lec12

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logic 1
VMAX VOH
undefined region logic 0
VOL VMIN 0
0
VIL
VIH
V+
VIN
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6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 12-9
Simplifications for hand calculations Hard to compute Av = −1 points in transfer function. Approximate calculation:
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 12-8
Quantify signal regeneration through noise margins. Consider chain of two inverters:
V VMAX logic 1 VOH VOL VMIN undefined region logic 0
• 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
-for VM ≤ VIN ≤ V + ⇒ VOU T = 0
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 12-5
Key property of ideal inverter: signal regeneration
Lecture 12-6
2 ”Real” inverter:
VOUT V+ slope=-1
v+
logic 1
VMAX VOH |Av|>1
undefined region logic 0
VOL VMIN 0
+ VIN -
+ VOUT -
0
V+
VIN
In a real inverter, valid logic levels defined as follows: • logic 0: VMIN ≡ output voltage when VIN = V + VOL ≡ smallest output voltage where slope=-1 • logic 1: VOH ≡ largest output voltage where slope=-1 VMAX ≡ output voltage when VIN = 0
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 12-11
2 Transient characteristics Look at inverter switching in the time domain:
VIN 90% 50% 10% 0 tR tF VOL t VOH
• to enhance noise margin: |Av (VM )| ↑
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 12-10
VOUT VOH=VMAX slope= Av(VM) VOUT=VIN VM
VOL=VMIN 0
VOUT V+ V+ + VOUT 0 0 VM= V
2 + 2
v+
VOUT=VIN
+ VIN -
V+ VIN
Define switching point or logic threshold: VM ≡ input voltage for which VOU T = VIN -for 0 ≤ VIN ≤ VM ⇒ VOU T = V +
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 12-12
Propagation delay: simplification for hand calculations • Input wavefunction = ideal square wave • Propagation delay times = delay times to 50% point
v+ VOUT V+ V+ + VOUT 0 0 VM= V
2 + 2
VOUT=VIN
+ VIN -
V+ VIN
Ideal inverter returns well defined logical outputs (0 or V +) even in the presence of considerable noise in VIN (from voltage spikes, crosstalk, etc.)
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 12-2
Key questions • What are the key figures of merit of logic circuits? • How can one make a simple inverter using a single MOSFET?
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 12-1
Lecture 12 - Digital Circuits (I) The inverter October 20, 2005
Contents: 1. Introduction to digital electronics: the inverter 2. NMOS inverter with resistor pull up Reading assignment: Howe and Sodini, Ch. 5, §§5.1-5.3.2
VIL ≡ smallest input voltage where slope=-1 VIH ≡ highest input voltage where slope=-1 To have signal regeneration: range of input values that produce acceptable logic output > range of valid logic values Key to signal regeneration in inverter: high voltage gain
noise
M
VOUT VMAX VOH NMH
N
VIN VMAX VIH VIL VMIN
VOL VMIN
NML
inverter M output
inverter N input
Define noise margins: N MH = VOH − VIH N ML = VIL − VOL noise margin high noise margin low
IN
OUT
VOUT
tPHL
90%
tPLH VOH 50%
10% 0 tF tR tCYCLE
VOL t
tR ≡ rise time between 10% and 90% of total swing tF ≡ fall time between 90% and 10% of total swing tP HL ≡ propagation delay from high-to-low between 50% points tP LH ≡ propagation delay from low-to-high between 50% points Propagation delay: (t + tP LH ) tP = 1 2 P HL
0
VIL VM VIH
V+
VIN
|Av (VM )| |Av (VM )|
VMAX − VM ⇒ VIL VM − VIL
VM −
VMAX − VM |Av (VM )|
VM − VMIN ⇒ VIH VIH − VM
VM (1 +
VMIN 1 )− |Av (VM )| |Av (VM )|
Then:
When signal is within noise margins: • logic 1 output from first inverter interpreted as logic 1 input by second inverter • logic 0 output from first inverter interpreted as logic 0 input by second inverter
6.012 - Microelectronic Devices and Circuits - Fall 2005