[time-nuts] Shorthand

[Tom Van Baak]

Hi Pete,

Yes, there are several ways to represent frequencies:

1) Absolute units of Hz. For example 60 Hz, or 32.768 kHz, or 3.579545 MHz, or 9.192631770 GHz. Note some modern texts use s⁻¹ (1/s or s-1) instead of Hz or Hertz. Or, you can always show your age and use cps (cycles per second).

2) Arithmetic error from some nominal value. For example 3 Hz above 1 MHz, or 17 Hz below 40 GHz. Your frequency is 10 MHz plus 0.005 Hz, or 5 mHz (milli-Hertz) too high.

3) Relative, or geometric error. For example, 60 Hz with 1% error, or 32.768 kHz with -10 ppm error, or 10 MHz with +0.5 ppb error. Note these errors values are unit-less. The general form is F = F0 x (1 + E) where F0 is the nominal frequency and E is the relative error.

In your example 10.000000005 MHz is 10 MHz x (1 + 0.0000000005). Note carefully the decimal point; 10.000 000 005 MHz is 10 MHz x (1.000 000 000 5) so E = 0.5 ppb.

In most cases one need only specify the relative error since F0 is either implied or irrelevant. For example, if you multiplied your oscillator to 1 GHz or divided it down to 1 PPS the relative frequency error would remain 0.5 ppb.

3½) When using percents, ppb (parts per million), or ppb (parts per billion) is not convenient, you can always use scientific notation. So instead of 0.5 ppb (or 500 ppt) it's more common to see 5e-10. This is much more informative than saying "10.000000005MHz" and making the poor reader count each of the zeros.

In summary,

10.000000005 MHz 
5 mHz above 10 MHz
+0.5 ppb error
+5e-10

/tvb

----- Original Message ----- 
From: <g4gjl at btopenworld.com>
To: <time-nuts at febo.com>
Sent: Monday, July 23, 2012 1:50 PM
Subject: [time-nuts] Shorthand


> Is there a commonly accepted shorthand for a frequency, say 10MHz, generated at the maximum accuracy of the lab generating it?
> 
> ie instead of writing 10.000000005MHz?
> 
> Pete
> G4GJL