Transformer — Step-Up & Step-Down

The Transformer Simulator is built around a nameplate, not a turns ratio. You set the rating, the primary voltage, the frequency and the turns; from those the simulator derives the core cross-section, the winding resistance and leakage reactance, and the magnetising branch — the whole equivalent circuit — and then solves it exactly. Change any slider and the machine changes with it.

That means you can explore step-up and step-down transformation and the turns ratio (a = N₂/N₁), but also the things a turns ratio alone cannot show: the EMF equation E = 4.44 f N Φₘ setting the core flux density, core saturation when the volts-per-turn-per-hertz is wrong, voltage regulation at any power factor including the leading loads that make it negative, and the load at which efficiency peaks because copper loss has grown to equal iron loss.

A separate Tests tab runs the two classical bench tests — open-circuit and short-circuit — on whichever machine you have set up, and shows how their meter readings recover the equivalent circuit you started from.

This tool is designed for electrical engineering students, power systems trainees, and physics learners studying Faraday’s law, voltage transformation, transformer testing, and real-world losses.

The canvas is at the top, and the control panel sits directly beneath it. The panel’s own top line is a ribbon holding everything that changes what machine this is and everything you can do to it: the Preset dropdown, the Real transformer and Leading load toggles, then Calculations and icon buttons for undo, redo, reset, CSV and PNG (hover any of them for its name). Below the panel sit the readout cards.

The simulator opens in Simulate mode with a 1.6 kVA machine: V₁ = 120 V, N₁ = 100 turns, N₂ = 200 turns, 50 Hz, feeding a 60 Ω resistor, ideal (lossless). That gives a turns ratio of 2.0, a 240 V step-up output, and a core flux density of 1.17 T — a sensible working point for silicon steel.

Nameplate & supply.

• N₁ and N₂ — 5 to 50,000 turns, and the first thing to reach for. If N₂ > N₁ the transformer steps up; if N₂ < N₁ it steps down. N₁ also sets the flux: fewer turns means more flux in the same iron.
• V₁ Primary (V) — 6 V to 132 kV. The slider steps through standard system voltages (110, 230, 415, 11 k, 33 k, 132 k…); type any value in the box.
• S Rating (kVA) — 0.05 kVA to 5,000 kVA. The slider walks the standard IEC ratings; the box beside it accepts anything in between. The rating decides the core cross-section and, through published per-unit design data, the winding resistance, the leakage reactance, the no-load current and the core loss.
• f Frequency (Hz) — 16 to 400 Hz, with 50 / 60 / 400 Hz shortcut chips beside the section heading. Frequency appears in the EMF equation, so it changes the core flux directly.

Load. The dropdown beside the Load heading offers two ways of asking for the same thing:

• A resistor across the secondary — a real resistor, so the power factor is 1. Good for the basic voltage-and-current story and for impedance matching.
• A current, as % of rated, at a power factor — a load current expressed as a percentage of rated secondary current, at a power factor you choose between 0.30 and 1.00. This is how every textbook problem is posed, and it is the only way to reach the regulation and power-factor lessons. The Leading load chip in the ribbon makes it capacitive; it stays greyed out while the load is a plain resistor, because a resistor has no power factor to lead or lag.

Every slider carries a live value with its unit, and a − / box / + stepper. On the rating, voltage, turns and load-resistance sliders the stepper walks the standard sizes — one press moves 11 kV to 22 kV rather than nudging it by a volt — while the box still accepts any value in between.

Tick Real transformer in the ribbon to switch from the ideal machine to the real one: winding drops, magnetising current, copper and iron losses, and a secondary voltage that sags under load. It is a lens over whatever machine you have loaded rather than a different machine, so it starts off — including on every preset — and the preset dropdown goes on naming the transformer once you switch it on.

Navigate through Simulate, Tests, Explore, Practice, and Quiz modes using the pill tabs at the top.

The View bar above the canvas switches between four ways of looking at the same solved machine:

• Machine — the physical picture. Two windings on a laminated core, flux animating through the iron at a clearly-labelled slow motion, an oscilloscope panel showing both voltage waveforms at a real volts-per-division scale, and (in real mode) a loss breakdown. The core caption shows the flux density Bₘ and turns red when the iron saturates.
• Equivalent Circuit — the exact T-model referred to the primary, with R₁, X₁, R₂′, X₂′, R₀ and Xₘ carrying the values your nameplate produces, plus the approximate circuit and %R, %X, %Z below it.
• Phasor Diagram — V₁, V₂′, I₁ and I₀ drawn to scale from the solved complex quantities, with the primary power-factor angle marked. The gap between the two voltage tips is the regulation.
• Efficiency Curve — efficiency and regulation swept across 0–125% load, with the copper and iron loss curves underneath. The peak is marked, and a second marker shows where your current operating point sits on it.

The readout cards show turns ratio, type, secondary voltage, both currents, the load as a percentage of rated, input and output power, efficiency, and — in real mode — voltage regulation, core flux density Bₘ, no-load current I₀, and the primary power factor. Cards that mean nothing in ideal mode are hidden rather than filled with a dash.

Explore mode organises transformer theory into three categories:

• Transformer Basics: Covers electromagnetic induction, Faraday’s law, turns ratio, ideal transformer equations (V₂/V₁ = N₂/N₁), and the principle that power is conserved in an ideal transformer.
• Losses & Efficiency: Explains copper losses (I²R heating in windings), iron losses (hysteresis loss from magnetic domain reversal and eddy current loss from circulating currents in the core), and how laminated silicon steel cores minimise eddy currents.
• Testing & Performance: The equivalent circuit and what each element represents, the open-circuit and short-circuit tests, voltage regulation including the leading-load case where it goes negative, and percentage impedance and the fault current it implies.
• Applications: Describes power transmission (step-up for long-distance, step-down for distribution), isolation transformers, instrument transformers (CTs and PTs), and autotransformers.

Each concept card provides formulas, explanations, and an interactive canvas illustration.

Nobody load-tests a 100 MVA transformer — you would need a 100 MVA load and would waste 100 MVA of energy doing it. Instead two small tests, together consuming about 1% of the rating, determine the whole equivalent circuit. The Tests tab runs both on whichever machine you set up in Simulate mode, so changing the nameplate there moves every reading here.

• Open-Circuit (no-load) test. Rated voltage on the LV winding, the HV winding open. Only the no-load current flows, so the I²R term is negligible and the wattmeter reads core loss. From V₀, I₀ and W₀ the panel derives cos φ₀, I_w, I_μ, and then R₀ and Xₘ.
• Short-Circuit (impedance) test. The LV winding is bolted shut and the HV winding is fed from a supply raised until rated current flows — only a few percent of rated voltage, and that percentage is %Z. The core is barely magnetised, so the wattmeter reads full-load copper loss. From V_sc, I_sc and W_sc the panel derives Z_eq, R_eq and X_eq.
• Load test — η & regulation. The direct test: efficiency and regulation measured point by point across the load range, with a table at the classical 25 / 50 / 75 / 100 / 125% points, the maximum-efficiency load worked out, and a demonstration that the same answer comes out of the OC and SC results alone.

Each test ends with a “does the test recover the machine?” table comparing the derived parameters against the ones the model actually holds. They agree to within a fraction of a percent — and the small residual is real, not rounding: the OC wattmeter also sees the I₀²R loss in its own winding, and the SC test ignores the magnetising branch. Those are exactly the approximations the standard method makes on a real bench.

Both CSV and PNG exports are available for whichever test is on screen.

Practice mode generates problems such as: “A transformer has N₁ = 200 turns and N₂ = 50 turns. If V₁ = 240 V, find V₂”, “Calculate primary current if secondary current is 2 A and turns ratio is 5:1”, or “Find efficiency if P_in = 500 W and total losses are 25 W.” Enter your answer and receive a step-by-step solution.

Quiz mode presents 5 multiple-choice questions covering turns ratio, step-up vs step-down identification, current transformation, copper and iron losses, and efficiency calculations. Review your score and detailed explanations at the end.

• Type exact values: every slider has a companion number box — type a precise V₁, N₁, N₂, or R_L instead of dragging.
• Preset dropdown: six machines that exist. Bench 1.6 kVA (the opening state), Doorbell 240/12 V (a 100 VA control transformer, and its 8.7% regulation is why they sag), 1:1 Isolation 2.5 kVA, Distribution 1 MVA (11 kV/415 V at 0.8 lagging, the case every power-systems course works through), Generator step-up 5 MVA (11 kV to a 132 kV line), and Under-turned core — the same bench machine with half the primary turns, so the iron is driven to 4.7 T and the core caption turns red before you have touched anything else.
  Every preset arrives as an ideal transformer, so you meet the machine as a clean turns-ratio problem first. Tick Real transformer to lay the winding drops, the magnetising current and the losses over the top of it — on the under-turned core that is when the magnetising current bolts to tens of amps and the efficiency collapses. The dropdown keeps naming the machine while you switch that lens on and off; only moving a slider makes it read — Custom —.
• Calculations: the first button in the ribbon opens the step-by-step derivation for whatever the machine is doing right now — core area, EMF equation, machine parameters, the circuit solve, regulation, losses, efficiency, and a power-balance check.
• View bar: Machine, Equivalent Circuit, Phasor Diagram and Efficiency Curve.
• Display Controls (the chip on the canvas): six switches over what the canvas draws.
  • Equation on canvas — the classical turns-ratio equation across the top of the machine view.
  • Labels & values — every value annotated on the drawing itself: turns, voltages, currents, the load, the nameplate line and the core flux density. Turning it off leaves a clean schematic worth printing or projecting. The core still turns red when it saturates, because that is a warning rather than a label.
  • Waveform scope — the oscilloscope panel under the machine.
  • Loss breakdown — the copper/iron loss box on the machine view, and the two dashed loss curves on the Efficiency Curve view.
  • Animate flux & current — freezes the flux arrows and the current dots where they are. The sliders still move everything else, so this is how you take a screenshot, or make a slow device comfortable.
  • Background grid — a reference grid behind every view.
  Reset display puts all six back. Your choices and your chosen view are remembered for next time.
• Live equations & What-if coach: collapsible panels below the controls show the substituted formulas and plain-language insights about your current settings.
• Show Equation / Show Grid: toggle the on-canvas turns-ratio equation and a background reference grid.
• Export: CSV sweeps the load from no load to 125% and records V₂, I₂, input and output power, copper and iron loss, efficiency and regulation at each point, with the machine's full parameter set in the header comments; PNG saves the canvas as a watermarked image. Both are also on the canvas right-click menu, and the Tests tab has its own pair.
• Keyboard: Ctrl+Z undo, Ctrl+Shift+Z redo, Esc closes the calculation modal.

• Every preset lands ideal on purpose. Read the turns-ratio story first — a, V₂, the two currents, power in equals power out — then tick Real transformer and watch what it costs: V₂ sags, I₀ appears, and the efficiency card drops off 100%.
• Set N₁ = N₂ to create a 1:1 isolation transformer — voltage stays the same but the circuits are galvanically isolated.
• Notice that when you step up voltage, current steps down proportionally — power is conserved (P = V × I).
• With the Real Transformer mode on, try increasing load current by lowering R_L. Watch copper losses (I²R) increase significantly while iron losses remain roughly constant.
• For maximum efficiency, transformers operate best at or near rated load. Very light loads give poor efficiency because iron losses dominate.
• Remember: turns ratio a = N₂/N₁. If a > 1, it steps up voltage; if a < 1, it steps down voltage.
• Halve N₁ and watch Bₘ double. The EMF equation Φₘ = V/(4.44 f N) is the whole reason a transformer has the number of turns it does — and past about 1.7 T the core saturates and the magnetising current runs away.
• Switch the frequency from 50 to 60 Hz at fixed voltage and the flux falls by a factor of 60/50. Now do it the other way: a 60 Hz transformer on a 50 Hz supply is over-fluxed by 20% and can overheat with nothing connected to it.
• In % of rated + PF mode, set the power factor to 0.8 and flip between lagging and leading. On the 1 MVA distribution preset the leading case gives negative regulation — the secondary voltage rises under load, because %X·sinφ has overtaken %R·cosφ.
• Open the Efficiency Curve view and find where the copper and iron loss curves cross. That crossing is the efficiency peak, and it is why distribution transformers are sized to run at 50–75% of rating rather than flat out.
• Run the Short-Circuit test and read %Z. A dead short at full voltage draws roughly 100/%Z times rated current — the number that sizes the switchgear.
• Use Practice mode to drill the equations: V₂ = a×V₁, E = 4.44 f N Φₘ, Reg% ≈ %R·cosφ ± %X·sinφ, and η = P_out/P_in × 100%.