frequency tolerance** – defined as the allowable deviation from the specified Frequency when measured at 25°C or room temperature [1].

**Background**

**What is an oscillator?**

**An oscillator is an electronic circuit that generates a periodic signal or waveform.** Its purpose is to provide stable and reliable timing signals for various applications. However, due to factors such as component ageing, temperature variations, and external disturbances or loading, an oscillator’s accuracy may deteriorate over time.

The accuracy of an oscillator refers to its ability to maintain a consistent and precise output frequency. If an oscillator becomes less accurate, it can lead to timing errors, which could negatively impact the operation of the system it is a part of.

**What is ppm?**

**ppm **stands for** parts-per-million.** It is a dimensionless quantity. ppm is a value that represents the part of a whole number in units of 1/10^{6}. 1 ppm is interpreted as one part in a million parts.

In the context of frequency, it is the ratio of **peak frequency variation** to the **center frequency** divided by one million.

**What is ppb?**

**ppb **stands for** parts-per-billion.** It is a dimensionless quantity. ppm is a value that represents the part of a whole number in units of 1/10^{9}.

- 1 ppb = 0.001 ppm
- 1 ppm = 1000 ppb

**What is frequency?**

Frequency is the number of cycles or repetitions per unit of time. If a sine wave repeats 100 times every second, its frequency is 100 Hz.

**How many Hz is 1 PPM?**

It depends on the frequency at which the Hz variation is calculated. For example:

- At 1 MHz, 1 PPM is equivalent to 1 Hz
- At 1000 MHz, 1 PPM is equivalent to 1000 Hz or 1 kHz

**References**

[1] ECS Frequency Tolerance and Stability