One of the most important parameters in the design process is how many LEDs are required to meet the design goals. The rest of the design decisions revolve around the number of LEDs, since it directly impacts the light output, power consumption, and cost of the luminaire.
It is tempting to calculate the number of LEDs by looking at the typical luminous flux listed on an LED’s data sheet and divide the target lumens from the design goals by that number. However, this approach is too simplified and will lead to a design that will not meet the application’s lighting requirements.
An LED’s luminous flux depends on a variety of factors, including drive current and junction temperature. To accurately calculate the necessary number of LEDs, the inefficiencies of the optical, thermal and electrical systems must be estimated first. Personal experience with previous prototypes, or the example numbers provided in this document, can serve as a guide to estimate these losses. This section walks through the process of estimating these system losses.
Optical System Efficiency
Optical system efficacy is estimated by examining light loss. There are two main sources of light loss to estimate:
1. Secondary Optics
Secondary optics are any optical system that is not part of the LED itself, such as a lens or diffuser placed over the LED. The losses associated with secondary optics vary depending on the particular element used. Typical optical efficiency through each secondary optical element is between 85% and 90%.
2. Light Loss Within the Fixture
Fixture light loss occurs when light rays from the light source strike the fixture housing before hitting the target. Some light is absorbed by the fixture housing, while some is reflected back into the fixture. The efficiency of the fixture is dictated by placement of the light source, the shape of the fixture housing, and materials used in the fixture housing. As Figure 2 (below) shows, the directional nature of LED light enables much higher fixture efficiencies than is possible with omni-directional light sources.
Light Source
Light-Source Efficacy
Coefficient of Utilization
Fixture Efficacy
CFL
65 lm/W
54%
35 lm/W
XLamp XR-E
Neutral White
58 lm/W
77%
44 lm/W
Figure 2 - Comparison of CFL & LED Coefficient of Utilization
Chart 2 - Light Ouput vs. Angle for CFL Fixture & XLamp XR-E LED
For the example luminaire, there will only be secondary optics loss if the luminaire requires secondary optics. The main purpose of secondary optics is to change the light output pattern of the LED. Chart 2 (above) compares the beam angle of the Cree XLamp XR-E LED to the light output pattern of the target fixture. The beam angle of the bare LED is similar enough to the target fixture that no secondary optic is required. Therefore, there is no optical loss due to secondary optics for the example luminaire.
To calculate fixture loss for the CFL example, we assumed 85% reflectivity for the fixture reflector cup and that 60% of the light will hit the reflector cup. Therefore, the optical efficiency will be:
Optical Efficiency = (100% x 40%) + (85% x 60%)
Optical Efficiency = 91%
Thermal Loss
LEDs will decrease in relative flux output as junction temperature (Tj) rises. Most LED data sheets list typical luminous flux at Tj = 25°C, while most LED applications use higher junction temperatures. When using Tj > 25°C, the luminous flux must be derated from the value listed on the LED’s data sheet.
LED data sheets include a chart showing the relative light output versus junction temperature, such as the one shown in Chart 3 (right) for XLamp XR-E white LEDs. By choosing either a specific relative light output or a specific junction temperature, this graph shows the value for the other characteristic.
Chart 3 - Example Relative Intensity vs Junction Temperature Graph for XLamp XR-E White LED
For the CFL example, this luminaire is only designed for commercial buildings with vented ceilings. Based on the listed design goals, this design will prioritize light output, efficacy and lifetime.
XLamp XR-E LEDs are rated to provide an average of 70% lumen maintenance after 50,000 hours, provided the junction temperature is kept at 80°C or lower. Therefore, the appropriate maximum junction temperature for the CFL example is 80°C. This corresponds to a minimum relative luminous flux of 85%, as shown in Chart 3 (right). This 85% relative luminous flux is the thermal efficacy estimate for the example luminaire.
Electrical Loss
The LED driving electronics convert the available power source (e.g., wall-plug AC or battery) to a stable current source. Just as with any power supply, this process is not 100% efficient. The electrical losses in the driver decrease the overall luminaire efficacy by wasting input power on heat instead of light. The electrical loss should be taken into account when beginning the LED system design.
Chart 4 - Example Efficiency vs Load Graph for LED Driver
Typical LED drivers have efficiencies between 80% and 90%. Drivers with efficiency over 90% will have much higher costs. Be aware that driver efficiency can vary with output load, as shown in Chart 4 (right). Drivers should be specified to run at greater than 50% output load to maximize efficiency and minimize cost.
For indoor applications, 87% is a good estimate for driver efficiency. Drivers meant for outdoor use or very long lifetimes will probably have lower efficiency.
Table 5 (below) summerises the efficiencies of the optical, thermal and electrical systems for the example luminaire.
System
Efficiency
Type
Optical
91%
Light
Thermal
85%
Electrical
87%
Power
Table 5 - Summary of Example CFL Replacement Efficiencies