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Transient PSpice Analysis (7.4) Dr. Holbert April 26, 2006 ECE201 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? ECE201 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? ECE201 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). ECE201 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. ECE201 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 ECE201 Lect-23 6 Computer RAM-1 Bit 3.3V Precharge Data Q1 Q2 Sense Amp C + Vout – ECE201 Lect-23 7 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. ECE201 Lect-23 8 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. ECE201 Lect-23 9 RAM Discharge Equivalent Circuit + 1MW 1000pF v(t) – The 1MW 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. ECE201 Lect-23 10 What is the time constant for this circuit? ECE201 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 3V. • What is the initial voltage? • What is the DC steady state (final) voltage? • What does the capacitor voltage v(t) look like? ECE201 Lect-23 12 Capacitor Voltage v(t) = 3Ve-t/RC 3 v(t) 2.5 2 1.5 1 0.5 0 0 0.001 0.002 0.003 0.004 0.005 t ECE201 Lect-23 13 Refresh Rate Suppose we must refresh before v(t) drops below 1.5V. How long can we wait before a refresh? 3 v(t) 2.5 2 t = 0.693ms 1.5 1 0.5 0 0 0.001 0.002 0.003 0.004 0.005 t ECE201 Lect-23 14 RAM Precharge • 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. ECE201 Lect-23 15 RAM Precharge Equivalent Circuit 10W 3.3V + – + v(t) 1000pF – The 10 W resistor models the “on” resistance of Q1. ECE201 Lect-23 16 What is the time constant for this circuit? ECE201 Lect-23 17 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? ECE201 Lect-23 18 Capacitor Voltage v(t) v(t) = 3.3V(1-e-t/RC) 3.5 3 2.5 2 1.5 1 0.5 0 0 1E-08 2E-08 3E-08 4E-08 5E-08 t ECE201 Lect-23 19 Precharge Time v(t) Suppose we must precharge the capacitor to 3V. How long does this take? 3.5 3 2.5 2 1.5 1 0.5 0 t = 24.0ns 0 1E-08 2E-08 3E-08 4E-08 5E-08 t ECE201 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) 50W resistor voltage, (2) capacitor voltage, and (3) clockwise inductor current • Find peak heart voltage and current • Determine charging time constant () ECE201 Lect-23 21 Heart Defibrillator Circuit t=5ms t=5ms 50 mH 20 W 30 µF + – 6000 V 50 W ECE201 Lect-23 22