Lecture 11 Digital Circuits (I) THE INVERTER Outline • Introduction to digital circuits –The inverter • NMOS inverter with resistor pull-up Reading Assignment: Howe and Sodini; Chapter 5, Sections 5.1-5.3 6.012 Spring 2009 Lecture 11 1 1. Introduction to digital circuits: the inverter In digital circuits, digitally-encoded information is represented by means of two distinct voltage ranges: V VMAX logic 1 VOH VOL undefined � region logic 0 VMIN The Static Definition • Logic 0: VMIN V VOL • Logic 1: VOH V VMAX • Undefined logic value: VOL V VOH Logic operations are performed using logic gates. Simplest logic operation of all: inversion inverter 6.012 Spring 2009 Lecture 11 2 Ideal inverter OUT=IN IN IN OUT 0 1 1 0 Circuit representation and ideal transfer function: VOUT v+ V+ + + VIN VOUT - - VOUT=VIN V+ 2 0 0 + V�M= V 2 V+ VIN Define switching point or logic threshold : • VM input voltage for which VOUT = VIN – For 0 VIN < VM – For VM < VIN V+ VOUT = V+ VOUT = 0 Ideal inverter returns well defined logical outputs (0 or V+) even in the presence of considerable noise in VIN (from voltage spikes, crosstalk, etc.) signal is regenerated! 6.012 Spring 2009 Lecture 11 3 “Real” inverter VOUT logic 1 VMAX VOH slope=-1 transition � region logic 0 VOL VMIN 0 0 V+ VIN In a real inverter, valid logic levels defined as follows: • Logic 0: – VMIN output voltage for which VIN = V+ – VOL smallest output voltage where slope = -1 • Logic 1: – VOH largest output voltage where slope = -1 – VMAX output voltage for which VIN = 0 6.012 Spring 2009 Lecture 11 4 Two other important voltages: VOUT VMAX VOH logic 1 slope=-1 undefined � region logic 0 VOL VMIN 0 0 VIL VIH V+ VIN � s� 1 e es ic 0 c u i l u l g a va log t v lid lo t u u p valid inp e va n i f of uce e o duc e g g d an t pro ran t pro r tha tha Define: VIL smallest input voltage where slope = -1 VIH highest input voltage where slope = -1 If range of output values VOL to VOH is wider than the range of input values VIL to VIH, then the inverter exhibits some noise immunity. (|Voltage gain| > 1) Quantify this through noise margins. 6.012 Spring 2009 Lecture 11 5 Chain of two inverters: noise M N VOUT VOH VOL VIN NMH VIH VIL NML inverter M� output inverter N� input Define noise margins: NMH VOH - VIH NML VIL - VOL 6.012 Spring 2009 noise margin high noise margin low Lecture 11 6 Simplifications for hand calculations: Logic levels and noise margins It is hard to compute points in transfer function with slope = -1. Approximate in the following way: VOUT VOH=VMAX slope= Av VOUT=VIN VM VOL=VMIN 0 • • 0 VIL VM VIH V+ VIN Assume VOL VMIN and VOH VMAX Trace tangent of transfer function at VM – Slope = small signal voltage gain (Av) at VM • • VIL intersection of tangent with VOUT = VMAX VIH intersection of tangent with VOUT = VMIN 6.012 Spring 2009 Lecture 11 7 Transient Characteristics Inverter switching in the time domain: VIN VOH 90% 50% 10% 0 VOL tPHL VOUT t tF tR tPLH VOH 90% 50% 10% 0 tF VOL t tR tCYCLE rise time between 10% and 90% of total swing tR tF fall time between 90% and 10% of total swing tPHL propagation delay from high-to-low between 50% points tPLH propagation delay from low-to-high between 50% points Propagation delay: 6.012 Spring 2009 tP = 1 (t PHL + t PLH ) 2 Lecture 11 8 Simplifications for hand calculations: Propagation delay • • Consider input waveform is an ideal square wave Propagation delay times = delay times to 50% point VIN VOH tCYCLE VOL t VOUT tPHL tPLH VOH VOH 50% tCYCLE VOL t • SPICE essential for accurate delay analysis 6.012 Spring 2009 Lecture 11 9 2. NMOS inverter with “pull-up” resistor V+=VDD R IR ID VIN VOUT CL load capacitance (from following� stages) Essential features: • • VBS = 0 (typically not shown) CL summarizes capacitive loading of the following stages (other logic gates, interconnect lines, etc.) Basic Operation: • If VIN < VT, MOSFET is OFF – VOUT = VDD • If VIN > VT, MOSFET is ON – VOUT small – Value set by resistor / nMOS divider 6.012 Spring 2009 Lecture 11 10 VDD + R IR VR - VOUT ID VIN Transfer function obtained by solving: IR = ID Can solve graphically: I–V characteristics of load: 6.012 Spring 2009 Lecture 11 11 Overlap I–V characteristics of resistor pull-up on I–V characteristics of transistor: load line IR=ID VGS=VDD VDD R VGS=VIN VGS=VT 0 0 VDD VDS =VOUT Transfer function: VOUT=VDS VDD � 0 6.012 Spring 2009 0 VT VDD Lecture 11 VIN=VGS 12 Logic levels: VOUT=VDS VMAX=VDD � VOUT=VIN VM VMIN 0 0 VT VM VDD VIN=VGS For VMAX, transistor is cut-off, ID = 0: VMAX = VDD For VMIN, transistor is in linear regime; solve: W V V VMIN μn Cox VDD MIN VT VMIN = IR = DD L 2 R ID = For VM, transistor is in saturation; solve: ID = W V VM 2 μn Cox (VM VT ) = I R = DD 2L R 6.012 Spring 2009 Lecture 11 13 Noise Margins: VOUT=VDS VMAX=VDD � VOUT=VIN Av VMIN 0 0 VDD VT VIN=VGS Small signal equivalent circuit model at VM (transistor in saturation): R D G + + vin vgs - - + gmvgs - Av = 6.012 Spring 2009 vout - S + vin ro + gmvin (ro//R) vout - v out = g m(ro // R) g mR vin Lecture 11 14 What did we learn today? Summary of Key Concepts • Logic circuits must exhibit immunity to noise in the input signal – Noise margins • Logic circuits must be regenerative – Able to restore clean logic values even if input is noisy. • Propagation delay: time for logic gate to perform its function. • Concept of load line: graphical technique to visualize transfer characteristics of inverter. • First-order solution (by hand) of inverter figures-of merit easy if regions of operation of transistor are correctly identified. • For more accurate solutions, use SPICE (or other CAD tool). 6.012 Spring 2009 Lecture 11 15 MIT OpenCourseWare http://ocw.mit.edu 6.012 Microelectronic Devices and Circuits Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.