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I'm having trouble finding a theoretical explanation about the transconductance photodiode behavior, the materials I find on the internet they talk about the connections, but not the behavior, in case someone could insert material or write here with the source please.

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    \$\begingroup\$ Can you link to the device you call the "transconductance photodiode". I've never heard of one so I'm keen to understand what one is. \$\endgroup\$
    – Andy aka
    Oct 10, 2022 at 14:58
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    \$\begingroup\$ are you possibly talking about either: photoconductive mode of operation, or transimpedance amplifiers? (I suppose calling them transconductance amplifiers wouldn't be wrong, just unusual) \$\endgroup\$
    – user253751
    Oct 10, 2022 at 15:01

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The expression does not make sense.

Transconductance is defined as:

$$g=\frac{dI_{\text{out}}}{dV_{\text{in}}}$$

The image shows the transfer characteristics for a photodiode (By Kennlinie_Photodiode_1.png: Gregor Hess (Ghe42)derivative work: Material scientist (talk) - Kennlinie_Photodiode_1.png, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=15579778)

A transfer characteristic can be defined as:

$$T=\frac{dI_{\text{out}}}{dE_{\text{in}}}$$

as shown in the diagram.

The photodiode mode is also called the photoconductive mode.

You should question your source for the phrase!

enter image description here

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