Calculate the transistor output impedance - we will also

Question

Question 1:

The following sketch shows a representative I_c vs. V_CE curve for two 18 values. Note that in the linear region, the curves look like a current source in parallel with an output impedance. We will use r_o = (dI_C/dV_CE)^-1 to calculate the transistor output impedance. We will also calculate a different parameter called the Early voltage. That is the projected intercept point where the extension of the straight-line portion of the I_c vs. V_CE curve intellects the zero current axis with a straight-line extension to the horizontal axis at the Early voltage, expressed as a negative value.

The expression for the straight line curve is given as I_C = I_se^V_BE/V_T ( 1 + V_CE/V_A). If you know I_C and V_CE at two different points on a curve with V_BE fixed (or I_B fixed), you can calculate V_A.

Derive an expression for V_A, given measurements of I_C and V_CE at two points on a constant I_B (constant V_BE) curve. Express V_A in terms of the four measured values for I_C1, I_C2, V_CE1, V_CE2

Question 2:

Effects of pole-zero near-cancellations

(a) Sketch the step response of a system whose transfer function has no (finite) zeros, poles at s = -1 ± j1, and a DC gain of one.

(b) Suppose, in addition there are a zero and a pole close to each other and close to s = -3. The DC gain remains 1. What effect will this change make to the response?

(c) Repeat part (b) only now the pole-zero pair are near s = 3.