AGL Brightness Step Formulas

AGL brightness step formulas: the circuit current at each step of a 6.6 A series circuit, and the lamp load, cable loss and regulator voltage at that step.

The formulas

The regulator sets the brightness by changing the circuit current. A five-step circuit usually uses 2.8, 3.4, 4.1, 5.2 and 6.6 A, and a three-step circuit 4.8, 5.5 and 6.6 A. Confirm the currents against your project specification. P6.6 is the lamp power of one fitting at 6.6 A. The lamp power at a lower step is taken as P6.6 × r^k, where k is an exponent that you choose. With k = 2 the lamp acts as a fixed resistance. A hot filament gives a lower power at a low step, so use the lamp data sheet where you have it. The efficiency of the transformer is taken as constant at every step. The highest step normally sets the regulator size, and the lower steps show the output voltage and the load for checking against the regulator curves. The values are examples.

Worked example: step 1 of a five-step circuit at 2.8 A

The circuit has 60 fittings of 45 W at 6.6 A on 4 km of cable at 3.08 Ω/km, the efficiency is 0.85 and k = 2.

1. r = 2.8 / 6.6 = 0.4242, which is 42.42% of full current
2. Plamps = 60 × 45 × 0.4242² / 0.85 = 571.7 W
3. Pcable = 2.8² × 3.08 × 4 = 96.59 W
4. Pt = 668.3 W and Vout = 668.3 / 2.8 = 238.7 V
5. The load is 18% of the 3,713 W at 6.6 A

The same circuit at each step of a five-step circuit

Frequently asked questions

Why does the regulator voltage fall at the lower steps?

The current is lower, so the lamps and the cable take less power and less voltage is needed to drive the current through the loop.

Why does the load fall faster than the current?

The lamp power falls roughly with the square of the current or faster, and the cable loss falls with the square of the current as well.

What exponent should I use?

k = 2 is a simple first estimate. A filament lamp can fall faster than that at a low step, so take the lamp power at each step from the data sheet where it is given.

Is the highest step the one to size for?

Yes. The regulator is sized at 6.6 A, and this method shows the lower steps so that you can check the output voltage and the load against the curves.

Related

AGL Series Circuit Load and CCR Sizing FormulasAGL CCR Input Power and Energy FormulasAGL Lamp Life FormulasLighting FormulasAirport and AGL calculatorsThree-Phase Power FormulasPower Factor and the Power TriangleAC Circuit Formulas: Reactance and ImpedanceVoltage Drop Formulas for CablesTransformer Formulas: Current and Fault LevelInduction Motor FormulasBattery Formulas: Capacity and RuntimeSolar PV Formulas: Array Size and StringsCapacitor Formulas: Energy and RC Time ConstantEarthing Formulas: Earth Rod and Fault LoopCable Size Formulas: Current and Short-CircuitEnergy and Cost Formulas: kWh and PaybackGenerator Formulas: kVA, Current and FuelUPS Formulas: kVA, DC Current and BatteryHarmonics Formulas: THD and True Power FactorShort-Circuit Formulas: Fault Level by MVAUnbalance Formulas: Voltage and Neutral CurrentResistor Formulas: Series, Parallel, DividerMotor Starting Formulas: DOL, Star-DeltaCircuit Breaker Formulas: Rating and TripCooling Formulas: Airflow and Heat LoadHeating Formulas: Energy and Heater PowerPer-Unit Formulas: Base Values and ImpedanceLED Formulas: Resistor Value and PowerConduit Fill Formulas: Percent Fill and SizeLightning Protection Formulas: Rolling SphereTransformer Efficiency and Regulation FormulasPump Formulas: Hydraulic, Shaft and Motor PowerFan Formulas: Air Power and Affinity LawsInductor Formulas: Energy and L/R Time ConstantRMS, Peak and Average Value FormulasResonance Formulas: Frequency, Q, BandwidthMotor Efficiency Formulas: Input and SavingsDemand, Load and Diversity Factor FormulasCable Tray Fill Formulas: Area and Cable CountConductor Resistance Formulas and TemperatureTransmission Line Formulas: Drop and LossesStar-Delta Conversion Formulas for Resistors4-20 mA Loop Formulas: Scaling and ResistorCable Loss Formulas: Power and Annual CostOp-Amp Formulas: Inverting and Non-Inverting555 Timer Formulas: Frequency and Duty CycleThévenin and Norton FormulasWheatstone Bridge Formulas: Balance and OutputConductor Force Formulas: Short-Circuit ForcesCT Burden Formulas: Lead Resistance and VAGear and Belt Drive Formulas: Speed and TorqueSkin Effect Formulas: Skin DepthRC Filter Formulas: Cutoff Frequency and GainRectifier Ripple Formulas: Capacitor FilterBuck and Boost Converter Formulas: Duty CycleHeat Sink Formulas: Junction TemperatureBattery Pack Formulas: Series and ParallelMotor Acceleration Time FormulasZener Regulator Formulas: Series ResistorBJT Bias Formulas: Voltage Divider BiasPt100 RTD Formulas: Resistance and TemperatureNTC Thermistor Formulas: Beta EquationFusing Current Formulas: Wire Fuse EstimateFlywheel Formulas: Stored EnergyLinear Regulator Formulas: Power and EfficiencyMOSFET Loss Formulas: Conduction and SwitchingRelay Coil Formulas: Current and ResistorTransformer Inrush Current FormulasBattery Charge Time FormulasWind Turbine Power Formulas: Betz LimitDetuning Reactor Formulas: Capacitor BanksTransformer Tap Changer FormulasCable Pulling Tension FormulasInsulation Resistance Formulas: PI and DARPower Transfer and Power Angle FormulasSolar Panel Temperature Derating FormulasVoltage Change and Flicker FormulasSoft Starter and VFD Sizing FormulasEarth Fault Loop and RCD FormulasBattery Internal Resistance FormulasBusbar Size and Short-Circuit FormulasADC Resolution and Sampling FormulasCapacitor Switching Inrush FormulasCable Charging Current FormulasSolar DC to AC Ratio FormulasMeasurement Uncertainty FormulasParallel Transformer Load Sharing FormulasPeukert Law and Battery Runtime FormulasCapacitor Discharge Time FormulasHydraulic Power and Cylinder Force FormulasThermocouple Voltage FormulasTransformer Vector Group FormulasPower Supply Hold-Up Time FormulasHoist and Lift Power FormulasCompressor Power FormulasRectifier Bridge Sizing FormulasPCB Trace Width and Current FormulasHeat Pump COP FormulasSound Level and dB Addition FormulasDuty Cycle and RMS Load FormulasSupercapacitor Energy FormulasStep and Touch Voltage FormulasContactor Sizing FormulasInverter-Fed Motor Cable FormulasPneumatic Cylinder Force and Air UseBusbar Temperature Rise FormulasMotor Temperature Rise FormulasBattery Storage Round-Trip EfficiencyThermal Time Constant FormulasSolar Charge Controller Sizing FormulasPoint Illuminance FormulasGenerator Droop and Load Sharing FormulasTwo-Wattmeter Method FormulasVFD Braking Resistor FormulasLoad Bank Test FormulasTransformer Cooling Class Rating FormulasEnergy Meter Multiplier FormulasOvercurrent Relay Curve FormulasSingle-Tuned Harmonic Filter FormulasCable Sheath Circulating Current FormulasDifferential Protection Slope FormulasEarth Electrode Spacing FormulasSolar Array Row Spacing FormulasDC Lighting Voltage Drop FormulasTransformer Loss of Life FormulasMotor Start Voltage Dip in the Cable FormulasNeutral Earthing Resistor FormulasCable I²t Withstand Check FormulasMotor Locked-Rotor Code Letter FormulasSynchronous Speed and Pole FormulasBattery C-Rate and Cycle Life FormulasEV Charging Time FormulasConveyor Belt Power FormulasParallel Plate Capacitor FormulasSolenoid and Coil Inductance FormulasPower Factor Correction Payback FormulasTransformer Through-Fault Current FormulasTransformer EMF Equation FormulasDelta-Star Resistor Conversion FormulasCurrent Shunt Resistor FormulasSolar Energy Yield and Degradation FormulasElectrolysis and Faraday’s Law FormulasAGL Maximum Fittings on a CCR FormulasAGL Isolating Transformer FormulasComplex Number Formulas: Polar and RectangularPhasor Addition Formulas: Sum and DifferencePercentage Error Formulas for MeasurementsTrigonometry Formulas for Electrical EngineersMean and Standard Deviation FormulasQuadratic, Logarithm and Power FormulasPercentage, Ratio and Rounding FormulasProbability, Combinations and Binomial FormulasConversion Centre