Transient Response of First-Order Circuits: RL and RC Circuits, Slides of Microelectronic Circuits

Download Transient Response of First-Order Circuits: RL and RC Circuits and more Slides Microelectronic Circuits in PDF only on Docsity! 1 Lecture 15, Slide 1EECS40, Fall 2003 Prof. King Lecture #15 ANNOUNCEMENTS • Prof. King’s office hour today is cancelled • Farhana’s office hours this week are cancelled • HW#5 will be available on Friday 10/3 (due 10/10) • Pick up graded midterms in discussion sections OUTLINE – Transient response of 1st-order circuits – Application: modeling of digital logic gate Reading Chapter 7.3-7.5 (with Prof. Sanders) Lecture 15, Slide 2EECS40, Fall 2003 Prof. King Transient Response of 1st-Order Circuits • In Lectures 13 and 14, we saw that the currents and voltages in RL and RC circuits decay exponentially with time, with a characteristic time constant τ, when an applied current or voltage is suddenly removed. • In general, when an applied current or voltage suddenly changes, the voltages and currents in an RL or RC circuit will change exponentially with time, from their initial values to their final values, with the characteristic time constant τ: where x(t) is the circuit variable (voltage or current) xf is the final value of the circuit variable t0 is the time at which the change occurs [ ] τ/)(0 0 )()( +−−+ −+= ttff extxxtx 2 Lecture 15, Slide 3EECS40, Fall 2003 Prof. King Procedure for Finding Transient Response 1. Identify the variable of interest • For RL circuits, it is usually the inductor current iL(t) • For RC circuits, it is usually the capacitor voltage vc(t) 2. Determine the initial value (at t = t0+) of the variable • Recall that iL(t) and vc(t) are continuous variables: iL(t0+) = iL(t0−) and vc(t0+) = vc(t0−) • Assuming that the circuit reached steady state before t0 , use the fact that an inductor behaves like a short circuit in steady state or that a capacitor behaves like an open circuit in steady state Lecture 15, Slide 4EECS40, Fall 2003 Prof. King Procedure (cont’d) 3. Calculate the final value of the variable (its value as t ∞) • Again, make use of the fact that an inductor behaves like a short circuit in steady state (t ∞) or that a capacitor behaves like an open circuit in steady state (t ∞) 4. Calculate the time constant for the circuit τ = L/R for an RL circuit, where R is the Thévenin equivalent resistance “seen” by the inductor τ = RC for an RC circuit where R is the Thévenin equivalent resistance “seen” by the capacitor 5 Lecture 15, Slide 9EECS40, Fall 2003 Prof. King When we perform a sequence of computations using a digital circuit, we switch the input voltages between logic 0 (e.g. 0 Volts) and logic 1 (e.g. 5 Volts). The output of the digital circuit changes between logic 0 and logic 1 as computations are performed. Application to Digital Integrated Circuits (ICs) Lecture 15, Slide 10EECS40, Fall 2003 Prof. King • Every node in a real circuit has capacitance; it’s the charging of these capacitances that limits circuit performance (speed) We compute with pulses. We send beautiful pulses in: But we receive lousy-looking pulses at the output: Capacitor charging effects are responsible! time vo lta ge time vo lta ge Digital Signals 6 Lecture 15, Slide 11EECS40, Fall 2003 Prof. King Circuit Model for a Logic Gate • Recall (from Lecture 1) that electronic building blocks referred to as “logic gates” are used to implement logical functions (NAND, NOR, NOT) in digital ICs – Any logical function can be implemented using these gates. • A logic gate can be modeled as a simple RC circuit: + Vout – R Vin(t) +− C switches between “low” (logic 0) and “high” (logic 1) voltage states Lecture 15, Slide 12EECS40, Fall 2003 Prof. King Transition from “0” to “1” (capacitor charging) time Vout 0 Vhigh RC 0.63Vhigh Vout Vhigh time RC 0.37Vhigh Transition from “1” to “0” (capacitor discharging) (Vhigh is the logic 1 voltage level) Logic Level Transitions ( )RCthighout eVtV /1)( −−= RCthighout eVtV /)( −= 0 7 Lecture 15, Slide 13EECS40, Fall 2003 Prof. King What if we step up the input, wait for the output to respond, then bring the input back down? time Vi n 0 0 time Vi n 0 0 Vout time Vi n 0 0 Vout Sequential Switching Lecture 15, Slide 14EECS40, Fall 2003 Prof. King The input voltage pulse width must be long enough; otherwise the output pulse is distorted. (We need to wait for the output to reach a recognizable logic level, before changing the input again.) 0 1 2 3 4 5 6 0 1 2 3 4 5 Time Vo ut Pulse width = 0.1RC 0 1 2 3 4 5 6 0 1 2 3 4 5 Time Vo ut 0 1 2 3 4 5 6 0 5 10 15 20 25 Time Vo ut Pulse Distortion + Vout – R Vin(t) C + – Pulse width = 10RCPulse width = RC