I. Digital Integrated Circuits - Logic Concepts

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1 I. Digital Integrated Circuits - Logic Concepts. Logic Fundamentals: binary mathematics: only operate on and (oolean algebra) simplest function -- inversion = symbol for the inverter INPUT OUTPUT EECS 6.2 Spring 998 Lecture

2 . Other Logic Functions ND and NND = not ND OR and NOR = not OR XOR ND NND INPUT OUTPUT ND NND OR NOR (a) INPUT OUTPUT OR NOR (b) INPUT OUTPUT XOR (c) One gate can have many inputs C = C XZ Practical limitations... set by need to maintain both adequate switching speed and valid logic levels fan-in -- maximum number logic gates connected to the input fan-out -- maximum number of logic gates connected to the output EECS 6.2 Spring 998 Lecture

3 C. n Ideal Inverter Let the logical variable be represented by a voltage. Let the correspond to a high voltage (say, 5 V) and the correspond to the low voltage (say, V). Voltage transfer curve for an inverter yields V when a high voltage is input and the high voltage,, when a low voltage is input. > = / 2 --> = < = / 2 --> = The ideal inverter returns correct logical outputs ( V or ) even when the input voltage is corrupted by noise, voltage spikes, etc. which are nearly half the supply voltage! + + = /2 V M = 2 (a) (b) EECS 6.2 Spring 998 Lecture

4 D. Real Inverters Inverters which we can build are approximations to the ideal inverter. typical inverter characteristic is: X = IN V IL V IH On the output and input axes, several voltages are defined: = input voltage for which = = voltage output low = max. output voltage for a valid = voltage output high = min. output voltage for a valid V IL = voltage input low = smaller input voltage where slope equals - V IH = voltage input high = larger input voltage where slope equals - X = for = V; usually, X =, the supply voltage IN = for = and is the minimum output voltage EECS 6.2 Spring 998 Lecture

5 E. Inverter Transfer Function - Hand Calculations Problem: evaluating where slope = - is an algebraic mess. dopt more convenient definitions of, V IL,V IH (new in H&S) = X Slope v = IN V IL V IH Use small-signal model to evaluate tangent to transfer curve = IN and = X = Input voltage at which = V IL = intersection of tangent to ( ) curve at and the line = X (=, typically) V IH = intersetion of tangent to ( ) curve at and the line = IN (= V, typically) If <V IL, then is considered a valid If >V IH, then is considered a valid EECS 6.2 Spring 998 Lecture

6 F. Noise Margins Cascade of two logic inverters-- output of # is input to #2 Output of inverter # is at least, Margin of - V IH2 to spare before the input to inverter #2 has an invalid high input. NM H = - V IH = noise margin (high) NM L = V IL - = noise margin (low) v NOISE 2 2 V IH NM H V IH2 Voltage V IL NM L V IL2 2 NM H = V IH NM L = V IL EECS 6.2 Spring 998 Lecture

7 G. Propagation Delay Time is required for an inverter to change states from to and vice versa Charging and discharging MOSFET and parasitic capacitance 9% 5% % t t R t F t PHL t PLH 9% 5% % t t t F R t CCLE Definitions:t R = risetime; t F = falltime -- both % to 9% of total swing t PHL = delay between 5% points on the input and output waveforms during the high-to-low transition t PLH = delay between 5% points on the input and output waveforms during the low-to-high transition EECS 6.2 Spring 998 Lecture

8 H. Propagation Delay - Hand Calculations For hand calculations, make the input waveform ideal Find delay in the output waveform before it reaches the 5% point. t CCLE t t PHL t PLH VOH 5% t CCLE t Transient analysis can only be roughly approximated in hand calculations SPICE is essential for accurate analysis. EECS 6.2 Spring 998 Lecture

9 II. Inverter Circuits: NMOS-Resistor Load. MOSFET is an excellent switch: open-circuit at control terminal (gate) drain-source connection is open for V GS < V Tn (cutoff region) drain-source connection is a resistor for V GS >V Tn (triode region). Qualitative Circuit Operation V DD R + C L _ = V DD = 5 V (typically) C L = load capacitance (from interconnections and from other inverters connected to the output V S = V -- bulk-to-source short circuit is typically not shown < V Tn MOSFET-OFF --- = V DD >> V Tn MOSFET - ON --- is small ( value is set by resistive divider) EECS 6.2 Spring 998 Lecture

10 C. Quantitative Calculation of Transfer Characteristic Key concept: the static output current is zero MOSFET drain current = I D = I R = current through resistor = = = V V DD OUT I I D R R V DD R -- V R OUT Plotting these equations on the drain characteristics of the MOSFET since V DS = : I D V DD R V DD The transfer characteristic can be found by plotting the intersections between the I D (, ) characteristics with the load line I R ( ) EECS 6.2 Spring 998 Lecture

11 D. Transfer Characteristic IN V IL V IH E. Small Signal Model Use small signal model to calculate the gain v out /v in at Gain is the slope of the inverter transfer characteristic at Gain =v out /v in = -g m (r o R) -g m R EECS 6.2 Spring 998 Lecture