Question

The plate current in a triode can be written as
ip=k(vg+Vpμ)3/2
Show that the mutual conductance is proportional to the cube root of the plate current.

Answer 1

EXPLANATION:

In the question, it is given:  

• With the grid voltage and the plate, the plate current varies as
• ip = Vpμ3/2 + KVg   …(1)
• With reference to VG, the equation is differentiated, and we obtain:
• dip = Vpμ1/2dVg + K32Vg
• ⇒ gm = dipdVg = 32KVg+Vpμ1/2
• From (1), in terms of transconductance, the plate current can be written as:
• ip = Vpμ1/23×K’ + 32KVg
• Here, the constant is K’ = 1K2ip x (23)3 = K'(gm)3
• ⇒ gm ∝ ip3