Next, we find relationships involving parameter and the times t1 and t2. We make use k of the fact that voltages less than 1.5 Volts are declared as LOW, while those over 3.5 Volts are declared as HIGH. Next, we subtract the term on the left from that on the right. We then develop an expression for parameter k. We are now ready to make use of the published rise time for TTL logic (50 ns) and solve for parameter k. Thus we can model the output voltage of a TTL digital logic circuit using the logistic function along with a judicious selection of parameters as below (L=5 and A=100). Extension of the Model Once a model for the output voltage undergoing a transition from the LOW to the HIGH state is obtained, it is very simple to extend it to the case when the output voltage drops from the HIGH state to the LOW state. Due to the equality of the rise and fall times associated with this class of digital circuits, a fall in voltage can be modeled by subtracting the logistic function from unity. Using the values for the parameters found earlier, a falling voltage can be written as .
Next, we find relationships involving parameter k and the times t1 and t2. We make use of the fact that voltages less than 1.5 Volts are declared as LOW, while those over 3.5 Volts are declared as HIGH. Next, we subtract the term on the left from that on the right. We then develop an expression for parameter k. We are now ready to make use of the published rise time for TTL logic (50 ns) and solve for parameter k. Thus we can model the output voltage of a TTL digital logic circuit using the logistic function along with a judicious selection of parameters as below (L=5 and A=100). Extension of the Model Once a model for the output voltage undergoing a transition from the LOW to the HIGH state is obtained, it is very simple to extend it to the case when the output voltage drops from the HIGH state to the LOW state. Due to the equality of the rise and fall times associated with this class of digital circuits, a fall in voltage can be modeled by subtracting the logistic function from unity. Using the values for the parameters found earlier, a falling voltage can be written as .