Editing Decca Navigator System (section)

=== Detailed principles of operation ===
When two stations transmit at the [[phase-locked loop|phase-locked frequency]], the difference in phase between the two signals is constant along a hyperbolic locus. However, if two stations transmit on the same frequency, it is impossible for the receiver to separate them. Instead, each chain was allocated a nominal frequency, known as 1''f'', and each station in the chain transmitted at a harmonic of this base frequency, as follows:

{| class="wikitable"
|-
! Station!! Harmonic !! Frequency (kHz)
|-
| Master || 6''f'' || 85.000
|-
| Purple || 5''f'' || 70.833
|-
| Red || 8''f'' || 113.333
|-
| Green || 9''f'' || 127.500
|}

The frequencies given are those for Chain 5B, known as the English Chain, but all chains used similar frequencies between 70&nbsp;kHz and 129&nbsp;kHz.

Decca receivers multiplied the signals received from the Master and each Slave by different values to arrive at a common frequency ([[least common multiple]], LCM) for each Master/Slave pair, as follows:

{| class="wikitable"
|-
! Pattern !! Slave Harmonic !! Slave Multiplier !! Master Harmonic !! Master Multiplier !! Common Frequency
|-
| Purple || 5''f'' || ×6 || 6''f'' || ×5 || 30''f''
|-
| Red || 8''f'' || ×3 || 6''f'' || ×4 || 24''f''
|-
| Green || 9''f'' || ×2 || 6''f'' || ×3 || 18''f''
|}

It was phase comparison at this common frequency that resulted in the hyperbolic lines of position. The interval between two adjacent hyperbolas on which the signals are in phase was called a ''lane''. Since the wavelength of the common frequency was small compared with the distance between the Master and Slave stations there were many possible lines of position for a given phase difference, and so a unique position could not be arrived at by this method.

Other receivers, typically for aeronautical applications, divided the transmitted frequencies down to the basic frequency (1''f'') for phase comparison, rather than multiplying them up to the LCM frequency.