How Thermal Energy is Rectified

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The Model

Thermal noise voltage is a random fluctuating source with a Gaussian distribution. The diode, being a dynamic resistor, rectifies thermal energy. Please see the home page for an outline of the mathematics. The mathematics involved in determining the DC voltage produced by a particular diode requires numerical analysis, kTC noise, Gaussian distribution, and diode modeling equations. Such mathematics is beyond the scope of this page. To understand how more thermal energy flows to the load, rather than diode, is outlined in the following model.

The above circuit is a realistic model of a load, R1, connected to a diode, D1, and the flow of thermal energy. The diode and the load have capacitance, and a thermal noise voltage source. The load is set to 5451.7 ohms to match the SMS7630 diode, but is not critical. The following outlines the results,

Power drained from Vd thermal noise source = 102.39 pW
Power drained from Vr thermal noise source = 99.548 pW
Result: More energy flows out of the diode Thermal noise source than the load Thermal noise source.

The above circuit shows in detail, by means of numerical analysis, the diode dynamic resistance rectifies thermal energy, resulting in more energy flowing from the diode thermal noise source than from the load thermal noise source. The reason is seen by the fact that the diode is a dynamic resistor, thus rectifying Johnson noise. Such rectification produces a flow of DC current in one direction through the load. The end result is thermal noise current being converted into DC.

The SMS7630 diode has a low rectification efficiency at so-called thermal equilibrium, as seen in the above data. The following data shows how a small diode array, using microscopic diodes, may perform,

Power consumed by Vd thermal noise source = 175.63 µW
Power consumed by Vr thermal noise source = 86.964 µW
Net flow of energy = 175.63 µW - 86.964 µW  = 88.666 uW

Does it matter?

Does it matter if a diode successfully moves more thermal energy from the diode to the load?  No, it does not matter. The diode is a dynamics resistor that reacts to the noise. What occurs is that the diode converts AC noise to DC. Such thermal noise comes from both the diode and the load. So it matters not if such thermal energy comes from both the diode and load, even though slightly more thermal energy would come from the diode than the load.

What is so important about diodes is their ability to aggregate the rectified DC power. Thermal noise power by itself cannot be aggregated. The sum of two random noise voltage sources equals sqrt(2). The impedance doubles, so the net power remains the same. On the other hand, placing two diodes in series offers twice the DC power since both the DC voltage and impedance doubles; i.e., P = V^2 / R.

What matters is that the diode rectifies thermal noise, produces a DC voltage. A DC voltage is usable energy.


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