1. Lecture 151 1st Order Circuit Examples

2. Lecture 152 Typical Problems What is the voltage as a capacitor discharges to zero? What is the voltage as a capacitor charges from one voltage (often zero) to another constant voltage? How does the current through an inductor increase from zero to a final value? How does the current through an inductor decrease from an initial value to zero?

3. Lecture 153 More Typical Problems What are the transient and AC steady state responses of an RC circuit to a sinusoidal source? What are the transient and AC steady state responses of an RL circuit to a sinusoidal source?

4. Lecture 154 Solutions Changes in capacitor voltages and inductor currents from one value to another are easily solved. Changes in other voltages or currents in the circuit may or may not be easy to solve directly; they are all easy to solve using LaPlace transforms.

5. Lecture 155 More Solutions Steady state responses to sinusoidal sources are easy to find using AC steady state analysis. Transient responses to sinusoidal sources are hard to find directly; they are easier to find using LaPlace transforms.

6. Lecture 156 Example Problems: Changes from one value to another Computer RAM –Refresh time –Write time Stator coil on a motor –Response to a step in current

7. Lecture 157 Computer RAM-1 Bit Q1 Q2 C Precharge Data 3.3V Sense Amp + - V out

8. Lecture 158 How the RAM Works When the Precharge line is high (> 3V) and the Data line is low (~0V), transistor Q1 is on and the capacitor charges up to 3V. If the Data line goes high after the capacitor is charged, then Q2 turns on and the capacitor discharges.

9. Lecture 159 RAM Discharge With Q1 and Q2 off, the capacitor holds a charge that represents the stored data bit. This charge leaks through Q2, the input of the sense amplifier, and the capacitor. To determine the time before a refresh is necessary, we can use a simple equivalent circuit.

10. Lecture 1510 RAM Discharge Equivalent Circuit 1M  100pF + - v(t) The 1M  resistor models the parallel combination of the off resistance of Q2, the input resistance of the sense amplifier, and the leakage resistance of the capacitor.

11. Lecture 1511 What is the time constant for this circuit?

12. Lecture 1512 The RAM Discharge Time The RAM discharge time is the time required for the capacitor to discharge to a given voltage from an initial voltage of 3V. What is the initial voltage? What is the DC steady state (final) voltage? What does the capacitor voltage v(t) look like?

13. Lecture 1513 Capacitor Voltage v(t) = 3Ve -t/RC

14. Lecture 1514 Refresh Rate Suppose we must refresh before v(t) drops below 1.5V. How long can we wait before a refresh? t = 0.693ms

15. Lecture 1515 RAM Pre-charge With Q2 off, Q1 is turned on to charge the capacitor. The current to charge the capacitor comes through Q1. To determine the time necessary to precharge the capacitor, we use a simple equivalent circuit.

16. Lecture 1516 RAM Precharge Equivalent Circuit The 100  resistor models the “on” resistance of Q1. 100  100pF + - 3.3V + - v(t)

17. Lecture 1517 What is the time constant for this circuit?

18. Lecture 1518 The RAM Precharge Time The RAM precharge time is the time required for the capacitor to charge to a voltage of 3V from an initial voltage of 0V. What is the initial voltage? What is the DC steady state (final) voltage? What does the capacitor voltage v(t) look like?

19. Lecture 1519 Capacitor Voltage v(t) = 3.3V(1-e -t/RC )

20. Lecture 1520 Precharge Time Suppose we must precharge the capacitor to 3V. How long does this take? t = 24.0ns