AGL Isolating Transformer Formulas

AGL isolating transformer formulas: the secondary lamp current, the lamp voltage, the primary voltage drop and the loading of a series transformer.

The formulas

A series isolating transformer passes the circuit current from its primary to its secondary in the ratio of its rated currents, so a 6.6/6.6 A unit gives the lamp the circuit current and a 6.6/20 A unit gives it about three times the circuit current. Ip is the circuit current at the brightness step, Ipr and Isr the rated primary and secondary currents from the nameplate, Plamp the lamp power at the secondary current, Prated the transformer rating and ηT its efficiency at that current. The current ratio is the ideal one, and the lamp power is taken as a fixed figure, so look it up at the secondary current that the result shows. Primary drop is the voltage the transformer takes from the series loop. An open secondary, such as a failed lamp, is not modelled and needs the manufacturer's data on open-circuit voltage and core saturation. The values are examples.

Worked example: a 6.6/6.6 A transformer with a 45 W lamp, rated 100 W

The circuit current is 6.6 A and the efficiency is 0.85.

1. Is = 6.6 × 6.6 / 6.6 = 6.6 A
2. Vs = 45 / 6.6 = 6.818 V
3. Pin = 45 / 0.85 = 52.94 W
4. Vp = 52.94 / 6.6 = 8.021 V
5. Loading = 45 / 100 = 45%

Worked example: a 6.6/20 A transformer at 3.4 A with a 30 W lamp, rated 200 W

The efficiency is 0.8.

1. Is = 3.4 × 20 / 6.6 = 10.3 A
2. Vs = 30 / 10.3 = 2.912 V
3. Pin = 30 / 0.8 = 37.5 W, so Vp = 37.5 / 3.4 = 11.03 V
4. Loading = 30 / 200 = 15%

Secondary current of a 6.6/20 A transformer at each step of a five-step circuit

Frequently asked questions

Why use an isolating transformer?

It separates each lamp from the series cable, so one failed lamp does not break the circuit and the lamp is not at the cable voltage.

Why is the lamp power a fixed number here?

A lamp is not a fixed resistance. Its power changes with the current, so the data sheet figure at the secondary current gives the right answer, not the figure at full current.

What does loading above 100% mean?

The lamp needs more power than the transformer is rated for. Use a larger transformer.

Where do the efficiency figures come from?

From the transformer data sheet at the circuit current. Efficiency is lower at light load, so it changes with the brightness step.

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