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Data supplied by Systel indicates that at 100 kHz, the impedance of one Systel 2 lamp 70 watt ballast is 380 0hms inductive. Thus three such ballasts connected in parallel have an impedance of 380 / 3 = 127 ohms inductive. The corresponding inductance value is given by:

127 / (6.28 X 10^5) = 202 uH.

Hence three parallel connected ballasts have about the same impedance as two series connected 100 uH inductors.

At low frequencies the same three ballasts at full load draw 3 X 70 = 210 watts. The equivalent resistance of these three parallel connected ballasts is given by: R = V^2/P = (120)^2/210 = 68.6 ohms. This resistance can be approximately simulated by two series connected 36 ohm resistors.

We can conduct cable attenuation tests using a measured 100 m length of #14 2 wire (plus ground) 3/8 inch diameter armour cable.

Thus, by using various terminations consisting of series/parallel combinations of 4 100 uH inductors and 4 36 ohm resistors, at 127 kHz we can prepare a table of the following form:

Termination------ | Equiv.No. of Ballasts------ | Transfer Ratio = Vb / Va |
---|---|---|

200 uH | 3 | |

100 uH | 6 | |

66.67 uH | 9 | |

50 uH | 12 | |

40 uH | 15 | |

33.3 uH | 18 | .439 |

25 uH | 24 | .382 |

72 R | 3 | |

36 R | 6 | |

24 R | 9 | |

18 R | 12 | |

14.4 R | 15 | |

12 R | 18 | |

9 R | 24 | .234 |

Consider the case of the 9 ohm resistive termination. If we assume that for a 200 m cable the loss is (Vb / Va)^2 = (.234)^2 = .0547, and if we operate under the guideline that the cable loss fraction should be greater than 1/20 = .05, then we find that the maximum allowable cable length may be as short as 200 m for a fully loaded lighting circuit that contains a substantial fraction of incandescent lamps. However, if all the fixtures are fluorescent only,then the data for the 25 uH termination indictes that (Vb / Va)^3 = (.382)^3 = .0557, pointing to a maximum branch lighting circuit length of 300 m. Note that the maximum branch lighting circuit length decreases as the connected load increases.

This web page last updated September 20, 2005

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