# Thermoelectric Cooler Calculation Example

Quote of the Day

You give it power.

Marilyn Vos Savant, her answer to the question ‘How do determine if something is good or evil?’ Unfortunately, this is a very dangerous test to perform in practice. Germany inadvertently applied this test with the Reichstag Fire Decree on February 4, 1933. This decree suspended civil rights so that Hitler could deal with a perceived terrorism problem. Hitler only relinquished power on his death at the end of WW2 in 1945.

Figure 1: Block Diagram of a Thermoelectric Cooler. (Source)

My team is working hard on developing  Dense Wavelength Division Multiplexing (DWDM) optical systems for communications applications. These systems put multiple wavelengths on a single fiber,  and they provide our customers the opportunity to deliver significantly more bandwidth without needing to additional fiber optic cables. To ensure reliable communication, each laser is is assigned a specific wavelength range. It must not leave that range, otherwise it will interfere with another communication channel.

The assigned wavelength ranges are ~0.8 nm wide. Because the wavelength of a semiconductor laser varies by 0.1 nanometer (nm) per °C,  this means we must control the laser’s temperature to within ±4 °C of an assigned value.  We normally control the laser temperature using a device called a Thermoelectric Cooler (TEC), which depends on the Peltier effect to provide refrigeration.

Most electrical engineers do not have much experience designing with TECs, and I need to put together some training material for our newbie design engineers. Fortunately, I found the following two articles were provided excellent background on designing with these devices.

The only problem with the design example is that there was a typo in one of the formulas and one of the matrices, and no worksheet implementation was provided. I marked up the design example and I provide a working spreadsheet implementation (Excel)  of the matrix-based solution here. The spreadsheet implementation is interesting because it demonstrates the use of matrix mathematics and data tables in Excel.

For those who prefer to see an algebraic approach, I include that here implemented in Mathcad 15 and PDF. As you can see in the algebra, there is an solution to TEC equations, but it is rather long (Figure 3).

Figure 3: Algebraic Solution to Simon’s Model.

I will be training my staff using this material in the coming weeks. As an example of the modeling output, Figures 3 and 4 show the design charts that the model generates.

Figure 3: Air Temperature into Electronics versus TEC Current.

Figure 4: Air Temperature into Electronics versus Electronics Power Dissipation.

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