Gilbert Multiplier cell

The Gilbert multiplier cell is a modification of the emitter coupled cell and this allows four – quadrant multiplication. Therefore, it forms the basis of most of the integrated circuit balanced Multipliers. Two cross- coupled emitter- coupled pairs in series connection with an emitter coupled pair form the structure of the Gilbert multiplier cell.

The collector current of Q₃ and Q₄ are given by

Similarly, the collector current of Q₅ and Q₆ are given by

 collector current I_C1 and I_C2 of transistors Q₁ and Q₂ can be expressed as

Substituting the above equation in I_C3 and I_C4, we get

Similarly substituting I_c2= in I_c5 and I_C6 , we get,

The differential output current I is given by

∆I =I_L1 - I_L2

= (I_C3 +I_C5) - ( I_C4+I_C6)

=I_C3 - I_C6)-(I_C4 - I_C5)

∆I=I_EE tanh( V₁/2V_T) tanh(V₂/2V_T)