8.2. DC Imbalances

In a real transistor, parameters k_n, V_tno, and λ_n can be slightly different such that, in general, I_D1 ≠ I_D2. The ratio of the currents is given by

Equation 8.3

where, in the circuit with the gate of M₁ grounded, V_GS1 = V_GS2 = V_GS. For the specific case of the project on the amplifier, we can assume that V_DS1 ≈ V_DS2 such that

Equation 8.4

To simplify the relation, it is advantageous to express parameters in terms of increments. For example, threshold voltage will be expressed as a mean value

Equation 8.5

and a difference between the threshold voltage of the two transistors

Equation 8.6

such that

Equation 8.7

and

Equation 8.8

Using these definitions along with V_eff = V_GS – V_tno, we have

Equation 8.9

or, approximately,

Equation 8.10

In the differential amplifier project (PMOS), we measure the drain currents along with V_SG over a range of drain current values. These are used to obtain, in the Mathcad project file, k_n1, k_n2, and the threshold voltages and thus, v_t∊. This will provide a comparison between the measured drain-current ratios and (8.10) as a function of V_eff and drain current.