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Question

The plate current in a triode can be written as
ip=kvg+Vpμ3/2
Show that the mutual conductance is proportional to the cube root of the plate current.

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Solution

Given: The plate current varies with plate and grid voltage as
ip = KVg+Vpμ3/2 ...(1)
Differentiating the equation w.r.t VG ,we get:
dip = K32Vg+Vpμ1/2dVg gm = dipdVg = 32KVg+Vpμ1/2
From (1), plate current can be written in terms of transconductance as:
ip = 32KVg+Vpμ1/23×K'Here, K' is a constant =(23)3×1K2ip = K'(gm)3 gm ip3

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