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Linearity Testing of 

Photovoltaic Cells 

Preprint 

K. Emery 

National Renewable Energy Laboratory 

S. Winter 

Physikalisch Technische Bundesanstalt (PTB) 

S. Pinegar 

Pomona High School 

D. Nalley 

Purdue University

Presented at the 2006 IEEE 4th World Conference on 

Photovoltaic Energy Conversion (WCPEC-4) 

Waikoloa, Hawaii 

May 7–12, 2006 

Conference Paper 

NREL/CP-520-39854 

May 2006 
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LINEARITY TESTING OF PHOTOVOLTAIC CELLS 

K. Emery,1 S. Winter,2 S. Pinegar,3 and D. Nalley4

1

National Renewable Energy Laboratory (NREL), Golden, CO, USA*

2

Physikalisch Technische Bundesanstalt (PTB), Braunschweig, Germany 3

Pomona High School, Arvada, CO 

4

Purdue University, South Bend, IN 

 

*

 This work has been authored by an employee or employees of the Midwest Research Institute under Contract No. DE-AC36-99GO10337 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States 

Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, 

for United States Government purposes. 

ABSTRACT 

Photovoltaic devices are rated in terms of their peak 

power with respect to a specific spectrum, total irradiance, 

and temperature. To rate photovoltaic devices, a reference detector is required whose response is linear with 

total irradiance. This paper describes a procedure to determine the linearity of the short-circuit current (Isc) versus

the total irradiance (Etot) by illuminating a reference cell 

with two lamps. A device is linear if the current measured 

with both lamps illuminating the cell is the same as the 

sum of the currents with each lamp illuminating the cell. 

The two-lamp method is insensitive to the light spectra or 

spatial nonuniformity changing with irradiance. The twolamp method is rapid, easy to implement, and does not 

require operator intervention to change the irradiances. 

The presence of room light only limits the lowest irradiance that can be evaluated. Unlike other methods, the 

two-lamp method does not allow the current to be corrected for nonlinear effects. 

INTRODUCTION 

International standards require that the short-circuit 

current or response of the reference device is linear with 

total irradiance [1,3]. Accredited calibration laboratories 

can not assume that their reference device is linear 

unless another accredited laboratory has performed the 

measurement [4]. The PV performance laboratory is ISO 

17025 accredited for primary reference cell, secondary 

reference cell and secondary module calibrations [5]. 

Limited labor resources necessitated the development of 

a technique to determine linearity without taking significant labor or skill. 

Traditional methods listed in the standards involve 

measuring Isc vs. Etot as Etot is varied, or measuring the 

differential spectral responsivity vs. bias light. Measuring 

Isc vs. Etot assumes that the temperature, spatial nonuniformity, and relative differential spectral irradiance are 

invariant with Etot. Calculating Isc from spectral responsivity vs. bias light gives the correct value for linearity under 

a given reference spectral irradiance in the absence of 

errors. All methods assume that the temperature does 

not change with irradiance and that the light-source spectrum resembles the solar spectrum. The two-lamp 

method assumes that the lamp intensities when individually irradiating the sample are the same as when both 

lamps irradiate the sample. 

The two-lamp method is insensitive to the spectrum 

of the light or spatial nonuniformity changing as the irradiance is varied. It does assume that the temperature does 

not change with irradiance and that the light-source spectrum resembles the solar spectrum. This requirement is 

only because nonlinear mechanisms in the photo-current 

are often wavelength dependent because surface recombination, band-gap or diffusion length changing with injection level result in wavelength dependent changes in the 

photo-current [6]. An extreme example would be a laser 

showing a device to be linear or very nonlinear with irradiance depending on the wavelength. The two-lamp 

method assumes that the lamp intensities when individually illuminating the sample are the same as when both 

lamps illuminate the sample. The presence of room light 

only limits the lowest irradiance that can be evaluated. 

Unlike other methods, the two-lamp method does not allow the current to be corrected for nonlinear effects. The 

 Figure 1. Experimental apparatus to verify linearity. 

1
most appealing aspect of the two-lamp method when 

compared with other methods for a high-volume calibration laboratory, when implemented as described below, is 

that it is fast and does not require operator intervention to 

change the irradiances. 

APPARATUS 

The experimental apparatus for the two-lamp method 

is shown in Fig. 1. The light box enclosing the system 

was removed for the photograph and is not essential. The 

minimum irradiance that the linearity measurement can be 

made is determined by the background irradiance and 

noise in the current measurement. The 8-position filter 

wheel has a 5-cm clear aperture and is controlled with 

RS-232 commands. The transmittances of the metallic 5-

cm-diameter neutral-density filters were standard values 

of 25, 33, 40, 50, 63, and 79%. The first two of eight positions are transparent and opaque. The filter wheel is 

placed so that no light from the lamp leaks out the sides. 

Any light leaking out the sides that the cell collects is an 

error if different filter positions leak different amounts of 

light. The sample is mounted on a temperature controlled 

plate. 

The software automatically adjusts the power supply 

current to the lamps until the maximum desired light level 

is reached. For 1-sun reference cells this value is typically 1.4 suns. The program waits for the lamps to stabilize and then rotates the wheels through the 64 combinations of positions. The data is saved and plotted in the 

groups standard format. 

If the intensity of the lamp or cell temperature drifts 

appreciably during the measurement it may be desirable 

to install high speed shutters between each lamp and filter 

wheel with the same constraints of no light leakage. With 

separate shutters the time for the 3 required measurements for each irradiance can be reduced to the shutter 

speed and time to read meter because the filter wheels do 

not need to rotate. Without the shutter the time between 

the 3 measurements approaches the time for the entire 

measurement. This also would free up another position 

on the filter wheel giving 7 filters and one transparent position. The major issue would be the additional expense 

of hardware and software to control the shutters with the 

computer. 

 

THEORY 

The two lamp method for linearity determination is 

based upon the linearity of the photo-current with the photon flux. It is assumed that the short-circuit current, Isc

equals the photo-current. If a PV device is linear then the 

superposition principle must be valid: The photo-current 

from a cell illuminated by two light sources must equal the 

sum of the photo-currents from the individual light sources 

or; 

[IA - Iroom ] + [IB - Iroom ] = [IAB - Iroom ] (1) 

where: 

IAB is the short-circuit current with lamps A and B 

 illuminating the cell, 

IA or IB is the short-circuit current with one lamp on the 

 cell and the light from the other lamp blocked, 

Iroom is the short-circuit current when the light from 

 both lamps are blocked. 

Expressing equation 1 as a percentage deviation from 

linearity, Dlin yields; 

Dlin = 100 • [(IAB-Iroom) / (IA + IB -2 • Iroom) – 1] , (2) 

A graph of Dlin versus the irradiance, Etot will show the 

percent deviation from linearity with irradiance. The irradiance, Etot can conveniently be expressed as the number of suns, 

Etot = IAB / Isc (1-sun) (3) 

where: 

Isc (1-sun) is the estimated short-circuit current under 

 standard reference conditions. 

The error in Etot because IAB is nonlinear with irradiance is unimportant because the pass / fail criteria as 

described below is based upon the maximum percentage 

deviation from nonlinearity and not the irradiance. For 

pass / fail criteria based upon the standard deviation of 

the slope of Elin versus Etot the standard deviation will be 

affected. However, the curve would not be made more 

linear by an error in Etot. 

RESULTS 

Both ASTM and IEC standards determine if a sample 

is nonlinear by the standard deviation of the slope expressed as a percentage [7,8]. A cell is deemed nonlinear 

if the standard deviation in the slope of a linear fit to Isc vs. 

Etot is greater than 2%. 

Figure 2 compares PTB calibration results with the 

two lamp method [9,10]. Nonlinear effects are not readily 

apparent when Isc versus the total irradiance is plotted. A 

better way to look at the data is shown in Fig. 3, where the 

data are normalized and expressed as a percentage deviation from linearity at 1-sun, Dlin. This form is also how 

PTB presents their linearity measurements in their reference-cell calibration certificates. The two-lamp method is 

similar, but shows more “scatter” because the nonlinearity 

over a range of irradiances is expressed at any given total 

irradiance. Another source of scatter in the two lamp 

method as implemented in this paper is the 0.3% maximum drift in the 2 lamps irradiance during the measurement period. 

An exact numerical calculation was performed to assess the differences between the two-lamp method and 

the more traditional approach of measuring Isc versus Etot. 

A quadratic function designed to give a 1-sun Isc of 

100 mA and linear fit to the function over a 0.3 to 1.4 sun 

irradiance range giving a standard deviation / slope of 2% 

yields; 

Isc = (75.28 + 23.74•Etot) • Etot (4) 

Figure 4 summarizes these results. The most notable 

feature of the exact calculation is that a standard deviation of 2% does not ensure that the maximum deviation 

2
from linearity is less than 2%, as suggested in ASTM 

standard E1143 section 8.2 or in IEC standard 60904-10. 

Differences between the two-lamp method and traditional 

measurements are a function of the nonlinearity. Because of these differences, the two-lamp method is limited 

to determining the nonlinearity over a relatively narrow 

irradiance range such as 0.3 to 1.4 suns. 

An example of a device showing nonlinear behavior 

because of internal series resistance is given in Fig. 5. 

This graph was produced by Labview software as part of 

the linearity test bed’s output. Figure 6 shows how series 

resistance can impact the linearity. At light levels above 

one sun values near Isc are reduced because of resistance losses. Similar behavior can also occur if the cell 

voltage is too large and the parameter being measured is 

not the photo-current but closer to the open-circuit voltage. 

The quality of the two-lamp method data is determined by the variation in the lamp output during the 

measurement and the range of temperatures during the 

measurement since the procedure assumes that the temperature does not change. Typically the lamp drifts in 

intensity less than 0.4% resulting in a 0.4% or large uncertainty in the nonlinearity. This value can be reduced by 

reducing the time between measuring IA , IB , and IAB as 

close together in time as possible. The temperature 

change during the measurement is an issue with all 

methods involving continuous light because the temperature gradient between the cell and sensor and between 

the sensor and the temperature controlled plate varies as 

a function of light level. For well behaved cells this 

change is typically less than 2 °C. For the cell shown in 

Fig. 5 the temperature varied by 6 °C during the measurement. 

SUMMARY 

In summary a method has been presented to determine if the short-circuit current is linear with light level 

over the range of interest for flat-plate photovoltaic technologies. The method is rapid, does not require operator 

intervention and produces a quantitative graph of percentage deviation form linearity as a function of light level. 

It is anticipated that this method will be incorporated into 

consensus standards. The standard deviation of the 

slope of Isc versus total irradiance is poor indicator of 

nonlinearity and should not be used. It is recommended 

that nonlinearity be expressed as a percentage deviation 

form linearity versus total irradiance. 

ACKNOWLEDGEMENTS 

This work is supported under Contract No. DE-AC36-

99GO10337. 

REFERENCES 

[1] IEC standard 60904-2, Photovoltaic devices-Part 2: 

Requirements for reference solar devices, International 

Electrotechncal Commission, Geneva, Switzerland. 

[2] ASTM Standard E948, Standard Test Methods for 

Electrical Performance of Non-Concentrator Photovoltaic 

Cells Using Reference Cells, Amer. Society for Testing 

Matls., West Conshocken PA, USA. 

[3] ASTM Standard E1121, Standard Test Method for 

Calibration of Primary Non-Concentrator Terrestrial 

Photovoltaic Reference Cells Using a Tabular Spectrum, 

Amer. Society for Testing Matls., West Conshocken PA, 

USA. 

[4] ISO / IEC 17025, General Requirements for the 

Competence of Testing and Calibration Laboratories, 

1999, International Standards Organization, Geneva, 

Switzerland. 

[5] American Association for Laboratory Accreditation 

certificate A2LA 2236.01 for Secondary Reference Cell, 

Primary Reference Cell, and Secondary Module Calibration, Web site: www.a2la.org, Frederick, MD. 

[6] H.J. Hovel, Semiconductor and Semimetals Volume II 

Solar Cells, Academic Press 1975, 

[7] ASTM Standard E1143-05, Standard Test Method for 

Determining the Linearity of a Photovoltaic Device Parameter with Respect To a Test Parameter, Amer. Society 

for Testing Matls., West Conshocken PA, USA, 1998. 

[8] IEC standard 60904-10, Photovoltaic devices – Part 

10: Methods of linearity measurement, International Electrotechncal Commission, Geneva, Switzerland.

[9] C.R. Osterwald, et. al, “Results of the PEP ‘93 Intercomparison of Reference Cell Calibrations and Newer 

Technology Performance Measurements,” 25th IEEE 

PVSC, 1996, pp. 1263-1266. see also March 1998, NREL 

Tech. Rep. NREL/TP-520-23477. 

[10] S. Winter, J. Metzdorf, S. Brachmann, K. Emery, F. 

Fabero, Y. Hishikawa, B. Hun, H. Müllejans, A. Sperling, 

W. Warta, “The Results of the Second World Photovoltaic 

Scale Recalibration,” Proc. 31st IEEE PVSC, Orlando FL, 

pp. 1011-1014, Jan. 3-7, 2005. 

Figure 2. Linearity measurement of WPVS primary 

reference cell 930216-1 from two calibrations at PTB 10 

years apart compared with the two-lamp method. 

3
Figure 3. Linearity measurement of WPVS primary reference cell 930216-1 expressed as a percentage deviation from linearity.

Figure 5. Standard plot from Two-Lamp Linearity 

Measurement system showing nonlinear behavior because of an internal series resistance in a reference 

cell at light levels above 1-sun.

Figure 4. Exact calculation of a simulated device that 

fails the ASTM and IEC linearity requirements, showing 

that the deviation from nonlinearity can be more than 

2% even though the standard deviation is 2%.

Figure 6. Normalized Current vs. voltage for nonlinear 

cell in Fig. 5 showing that at light levels above 1-sun the 

photo-current is not Isc. 

4