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I have been reading about the voltage gain of JFET, but I am unable to understand how to write the equation for the input side. Can somebody explain the method to write the equation for the input side?

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The text has provided \$V_i=V_{gs}+V_{Rs}\$ but I do not understand how this equation came up.

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I do not understand how this equation came up

It's as easy as this: what ever voltage you have at the input with respect to 0 volts (\$V_i\$) must equal the voltage between gate and source (\$V_{GS}\$) plus the voltage between source and 0 volts (the voltage across \$R_S\$).

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The text has provided Vi=Vgs+VRs but I do not understand how this equation came up.

This equation is a KVL equation. The left side is a voltage rise from 0V across RG. The right side is the sum of two voltage drops from gate to source and from the source back to 0V.

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