## Introduction

Industrial grade devices for measuring solar radiation are delicate and expensive. The "pyranometer" is basically a flat plate (covered with a transparent dome) that is coated with an extremely absorptive surface. As the sun strikes it, the surface gets hot. The temperature of the surface is measured with a thermopile, giving an output voltage related to the amount of solar radiation striking the surface.

You can build a "poor man's" pyranometer that works pretty well out of inexpensive and readily available components. Although it will not be of laboratory quality, it will suffice for comparative measurements and educational purposes.

## Making the Meter

The obvious component to consider as the basis for our meter is a silicon photovoltaic cell. When sunlight strikes it, it produces electricity, and the more sunlight strikes it, the more electricity it produces.

At first glance, you might think that you could just hook a voltmeter up to it and measure the output voltage. Unfortunately, if you do this, you will get very erroneous results (visit the Appendix if you want to understand why).

Instead, you will need to measure the cell's output current. If you short out (hook a perfect wire between) the positive and negative terminals of your cell, a current flows through that wire. That is the current that you would like to measure. It varies linearly with the amount of sunlight striking the surface of the cell. This is actually a little trickier than one might think, for reasons that are explained in the Appendix.

You can measure the cell's current by measuring the voltage across a very small resistor. Here we show how to do this with a digital panel meter or digital VOM. This is shown in the following schematic: PV represents the PV cell, and M represents the voltmeter. Rsh is the resistor through which most of the current from the PV flows, and across which we will measure the voltage.

Following are the steps in making the meter.

• Our goal is to make full sunlight give a 100 mVolt reading on the digital meter (full sunlight is about 1000 watts per square meter), so our meter will read 1 mVolt per 10 Watts/m2.
• Get a 3 1/2 digit digital panel meter (try Marlin P. Jones, which sells such things for about \$7...they do require a battery) that has a 0-199.9 mVolt scale (this is a common item). Or, just plan on using a digital multimeter on the 0-200 mVolt scale.
• First, estimate how much current your cell will produce in full sunlight. A good first assumption is that your cell puts out about 0.025 amps per square centimeter. So measure your cell, calculate its area, and multiply by 0.025. For example, if your cell is 8 cm square, guess that your full sunlight cell current is 8 * 8 * 0.025 = 1.6 amps.
• Calculate the resistance that is required to give 100 mVolt drop when I is flowing through it. Ohms law says that R = V / I, or 0.1 volt / I. For our example, this is 0.1 Volts / 1.6 Amp, or 0.0625 ohms.
• Make the resistor. For very small resistors like this, a good way is to use a length of small wire. I used number 30 wire wrap wire. Appendix B shows the resistance per foot for various small copper wire sizes. Number 30 wire has a resistance of about 0.121 ohms per foot. So, to make a 0.0625 ohm resistor, only requires 0.52 feet, or 6.2 inches!
• Connect your resistor across the PV cell. You will need to solder it, because of the very low resistances involved. And, bear in mind that wiring connected to the cell also has resistance, so either account for it or cut it short.

At this point, you should be able to connect your digital meter across the terminals. It should be configured for 200 millivolts full scale. Note that because the meter is measuring voltage now, the length of your meter wires is not too important. If you take your apparatus out into full sunlight, you will hopefully see a reading on your meter that is not too far from 100 mVolts.

At this point, you will want to calibrate your meter. The best way is to have a calibrated instrument of some sort. Lacking this, you do a fair job by finding a time when the sun is high (noon on a summer day) on a very clear day. Then assume that the solar radiation is 1000 watts per square meter.

The following steps show how to calibrate the meter by altering your resistor. It will assume that you are calibrating without a reference. If you have an actual reference instrument, then use whatever value it supplies instead of 1000.

• In full sunlight, note the reading of your meter. We would like for it to be exactly 100 mVolts. It is probably something different.
• We are going to make a new resistor wire of the proper length to make the meter read 100 mVolts.
• Calculate Lnew = L0 * 100 / reading. (L0 is the original length of the resistor wire). For example if my original wire was 6.2 inches, and my meter reads 88, I need a new resistor wire of length Lnew = 6.2 * 100 / 88 = 7.05 inches.
• Cut a new resistor wire and replace your original.

At this point, your silicon solar cell and digital voltmeter should be doing a fair job of measuring solar radiation.

## Things to do With Your Meter

Here are some interesting experiments to do using your meter.

• Check the effect of angle of incidence. Point the cell directly at the sun and measure output. Then turn the cell at various angles, and see how the "angle of incidence" affects output. Theory says that direct radiation striking the surface is proportional to the cosine of the angle of incidence.
• Experiment with measuring direct versus diffuse radiation.

Sunshine consists of the rays that come straight from the sun (direct radiation) plus light that has been reflected from air molecules, dust in the atmosphere, etc.

• Set the PV cell on a horizontal surface. You are measuring Global Horizontal radiation.
• While the cell is sitting on a horizontal surface, cast a shadow on in with your hand, held several feet away. You have shaded the direct radiation, and what is left is the diffuse radiation. Compare this to the global horizontal.
• Get a mailing tube mount the PV cell to it, so that the cell's surface is perpendicular to the length of the tube. Point the assembly at the sun. You are measuring "direct" solar radiation.
• measure the energy striking the outside of a window.
• Put the cell flat against the inside of a window.
• How does the radiation measured here compare to that measured on the outside of the window.
• You are measuring radiant energy that will warm your house. In the winter, this is free heat. In the summer, you don't want it.
• Compare the results for different windows of your house, and consider the relationship between this radiant gain and the amount of sky that your window sees.
• measure the effectiveness of shade cloth
• Turn the cell upside down, hold it above the shade cloth, and measure the amount of radiation reflected back from the shade cloth.
• Do the same experiment with black and with white shade cloth. Which is likely to result in a cooler patio?
• Investigate the effects of surface reflectance on road, sidewalk, and driveway heating.
• Using the upside down cell, measure the amount of reflected radiation from various surfaces.
• How does this compare with the temperature of the surface?
• Compare sunlight to strong artificial light.
• Compare the reading some distance from an incandescant light to that of a compact flourescent light of the same lumens rating, the same distance away. Is there a difference? Can you explain why there might be a difference?

## Appendix A: The I-V Characteristic of PV cells

### Basic Electricity

Remember that voltage and current are not the same. Voltage represents the strength of the electricity, analogous to water pressure (say, in pounds per square inch). Current represents the flow rate, analogous to water flow rate (say, in gallons per second). The units of voltage are Volts. The units of current are Amps.

A Resistor is a device that resists the flow of electricity. Its behavior s governed by Ohm's Law, which says that the voltage across a resistor (in Ohms) is equal to the Current (in Amps) flowing through it times the Voltage across it. Note that current is always through an element, and voltage is always across an element.

A Current Source is an element that delivers a constant current, regardless of the voltage across it. It is an ideal element that is approached by certain circuits over certain operational ranges.

A Voltage Source is an element that delivers a constant voltage at its terminals. Like a Current Source, it is an ideal device, approached over particular operating ranges by real devices.

### PV Cells

Over part of its operating region, PV cells act like a current source. Over part of their region, they act like a voltage source. The following figure is what is known as an I-V curve. It shows how current and voltage relate to each other in a typical PV cell. Each of the colored lines describes behavior at one level of incoming radiation. Note that when voltage is very low, the cell acts like a current source. That is, it delivers a rather constant current, independent of the voltage.

The point at which the I/V curve intersects the vertical axis is called the "short circuit current", or Isc. Isc is directly proportional to the solar radiation striking the cell. If you could short out the cell and measure the current, your reading would be proportional to the incoming radiation.

The point at which the curve intersects the horizontal axis corresponds to what a voltmeter (which takes its reading without drawing hardly any current) will read if connected to a PV cell. It is called the Open Circuit Voltage, or Voc. Voc is NOT proportional to to incoming radiation.

### Pitfalls

To use a PV cell to measure solar radiation, you want to measure its current output. Ideally, a current meter would have zero resistance. In reality, they all have some resistance. Here we investigate the effect of current meter resistance on our measurement.

In addition to the PV cell I/V curves, the above graph shows I/V curves for three different resistors, 0.0667 ohms, 0.4 ohms, and 1.5 ohms (note how it obeys Ohm's Law). If a resistor is connected across the terminals of a PV cell, the operating point will be described by the intersection of the resistor's line and the PV cell's curve (for the current incoming radiation).

Note how for the smallest resistor, the points of intersection fall along the constant current portion of the PV cell's characteristic. So, the current through the resistor is proportional to the incoming radiation.

For the other resistors, though, we are not operating within the constant current region, so the current through our load will NOT be proportional to the incoming radiation.

My first attempt at measuring PV current was using a digital Volt/Amp/Ohmmeter, set to the current scale. I got totally crazy results, with a mostly shaded cell showing nearly as much output as an unshaded cell. Investigation showed that the resistance of the ammeter was over 2 ohms, which was drastically altering the result.

If you are going to use a silicon PV cell for measuring solar radiation you MUST first consider the resistance of your current measuring circuit, making sure that it is low enough to be mostly in the constant current region of the cell. The method described above limits PV output voltage to about 0.4 volts, which keeps the measurement reasonably linear with radiation variation.

## Appendix B: Wire resistance

The following table shows resistance per foot for various wire gauges:

Copper Wire Resistance
Gauge Ohms/ft
24 0.0302
26 0.048
28 0.0764
30 0.121
32 0.193
34 0.307
36 0.488

## Deficiencies in this Measurement Device

A pyranometer based on silicon cells is not a laboratory device. A good pyranometer has a very flat spectral response. This means that it responds equally to all wavelengths that strike it. Silicon photocells tend to have an irregular spectral response, responding less well to longer wavelength photons. Below a certain wavelength in the infrared, they cease to respond at all.

In spite of the limitations, the simple device shown here is useful as a learning tool.