This article presents the equivalent circuit for a solar cell and discusses some implementation details.

The astonishing abundance of life found on earth requires a corresponding abundance of energy. This is nothing new, but the situation is a bit different in the modern world because human beings—in contrast to plants, and the animals that eat plants, and the animals that eat the animals that eat the plants—are not satisfied with energy in the form of solar radiation. We want electricity, and lots of it.

It’s no surprise, then, that the idea of generating electricity directly from sunlight is so appealing. Wouldn’t it be great if we could fuel our modern lives using only the earth’s primordial energy source? It would indeed, though if we actually attempted this, the inherent limitations of sunlight-to-electricity conversion would impose some seriously unpopular lifestyle adjustments.

Fortunately, powering a small electronic device is much easier than powering the entire world, especially when the device incorporates the low-current, energy-efficient design techniques that are typically associated with extending battery life rather than making something more compatible with solar power. But before we all go out and start designing solar-powered PCBs, we should try to understand 1) what exactly a solar cell is within the context of circuit design and 2) how the solar cell interacts with load components.

 

The Equivalent Circuit

If you want to carefully analyze the behavior of a circuit that includes a solar (aka photovoltaic, or PV) cell, you need to use an “equivalent circuit”—i.e., you need to replace the cell with a group of basic components that can produce similar electrical behavior. This is the equivalent circuit for a solar cell:

 

 

The idea here is that the solar cell generates an internal current corresponding to the light intensity. Not all of this current is available to the load, though, because some flows through the parallel diode (recall that photovoltaic conversion is implemented using a pn junction) and some flows through the parallel resistance (RP).

When no load resistance is present, the voltage available at the terminals of the solar cell is determined by the interaction of the current source with the parallel diode and the parallel resistance. This is called the “open-circuit voltage.” If the cell is supplying load current, the voltage at the terminals will be lower than the open-circuit voltage, because some of the voltage is dropped across the series resistance (RS).

 

Voltage Source or Current Source?

You may be accustomed to thinking of a solar cell as similar to a battery, except that the “battery” voltage varies according to light intensity. However, the equivalent circuit makes a PV cell look like a current source rather than a voltage source. This could be rather awkward since we’re all accustomed to powering circuits using voltage sources, not current sources.

A solar cell is not really a voltage source or a current source as we usually think of them, but it can power a circuit in the typical voltage-source style. The additional components in the equivalent circuit indicate that the internal current source is not in direct interaction with the load components. Furthermore, the cell will always generate a voltage (even when nothing is connected to the terminals) because the internally generated current flows through the internal diode and RP.

However, if you choose to think of a solar cell as a battery, keep in mind that it’s a rather mediocre battery. First of all, the voltage is highly unpredictable. As an example, consider this plot of open-circuit voltage vs. irradiance:

 

This is taken from the datasheet (PDF) for a compact, surface-mount solar cell manufactured by IXYS. I recently designed a solar-powered microcontroller board, and this is the solar cell that I used.

 

The irradiance in an indoor environment might be 10 or 20 W/m2, and direct sunlight outdoors might give you 900 W/m2. So if you take your device from the garage into the backyard, your circuit’s supply voltage could jump from 3.5 V to 4.6 V.

The second problem is that the internal series resistance is large. In other words, the cell’s ability to supply current is very limited. The IXYS cell maxes out at 4.4 mA—not ideal for driving motors or an array of LEDs, but more than enough for a microcontroller operating at low frequency.

Before we move on, I should mention that a solar cell can be manufactured in such a way as to favor voltage or current: high current capacity is obtained by filling the available area with one pn junction, and higher voltage is obtained by splitting the area up into multiple junctions and connecting them in series. The IXYS cell that I used in my design favors voltage, but there are two other versions of the same part that provide higher current (and lower voltage).

 

Peak Power

Manufacturers can control current and voltage characteristics by changing the device’s physical configuration, but it’s not so easy to increase power, which is the true representation of what you can accomplish with a solar cell.

By looking at a cell’s current-voltage characteristic, you can identify the power sweet spot, denoted by PSS (well, that’s not the official symbol, but it should be). This is the point at which the cell is operating at maximum power. For example:

 

 

In this example, the red curve is power, and the blue curve shows the voltage provided by the cell at a given load current. You can see that maximum power is obtained when the voltage at the cell’s terminals is 3.4 V. The plot also shows that operating at maximum load current is not a good way to extract maximum power from the sunlight falling on the solar cell; in the case of this particular product, the region of maximum and near-maximum power corresponds to a voltage range of about 2.7 V to 3.7 V, or to a current range of about 3.3 mA to 4.3 mA.

 

Conclusion

We looked at the equivalent circuit for a photovoltaic cell, and we discussed some important characteristics of the voltages generated by PV devices. There is much more that could be said on this topic, but I hope that this article has provided a good introduction to the practical aspects of incorporating solar power into an electronic device.

 

Supporting Information

 

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