Split transformer loss into core and copper, find efficiency at your actual loading, and see what the loss costs across a circuit.
A series isolating transformer is never lossless. Core loss follows the voltage across the transformer and copper loss follows the current through it, and on a constant-current circuit these two behave differently from a mains transformer. This tool uses the data-sheet efficiency to rebuild both losses, then shows efficiency against loading, the best-efficiency point, the heat each unit gives off and the yearly energy it wastes.
Current at which the data-sheet efficiency is quoted, normally 6.6 A. For a 20/6.6 A transformer enter 6.6 A (the secondary), not the 20 A primary current. The 300 W and 500 W types with a 20 A secondary are the exception: enter 20 A.
Efficiency at full rated load, power factor 1. FAA AC 150/5345-47C sets minimums of 80 % for 30/45 W and 65 W, 85 % for 100 W and 150 W, 90 % for 200 W and above, and 70 % for 10/15 W and 20/25 W. The core share is a planning assumption; use the manufacturer's no-load and load test figures when you have them.
Series: copper loss is set by the circuit current, core loss by the secondary voltage. Conventional: core loss is fixed and copper loss follows load squared.
Power at the operating current, from the fixture data sheet.
Used for circuit heat and energy totals. Set 0 to skip them.
Hours the circuit runs at this current. Use your own operating profile.
The curve is drawn at the rated current. The “Your load” marker uses your operating current, so it can sit off the curve when the two differ.
| Loading (%) | Output (W) | Core loss (W) | Copper loss (W) | Total loss (W) | Efficiency (%) |
|---|
Every step is shown so the result can be checked by hand.
At full rated load (power factor 1) the output equals the VA rating, so the data-sheet efficiency fixes the total loss. It is then split into core and copper.
If you have test figures, choose the watts option and enter them directly.
The circuit current is fixed, so copper loss stays at I²R. The voltage across the secondary rises and falls with the load, and core loss follows the square of that voltage.
V is the secondary load VA divided by the current, and V_rated is the rated VA divided by the rated current.
For a transformer fed at fixed voltage, core loss is constant and copper loss follows the square of loading x.
Efficiency peaks where the variable loss equals the fixed one. In the series model the best loading is the square root of Cu ÷ Core. In the constant-voltage model it is the square root of Core ÷ Cu.
| Item | Value |
|---|---|
| 45 VA, 6.6 A, 90 % rated, 40 % core | L = 5 W |
| Core / copper at rated | 2 W / 3 W |
| Load: 1 × 30 W, PF 1.00 | x = 0.667 |
| Core at 0.667² × 2 W (series) | 0.89 W |
| Copper (current unchanged) | 3.00 W |
| Total loss | 3.89 W |
| Efficiency 30 ÷ 33.89 | 88.5 % |
| 100 transformers | 0.39 kW |
| 3,000 h per year | 1,167 kWh |
| At ₹8 per kWh | ₹9,333 |
It does not model temperature rise, magnetising current, saturation, secondary open-circuit behaviour or lamp-out conditions, and it treats the lamp load as fixed in resistance. Size is nominal, and efficiency is a two-point fit, not a measured curve. Use the manufacturer's test report for acceptance values. To size the transformer first, use Calculator #17.
FAA AC 150/5345-47C (series-to-series isolation transformers, Table 2 gives the minimum efficiency and power factor for each size), IEC 61823 (AGL series transformers) and ICAO Aerodrome Design Manual, Doc 9157, Part 5. Use the current edition of each.
Quick answers on core and copper loss, efficiency at your actual loading, and the cost of the loss.
It splits the loss of a series isolating transformer into core and copper, finds the efficiency at your actual loading, and shows what the loss costs across a circuit. It uses the data-sheet efficiency to rebuild both losses, then shows efficiency against loading, the best-efficiency point, the heat each unit gives off and the yearly energy it wastes.
At full rated load with a power factor of 1, the output equals the VA rating, so the data-sheet efficiency fixes the total loss. The rated loss is the VA rating times (1 divided by the efficiency, minus 1). It is then split into core and copper using a core share, which is a planning assumption. If you have test figures, choose the watts option and enter the core and copper loss directly from the transformer test report.
In the series model the circuit current is fixed, so copper loss stays at the rated copper loss times the square of the current ratio, while core loss follows the square of the secondary voltage. In the constant-voltage model, for a transformer fed at fixed voltage, core loss is constant and copper loss follows the square of the loading.
Efficiency is the output power divided by the output power plus the core and copper loss. It peaks where the variable loss equals the fixed one. In the series model the best loading is the square root of the copper loss divided by the core loss, and in the constant-voltage model it is the square root of the core loss divided by the copper loss.
Use the efficiency at full rated load and power factor 1 from the data sheet. FAA AC 150/5345-47C sets minimums of 80 percent for 30/45 W and 65 W, 85 percent for 100 W and 150 W, 90 percent for 200 W and above, and 70 percent for 10/15 W and 20/25 W. For a 20/6.6 A transformer, enter 6.6 A as the rated secondary current, not the 20 A primary current. The 300 W and 500 W types with a 20 A secondary are the exception: enter 20 A.
The circuit loss is the loss per transformer times the number of transformers on the circuit. Yearly energy is that loss in kW times the operating hours, and the cost is the energy times your tariff. Set the number of transformers to 0 to skip the circuit totals.
A 45 VA transformer at 6.6 A with 90 percent rated efficiency and a 40 percent core share has a rated loss of 5 W, split into 2 W core and 3 W copper. With one 30 W fixture at a power factor of 1.00, the loading is 0.667, so the core loss is 0.89 W and the copper loss stays at 3.00 W. The total loss is 3.89 W and the efficiency is 88.5 percent. For 100 transformers that is 0.39 kW, or 1,167 kWh over 3,000 hours, which costs 9,333 rupees at 8 rupees per kWh.
It does not model temperature rise, magnetising current, saturation, secondary open-circuit behaviour or lamp-out conditions, and it treats the lamp load as fixed in resistance. The size is nominal, and the efficiency is a two-point fit and not a measured curve, so treat the result as a planning figure. Use the manufacturer's test report for acceptance values. To size the transformer first, use Calculator #17.
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