Transient PSpice Analysis 7 4 Dr Holbert April

Transient PSpice Analysis (7. 4) Dr. Holbert April 26, 2006 ECE 201 Lect-23 1

Typical Transient 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? ECE 201 Lect-23 2

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? ECE 201 Lect-23 3

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 (EEE 302). ECE 201 Lect-23 4

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. ECE 201 Lect-23 5

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 ECE 201 Lect-23 6

Computer RAM-1 Bit 3. 3 V Precharge Data Q 1 Q 2 Sense Amp C + Vout – ECE 201 Lect-23 7

How the RAM Works • When the Precharge line is high (> 3 V) and the Data line is low (~0 V), transistor Q 1 is on and the capacitor charges up to 3 V. • If the Data line goes high after the capacitor is charged, then Q 2 turns on and the capacitor discharges. ECE 201 Lect-23 8

RAM Discharge • With Q 1 and Q 2 off, the capacitor holds a charge that represents the stored data bit. • This charge leaks through Q 2, 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. ECE 201 Lect-23 9

RAM Discharge Equivalent Circuit + 1 M 1000 p. F v(t) – The 1 M resistor models the parallel combination of the off resistance of Q 2, the input resistance of the sense amplifier, and the leakage resistance of the capacitor. ECE 201 Lect-23 10

What is the time constant for this circuit? ECE 201 Lect-23 11

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 3 V. • What is the initial voltage? • What is the DC steady state (final) voltage? • What does the capacitor voltage v(t) look like? ECE 201 Lect-23 12

Capacitor Voltage v(t) = 3 Ve-t/RC ECE 201 Lect-23 13

Refresh Rate Suppose we must refresh before v(t) drops below 1. 5 V. How long can we wait before a refresh? t = 0. 693 ms ECE 201 Lect-23 14

RAM Precharge • With Q 2 off, Q 1 is turned on to charge the capacitor. • The current to charge the capacitor comes through Q 1. • To determine the time necessary to precharge the capacitor, we use a simple equivalent circuit. ECE 201 Lect-23 15

RAM Precharge Equivalent Circuit 10 3. 3 V + – + v(t) 1000 p. F – The 10 resistor models the “on” resistance of Q 1. ECE 201 Lect-23 16

What is the time constant for this circuit? ECE 201 Lect-23 17

The RAM Precharge Time • The RAM precharge time is the time required for the capacitor to charge to a voltage of 3 V from an initial voltage of 0 V. • What is the initial voltage? • What is the DC steady state (final) voltage? • What does the capacitor voltage v(t) look like? ECE 201 Lect-23 18

Capacitor Voltage v(t) = 3. 3 V(1 -e-t/RC) ECE 201 Lect-23 19

Precharge Time Suppose we must precharge the capacitor to 3 V. How long does this take? t = 24. 0 ns ECE 201 Lect-23 20

PSpice Defibrillator Example • • • Start PSpice and enter circuit diagram Set capacitor and inductor initial conditions Setup Transient analysis, 0. 01 ms step to 15 ms end Run simulation; Probe starts automatically Plot: (1) 50 resistor voltage, (2) capacitor voltage, and (3) clockwise inductor current • Find peak heart voltage and current • Determine charging time constant ( ) ECE 201 Lect-23 21

Heart Defibrillator Circuit t=5 ms 50 m. H 20 30 µF + – 6000 V 50 ECE 201 Lect-23 22