Intuitive Analog Circuit Design

Next, we ll see how to use the charge control model by working through a number of examples.
In this problem, a transistor is controlled by driving a base current as in Figure 10-10. Let s analyze the dynamics of the transistor, assuming transistor parameters: ? F = 0.3 nanoseconds, ? F = 416, ? R = 240 nanoseconds, and ? R = 0.7. We ll ignore space charge capacitances. We ll find the switching profile of this transistor circuit under these conditions. Assume that the current pulse transitions high at t = 0. Much later, after all transients have died down, the current pulse transitions back to zero.
Crossing the forward-active region
Ignoring space charge capacitances, we ll find base charge q F (t) and collector current i c (t) when crossing through the forward-active region. Since we re ignoring space charge capacitances, the necessary charge control equation is relatively simple. First, recognize that when we first step the base current, the transistor will enter the forward active region. There s no turn-on delay time in this example since we have assumed that junction capacitances are negligible. After a while, the transistor will saturate, since
When the transistor is in the forward-active region, the charge control equations are:
Since we are driving the base with a stepped current source, the differential equation for the base current is:
where