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Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-1 
LECTURE 320 – IMPROVED OPEN-LOOP COMPARATORS 
AND LATCHES 
LECTURE ORGANIZATION 
Outline 
• Autozeroing 
• Hysteresis 
• Simple Latches 
• Summary 
CMOS Analog Circuit Design, 2nd Edition Reference 
Pages 464-483 
CMOS Analog Circuit Design © P.E. Allen - 2010 
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-2 
AUTOZEROING 
Principle of Autozeroing 
Use the comparator as an op amp to sample the dc input offset voltage and cancel the 
offset during operation. 
Comparator 
+ - 
- 
Ideal 
Comparator 
+ - 
Ideal 
VOS VOS 
vIN vOUT 
CAZ VOS 
+ 
VOS 
+ 
- 
Comparator 
+ - 
VOS 
Ideal 
CAZ 
Model of Comparator. Autozero Cycle Comparison Cycle 
Fig. 8.4-1 
Comments: 
• The comparator must be stable in the unity-gain mode (self-compensating comparators 
are ideal, the two-stage comparator would require compensation to be switched in 
during the autozero cycle.) 
• Complete offset cancellation is limited by charge injection 
CMOS Analog Circuit Design © P.E. Allen - 2010
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-3 
Differential Implementation of Autozeroed Comparators 
+ 
- 
VOS 
Ideal 
φ1 
Comparator 
φ2 + - 
+ - 
VOS 
CAZ 
vIN-vOUT 
φ1 
φ1 
VOS 
vOUT = VOS 
Comparator during φ1 phase 
+ - + - 
VOS 
VOS 
vOUT 
φ2 
vIN-Lecture 
vIN+ 
Differential Autozeroed Comparator Comparator during φ2 phase 
Fig. 8.4-2 
vIN+ 
CMOS Analog Circuit Design © P.E. Allen - 2010 
320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-4 
Single-Ended Autozeroed Comparators 
Noninverting: 
vOUT vIN 
+ - 
φ2 
φ2 
φ1 CAZ 
φ1 
φ1 
Fig. 8.4-3 
Inverting: 
vIN vOUT 
+ - 
φ2 
CAZ 
φ1 
φ1 
Fig. 8.4-4 
Comment on autozeroing: 
Need to be careful about noise that gets sampled onto the autozeroing capacitor and 
is present on the comparison phase of the process. 
CMOS Analog Circuit Design © P.E. Allen - 2010
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-5 
HYSTERESIS 
Influence of Input Noise on the Comparator 
Comparator without hysteresis: 
vin 
vout 
Comparator 
threshold 
VOH 
VOL 
t 
t 
Fig. 8.4-6A 
Comparator with hysteresis: 
vin 
vout 
VTRP+ 
VTRP-Fig. 
VOH 
VOL 
t 
t 
8.4-6B 
CMOS Analog Circuit Design © P.E. Allen - 2010 
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-6 
Use of Hysteresis for Comparators in a Noisy Environment 
Transfer curve of a comparator with hysteresis: 
vOUT 
VTRP+ 
vIN 
VTRP-VOH 
VOL 
(VOH-VOL) VTRP+ 
vIN 
Fig. 8.4-5 
vOUT 
VOH 
VOL 
0 
0 
R1 
R2 
VTRP-Counterclockwise 
Bistable Clockwise Bistable 
Hysteresis is achieved by the use of positive feedback 
• Externally 
• Internally 
CMOS Analog Circuit Design © P.E. Allen - 2010
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-7 
Noninverting Comparator using External Positive Feedback 
Circuit: 
Upper Trip Point: 
Assume that vOUT = 
R2 
+- 
vIN R1 
Fig. 8.4-7 
VOL, the upper trip point occurs when, 
0 =  
 
R1 
R1+R2 
VOL +  
 
R2 
R1+R2 
VTRP 
vOUT 
R1VOH 
R2 
- 
+  VTRP 
R1 
R2 
+ = - 
vOUT 
(VOH-VOL) - 
0 
R1 
R2 
VOH 
VOL 
0 
VOL 
Lower Trip Point: 
Assume that vOUT = VOH, the lower trip point occurs when, 
0 =  
 
R1 
R1+R2 
VOH +  
 
R2 
R1+R2 
VTRP 
-  VTRP 
- = - 
R1 
R2 
VOH 
Width of the bistable characteristic: 
Vin = VTRP+-VTRP- =  
R1 
R2 
 
 
VOH-VOL 
 
R1VOL 
R2 
vIN 
CMOS Analog Circuit Design © P.E. Allen - 2010 
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-8 
Inverting Comparator using External Positive Feedback 
Circuit: 
+ - 
vOUT 
vIN 
R1 
R2 
vOUT 
vIN 
VOH 
(VOH-VOL) 
0 
0 
R1 
R1+R2 
R1VOL R1VOH 
R1+R2 R1+R2 
VOL 
Fig. 8.4-8 
Upper Trip Point: 
vIN = VTRP 
+ =  
 
R1 
R1+R2 
VOH 
Lower Trip Point: 
vIN = VTRP 
- =  
 
R1 
R1+R2 
VOL 
Width of the bistable characteristic: 
Vin = VTRP+-VTRP- =  
 
R1 
R1+R2 
 
VOH-VOL 
 
CMOS Analog Circuit Design © P.E. Allen - 2010
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-9 
Horizontal Shifting of the CCW Bistable Characteristic 
Circuit: 
Upper Trip Point: 
VREF =  
 
R1 
R1+R2 
vIN R1 
VREF 
Fig. 8.4-9 
VOL +  
 
R2 
R1+R2 
R2 
+- 
VTRP 
vOUT 
VOH 
VOL 
vOUT 
0 
0 
+  VTRP 
R1 
R2 
(VOH-VOL) 
R1+R2 
R2 
VREF 
R1VOH 
R2 
+ =  
R1|VOL| 
R2 
 
R1+R2 
R2 
VREF - 
vIN 
R1 
R2 
VOL 
Lower Trip Point: 
VREF =  
 
R1 
R1+R2 
VOH +  
 
R2 
R1+R2 
VTRP 
-  VTRP 
- =  
 
R1+R2 
R2 
VREF - 
R1 
R2 
VOH 
Shifting Factor: 
± 
R2 
R1+R2 
 
VREF 
CMOS Analog Circuit Design © P.E. Allen - 2010 
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-10 
Horizontal Shifting of the CW Bistable Characteristic 
Circuit: 
+ - 
vOUT 
vIN 
R1 R2 
vIN 
R1 (VOH-VOL) 
Fig. 8.4-10 
VREF 
vOUT 
VOH 
0 
VOL 
R1+R2 
R2 VREF 
R1+R2 
R1|VOL| 
0 
R1VOH 
R1+R2 
R1+R2 
Upper Trip Point: 
vIN = VTRP 
+ =  
 
R1 
R1+R2 
VOH +  
 
R2 
R1+R2 
VREF 
Lower Trip Point: 
vIN = VTRP 
- =  
 
R1 
R1+R2 
VOL +  
 
R2 
R1+R2 
VREF 
Shifting Factor: 
± 
R2 
R1+R2 
 
VREF 
CMOS Analog Circuit Design © P.E. Allen - 2010
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-11 
Example 320-1 Design of an Inverting Comparator with Hysteresis 
Use the inverting bistable to design a high-gain, open-loop comparator having an 
upper trip point of 1V and a lower trip point of 0V if VOH = 2V and VOL = -2V. 
Solution 
Putting the values of this example into the above relationships gives 
1 =  
R1 
R1+R2 
 
2 +  
R2 
R1+R2 
 
VREF 
and 
0 =  
R1 
R1+R2 
 
(-2) +  
R2 
R1+R2 
 
VREF 
Solving these two equations gives 3R1 = R2 and VREF = (2/3)V. 
CMOS Analog Circuit Design © P.E. Allen - 2010 
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-12 
Hysteresis using Internal Positive Feedback 
Simple comparator with internal positive feedback: 
VDD 
M3 M6 M7 M4 
vo1 vo2 
vi1 M1 M2 vi2 
M8 M5 
VSS 
IBias 
Fig. 8.4-11 
CMOS Analog Circuit Design © P.E. Allen - 2010
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-13 
Internal Positive Feedback - Upper Trip Point 
Assume that the gate of M1 is on ground and the 
input to M2 is much smaller than zero. The 
resulting circuit is: 
M1 on, M2 off  M3 on, M6 on (active), M4 and 
M7 off. 
 vo2 is high. 
M6 wants to source the current i6 = 
W6/L6 
W3/L3 
i1 
As vin begins to increase towards the trip point, the 
current flow through M2 increases. When i2 = i6, 
the upper trip point will occur. 
 i5 = i1+i2 = i3+i6 = i3+
W6/L6 
W3/L3 
i3 = i3 

 
 
W6/L6 
W3/L3 
1+ 
VDD 
M3 M6 M7 M4 
vo1 vo2 
M1 M2 
i1 = i3 
 i1 = i3 = 
i2 = i6 
i5 
M5 
VSS 
vin 
Fig. 8.4-12A 
I5 
1+[(W6/L6)/(W3/L3)] 
Also, i2 = i5 - i1 = i5 - i3 
Knowing i1 and i2 allows the calculation of vGS1 and vGS2 which gives 
VTRP+ = vGS2 - vGS1 = 
2i2 
2 
+ VT2 - 
2i1 
1 
- VT1 
CMOS Analog Circuit Design © P.E. Allen - 2010 
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-14 
Internal Positive Feedback - Lower Trip Point 
Assume that the gate of M1 is on ground and the input 
to M2 is much greater than zero. The resulting circuit 
is: 
M2 on, M1 off  M4 and M7 on, M3 and M6 off. 
 vo1 is high. 
M7 wants to source the current i7 = 
W7/L7 
W4/L4 
i2 
As vin begins to decrease towards the trip point, the 
current flow through M1 increases. When i1 = i7, the 
lower trip point will occur. 
 i5 = i1+i2 = i7+i4 =
W7/L7 
W4/L4 
i4 +i4 = i4 

 
 
W7/L7 
W4/L4 
1+ 
VDD 
M3 M6 M7 M4 
vo1 vo2 
vi1 
M1 M2 
 i2 = i4 = 
i1 = i7 
M5 
I5 
i2 = i4 
vi1 
V Fig. 8.4-12B SS 
i5 
vi 
1+[(W7/L7)/(W4/L4)] 
Also, i1 = i5 - i2 = i5 - i4 
Knowing i1 and i2 allows the calculation of vGS1 and vGS2 which gives 
VTRP- = vGS2 - vGS1 = 
2i2 
2 + VT2 - 
2i1 
1 - VT1 
CMOS Analog Circuit Design © P.E. Allen - 2010
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-15 
Example 320-2 - Calculation of Trip Voltages for a Comparator with Hysteresis 
Consider the circuit shown. If KN’ = 110μA/V2, 
KP’ = 50μA/V2, and VTN = |VTP| = 0.7V, 
calculate the positive and negative threshold 
points if the device lengths are all 1 μm and the 
widths are given as: W1 = W2 = W6 = W7 = 10 μm 
and W3 = W4 = 2 μm. The gate of M1 is tied to 
ground and the input is the gate of M2. The 
current, i5 = 20 μA 
Solution 
To calculate the positive trip point, assume 
that the input has been negative and is heading 
positive. 
i6 = 
(W/L)6 
(W/L)3 i3 = (5/1)(i3)  i3 = 
i5 
IBias 
VDD 
M3 M6 M7 M4 
vo1 vo2 
vi1 M1 M2 vi2 
M8 M5 
1+[(W/L)6/(W/L)3] = i1 = 
VSS 
Fig. 8.4-11 
20μA 
1+5 = 3.33 μA 
i2 = i5  i1 = 20  3.33 = 16.67 μA  vGS1 = 

 
	 
2i1 
1 
1/2 
+VT1 = 

 
2·3.33 
(5)110 
	 
1/2 
+0.7 = 0.81V 
vGS2 = 

 
	 
2i2 
2 
1/2 
+ VT2 = 

 
	 
2·16.67 
(5)110 
1/2 
+ 0.7 = 0.946V 
 VTRP+  vGS2vGS1 = 0.9460.810 = 0.136V 
CMOS Analog Circuit Design © P.E. Allen - 2010 
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-16 
Example 320-2 - Continued 
Determining the negative trip point, similar analysis yields 
i4 = 3.33 μA 
i1 = 16.67 μA 
vGS2 = 0.81V 
vGS1 = 0.946V 
VTRP-  vGS2  vGS1 = 0.81  0.946 = 0.136V 
PSPICE simulation results of this circuit are shown below. 
2.6 
2.4 
2.2 
2 
1.8 
1.6 
1.4 
1.2 
1 
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 
vo2 
(volts) 
vin (volts) Fig. 8.4-13 
CMOS Analog Circuit Design © P.E. Allen - 2010
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-17 
Complete Comparator with Internal Hysteresis 
VDD 
M3 M6 M7 M4 
M9 M8 
vi1 vi2 
M1 M2 
M10 M11 
M8 M5 
VSS 
IBias 
vout 
Fig. 8.4-14 
CMOS Analog Circuit Design © P.E. Allen - 2010 
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-18 
Schmitt Trigger 
The Schmitt trigger is a circuit that has better defined switching points. 
Consider the following circuit: 
How does this circuit work? 
Assume the input voltage, vin, is low and the output 
voltage, vout , is high. 
M3, M4 and M5 are on and M1, M2 and M6 are off. 
When vin is increased from zero, M2 starts to turn on causing 
M3 to start turning off. Positive feedback causes M2 to turn 
on further and eventually both M1 and M2 are on and the 
output is at zero. 
The upper switching point, VTRP+ is found as follows: 
When vin is low, the voltage at the source of M2 (M3) is 
vS2 = VDD-VTN3 
VTRP+ = vin when M2 turns on given as VTRP+ = VTN2 + vS2 
vin 
VDD 
M3 
M5 
M4 
M2 
M1 
M6 
vout 
Fig. 8.4-15 
VTRP+ occurs when the input voltage causes the currents in M3 and M1 to be equal. 
CMOS Analog Circuit Design © P.E. Allen - 2010
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-19 
Schmitt Trigger – Continued 
Thus, iD1 = 1( VTRP+ - VTN1)2 = 3( VDD - vS2- VTN3) 2 = iD3 
which can be written as, assuming that VTN2 = VTN3, 
1( VTRP+ - VTN1) 2 = 3( VDD – VTRP+)2  VTRP+ = 
VTN1+ 3/1VDD 
1+ 3/1 
The switching point, VTRP- is found in a similar manner and is: 
5( VDD - VTRP- - VTP5)2 = 6( VTRP-)2  VTRP- = 
5/6(VDD-VTP5) 
1+ 5/6 
The bistable characteristic is, 
vin 
vout 
VDD 
VDD 
0 0 VTRP- VTRP+ 
Fig. 8.4-16 
CMOS Analog Circuit Design © P.E. Allen - 2010 
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-20 
SIMPLE LATCHES 
Regenerative Comparators 
Regenerative comparators use positive feedback to accomplish the comparison of two 
signals. Latches can have a faster switching speed than the previous comparators. 
NMOS and PMOS latch: 
VDD 
I1 I2 
vo1 vo2 
M1 M2 
VDD 
M1 M2 
vo1 vo2 
I1 I2 
Fig. 8.5-3 
NMOS latch PMOS latch 
CMOS Analog Circuit Design © P.E. Allen - 2010
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-21 
Operating Modes of the Latch 
The latch has two modes of operation – enable or latch and Enable (enable_bar) or Latch 
(latch_bar). 
1.) During the Enable_bar, the latch is turned off (currents are removed) and the 
unknown inputs are applied to it. The parasitic capacitance at the latch nodes hold the 
unknown voltage. 
2.) During Enable, the latch is turned on, and the positive feedback acts on the applied 
inputs and causes one side of the latch to go high and the other side to go low. 
Enable_bar: 
Enable Enable 
Vo2ʼ 
060808-09 
VDD 
I1 I2 
Enable Enable 
M1 M2 
Vo1ʼ 
VDD 
M1 M2 
I1 I2 
Vo2ʼ Vo1ʼ 
NMOS latch PMOS latch 
The inputs are initially applied to the outputs of the latch. 
Vo1’ = initial input applied to vo1 
CMOS Analog Circuit Design © P.E. Allen - 2010 
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-22 
Step Response of a Latch (Enable) 
Circuit: 
Ri and Ci are the 
resistance and capacitance 
seen to ground from the 
i-th transistor. 
Nodal equations: 
gm1Vo2+G1Vo1+sC1 
VDD VDD 
I1 I2 
vo2 
M1 M2 
vo1 
+ 
+ 
Vo2 Vo1 
gm1Vo2 R1 
C1 
Vo1' 
s 
- 
- 
gm2Vo1 R2 
Vo1’ 
s = gm1Vo2+G1Vo1+sC1V o1-C1Vo1’ = 0 
 
Vo1- 
gm2Vo1+G2Vo2+sC2 
Vo2’ 
s = gm2Vo1+G2Vo2+sC2V o2-C2Vo2’ = 0 
 
Vo2- 
Solving for Vo1 and Vo2 gives, 
Vo1 = 
R1C1 
sR1C1+1 Vo1’ - 
gm1R1 
sR1C1+1 Vo2 = 
1 
s1+1 Vo1’ - 
gm1R1 
s1+1 Vo2 
Vo2 = 
R2C2 
sR2C2+1 Vo2’ - 
gm2R2 
sR2C2+1 Vo1 = 
2 
s2+1 Vo2’ - 
gm2R2 
s2+1 Vo1 
Defining the output, Vo, and input, Vi, as 
Vo = Vo2-Vo1 and Vi = Vo2’-Vo1’ 
C2 
Vo2' 
s 
+ 
Vo2 
- 
Fig. 8.5-4 
CMOS Analog Circuit Design © P.E. Allen - 2010
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-23 
Step Response of the Latch - Continued 
Solving for Vo gives, 
Vo = Vo2-Vo1 = 
 
s+1 Vi + 
gmR 
s+1 Vo 
or 
Vo = 
Vi 
s+(1-gmR) = 
Vi 
1-gmR 
s 
1-gmR+1 
= 
’Vi 
s’+1 
where 
’ = 
 
1-gmR 
Taking the inverse Laplace transform gives 
vo(t) = Vi e-t/’ = Vi e-t(1-gmR) /  egmRt/Vi, if gmR 1. 
Define the latch time constant as 
L = |’|  
 
gmR = 
C 
gm 
= 
0.67WLCox 
2K’(W/L)I = 0.67Cox 
WL3 
2K’I 
if C  Cgs. 
 Vout(t) = et/L Vi 
CMOS Analog Circuit Design © P.E. Allen - 2010 
Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-24 
Step Response of a Latch - Continued 
Normalize the output voltage by (VOH-VOL) to get 
Vout(t) 
VOH-VOL 
= et/L 
Vi 
VOH-VOL 
which is plotted as, 
The propagation delay time is 
tp = L ln  
VOH-VOL 
2Vi 
 
Note that the larger the Vi, the 
faster the response. 
1 
0.8 
0.6 
0.5 
0.4 0.3 
0.2 
0.1 
0.05 
ΔVi 
VOH-VOL 
0.03 
ΔVout 
VOH-VOL 0.01 
0.4 
0.2 
0 
0.005 
0 1 2 t 3 4 5 
τL 
Fig. 8.5-5 
CMOS Analog Circuit Design © P.E. Allen - 2010

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Lect2 up320 (100328)

  • 1. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-1 LECTURE 320 – IMPROVED OPEN-LOOP COMPARATORS AND LATCHES LECTURE ORGANIZATION Outline • Autozeroing • Hysteresis • Simple Latches • Summary CMOS Analog Circuit Design, 2nd Edition Reference Pages 464-483 CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-2 AUTOZEROING Principle of Autozeroing Use the comparator as an op amp to sample the dc input offset voltage and cancel the offset during operation. Comparator + - - Ideal Comparator + - Ideal VOS VOS vIN vOUT CAZ VOS + VOS + - Comparator + - VOS Ideal CAZ Model of Comparator. Autozero Cycle Comparison Cycle Fig. 8.4-1 Comments: • The comparator must be stable in the unity-gain mode (self-compensating comparators are ideal, the two-stage comparator would require compensation to be switched in during the autozero cycle.) • Complete offset cancellation is limited by charge injection CMOS Analog Circuit Design © P.E. Allen - 2010
  • 2. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-3 Differential Implementation of Autozeroed Comparators + - VOS Ideal φ1 Comparator φ2 + - + - VOS CAZ vIN-vOUT φ1 φ1 VOS vOUT = VOS Comparator during φ1 phase + - + - VOS VOS vOUT φ2 vIN-Lecture vIN+ Differential Autozeroed Comparator Comparator during φ2 phase Fig. 8.4-2 vIN+ CMOS Analog Circuit Design © P.E. Allen - 2010 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-4 Single-Ended Autozeroed Comparators Noninverting: vOUT vIN + - φ2 φ2 φ1 CAZ φ1 φ1 Fig. 8.4-3 Inverting: vIN vOUT + - φ2 CAZ φ1 φ1 Fig. 8.4-4 Comment on autozeroing: Need to be careful about noise that gets sampled onto the autozeroing capacitor and is present on the comparison phase of the process. CMOS Analog Circuit Design © P.E. Allen - 2010
  • 3. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-5 HYSTERESIS Influence of Input Noise on the Comparator Comparator without hysteresis: vin vout Comparator threshold VOH VOL t t Fig. 8.4-6A Comparator with hysteresis: vin vout VTRP+ VTRP-Fig. VOH VOL t t 8.4-6B CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-6 Use of Hysteresis for Comparators in a Noisy Environment Transfer curve of a comparator with hysteresis: vOUT VTRP+ vIN VTRP-VOH VOL (VOH-VOL) VTRP+ vIN Fig. 8.4-5 vOUT VOH VOL 0 0 R1 R2 VTRP-Counterclockwise Bistable Clockwise Bistable Hysteresis is achieved by the use of positive feedback • Externally • Internally CMOS Analog Circuit Design © P.E. Allen - 2010
  • 4. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-7 Noninverting Comparator using External Positive Feedback Circuit: Upper Trip Point: Assume that vOUT = R2 +- vIN R1 Fig. 8.4-7 VOL, the upper trip point occurs when, 0 = R1 R1+R2 VOL + R2 R1+R2 VTRP vOUT R1VOH R2 - + VTRP R1 R2 + = - vOUT (VOH-VOL) - 0 R1 R2 VOH VOL 0 VOL Lower Trip Point: Assume that vOUT = VOH, the lower trip point occurs when, 0 = R1 R1+R2 VOH + R2 R1+R2 VTRP - VTRP - = - R1 R2 VOH Width of the bistable characteristic: Vin = VTRP+-VTRP- = R1 R2 VOH-VOL R1VOL R2 vIN CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-8 Inverting Comparator using External Positive Feedback Circuit: + - vOUT vIN R1 R2 vOUT vIN VOH (VOH-VOL) 0 0 R1 R1+R2 R1VOL R1VOH R1+R2 R1+R2 VOL Fig. 8.4-8 Upper Trip Point: vIN = VTRP + = R1 R1+R2 VOH Lower Trip Point: vIN = VTRP - = R1 R1+R2 VOL Width of the bistable characteristic: Vin = VTRP+-VTRP- = R1 R1+R2 VOH-VOL CMOS Analog Circuit Design © P.E. Allen - 2010
  • 5. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-9 Horizontal Shifting of the CCW Bistable Characteristic Circuit: Upper Trip Point: VREF = R1 R1+R2 vIN R1 VREF Fig. 8.4-9 VOL + R2 R1+R2 R2 +- VTRP vOUT VOH VOL vOUT 0 0 + VTRP R1 R2 (VOH-VOL) R1+R2 R2 VREF R1VOH R2 + = R1|VOL| R2 R1+R2 R2 VREF - vIN R1 R2 VOL Lower Trip Point: VREF = R1 R1+R2 VOH + R2 R1+R2 VTRP - VTRP - = R1+R2 R2 VREF - R1 R2 VOH Shifting Factor: ± R2 R1+R2 VREF CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-10 Horizontal Shifting of the CW Bistable Characteristic Circuit: + - vOUT vIN R1 R2 vIN R1 (VOH-VOL) Fig. 8.4-10 VREF vOUT VOH 0 VOL R1+R2 R2 VREF R1+R2 R1|VOL| 0 R1VOH R1+R2 R1+R2 Upper Trip Point: vIN = VTRP + = R1 R1+R2 VOH + R2 R1+R2 VREF Lower Trip Point: vIN = VTRP - = R1 R1+R2 VOL + R2 R1+R2 VREF Shifting Factor: ± R2 R1+R2 VREF CMOS Analog Circuit Design © P.E. Allen - 2010
  • 6. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-11 Example 320-1 Design of an Inverting Comparator with Hysteresis Use the inverting bistable to design a high-gain, open-loop comparator having an upper trip point of 1V and a lower trip point of 0V if VOH = 2V and VOL = -2V. Solution Putting the values of this example into the above relationships gives 1 = R1 R1+R2 2 + R2 R1+R2 VREF and 0 = R1 R1+R2 (-2) + R2 R1+R2 VREF Solving these two equations gives 3R1 = R2 and VREF = (2/3)V. CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-12 Hysteresis using Internal Positive Feedback Simple comparator with internal positive feedback: VDD M3 M6 M7 M4 vo1 vo2 vi1 M1 M2 vi2 M8 M5 VSS IBias Fig. 8.4-11 CMOS Analog Circuit Design © P.E. Allen - 2010
  • 7. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-13 Internal Positive Feedback - Upper Trip Point Assume that the gate of M1 is on ground and the input to M2 is much smaller than zero. The resulting circuit is: M1 on, M2 off M3 on, M6 on (active), M4 and M7 off. vo2 is high. M6 wants to source the current i6 = W6/L6 W3/L3 i1 As vin begins to increase towards the trip point, the current flow through M2 increases. When i2 = i6, the upper trip point will occur. i5 = i1+i2 = i3+i6 = i3+
  • 8.
  • 9. W6/L6 W3/L3 i3 = i3 W6/L6 W3/L3 1+ VDD M3 M6 M7 M4 vo1 vo2 M1 M2 i1 = i3 i1 = i3 = i2 = i6 i5 M5 VSS vin Fig. 8.4-12A I5 1+[(W6/L6)/(W3/L3)] Also, i2 = i5 - i1 = i5 - i3 Knowing i1 and i2 allows the calculation of vGS1 and vGS2 which gives VTRP+ = vGS2 - vGS1 = 2i2 2 + VT2 - 2i1 1 - VT1 CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-14 Internal Positive Feedback - Lower Trip Point Assume that the gate of M1 is on ground and the input to M2 is much greater than zero. The resulting circuit is: M2 on, M1 off M4 and M7 on, M3 and M6 off. vo1 is high. M7 wants to source the current i7 = W7/L7 W4/L4 i2 As vin begins to decrease towards the trip point, the current flow through M1 increases. When i1 = i7, the lower trip point will occur. i5 = i1+i2 = i7+i4 =
  • 10.
  • 11. W7/L7 W4/L4 i4 +i4 = i4 W7/L7 W4/L4 1+ VDD M3 M6 M7 M4 vo1 vo2 vi1 M1 M2 i2 = i4 = i1 = i7 M5 I5 i2 = i4 vi1 V Fig. 8.4-12B SS i5 vi 1+[(W7/L7)/(W4/L4)] Also, i1 = i5 - i2 = i5 - i4 Knowing i1 and i2 allows the calculation of vGS1 and vGS2 which gives VTRP- = vGS2 - vGS1 = 2i2 2 + VT2 - 2i1 1 - VT1 CMOS Analog Circuit Design © P.E. Allen - 2010
  • 12. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-15 Example 320-2 - Calculation of Trip Voltages for a Comparator with Hysteresis Consider the circuit shown. If KN’ = 110μA/V2, KP’ = 50μA/V2, and VTN = |VTP| = 0.7V, calculate the positive and negative threshold points if the device lengths are all 1 μm and the widths are given as: W1 = W2 = W6 = W7 = 10 μm and W3 = W4 = 2 μm. The gate of M1 is tied to ground and the input is the gate of M2. The current, i5 = 20 μA Solution To calculate the positive trip point, assume that the input has been negative and is heading positive. i6 = (W/L)6 (W/L)3 i3 = (5/1)(i3) i3 = i5 IBias VDD M3 M6 M7 M4 vo1 vo2 vi1 M1 M2 vi2 M8 M5 1+[(W/L)6/(W/L)3] = i1 = VSS Fig. 8.4-11 20μA 1+5 = 3.33 μA i2 = i5 i1 = 20 3.33 = 16.67 μA vGS1 = 2i1 1 1/2 +VT1 = 2·3.33 (5)110 1/2 +0.7 = 0.81V vGS2 = 2i2 2 1/2 + VT2 = 2·16.67 (5)110 1/2 + 0.7 = 0.946V VTRP+ vGS2vGS1 = 0.9460.810 = 0.136V CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-16 Example 320-2 - Continued Determining the negative trip point, similar analysis yields i4 = 3.33 μA i1 = 16.67 μA vGS2 = 0.81V vGS1 = 0.946V VTRP- vGS2 vGS1 = 0.81 0.946 = 0.136V PSPICE simulation results of this circuit are shown below. 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 vo2 (volts) vin (volts) Fig. 8.4-13 CMOS Analog Circuit Design © P.E. Allen - 2010
  • 13. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-17 Complete Comparator with Internal Hysteresis VDD M3 M6 M7 M4 M9 M8 vi1 vi2 M1 M2 M10 M11 M8 M5 VSS IBias vout Fig. 8.4-14 CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-18 Schmitt Trigger The Schmitt trigger is a circuit that has better defined switching points. Consider the following circuit: How does this circuit work? Assume the input voltage, vin, is low and the output voltage, vout , is high. M3, M4 and M5 are on and M1, M2 and M6 are off. When vin is increased from zero, M2 starts to turn on causing M3 to start turning off. Positive feedback causes M2 to turn on further and eventually both M1 and M2 are on and the output is at zero. The upper switching point, VTRP+ is found as follows: When vin is low, the voltage at the source of M2 (M3) is vS2 = VDD-VTN3 VTRP+ = vin when M2 turns on given as VTRP+ = VTN2 + vS2 vin VDD M3 M5 M4 M2 M1 M6 vout Fig. 8.4-15 VTRP+ occurs when the input voltage causes the currents in M3 and M1 to be equal. CMOS Analog Circuit Design © P.E. Allen - 2010
  • 14. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-19 Schmitt Trigger – Continued Thus, iD1 = 1( VTRP+ - VTN1)2 = 3( VDD - vS2- VTN3) 2 = iD3 which can be written as, assuming that VTN2 = VTN3, 1( VTRP+ - VTN1) 2 = 3( VDD – VTRP+)2 VTRP+ = VTN1+ 3/1VDD 1+ 3/1 The switching point, VTRP- is found in a similar manner and is: 5( VDD - VTRP- - VTP5)2 = 6( VTRP-)2 VTRP- = 5/6(VDD-VTP5) 1+ 5/6 The bistable characteristic is, vin vout VDD VDD 0 0 VTRP- VTRP+ Fig. 8.4-16 CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-20 SIMPLE LATCHES Regenerative Comparators Regenerative comparators use positive feedback to accomplish the comparison of two signals. Latches can have a faster switching speed than the previous comparators. NMOS and PMOS latch: VDD I1 I2 vo1 vo2 M1 M2 VDD M1 M2 vo1 vo2 I1 I2 Fig. 8.5-3 NMOS latch PMOS latch CMOS Analog Circuit Design © P.E. Allen - 2010
  • 15. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-21 Operating Modes of the Latch The latch has two modes of operation – enable or latch and Enable (enable_bar) or Latch (latch_bar). 1.) During the Enable_bar, the latch is turned off (currents are removed) and the unknown inputs are applied to it. The parasitic capacitance at the latch nodes hold the unknown voltage. 2.) During Enable, the latch is turned on, and the positive feedback acts on the applied inputs and causes one side of the latch to go high and the other side to go low. Enable_bar: Enable Enable Vo2ʼ 060808-09 VDD I1 I2 Enable Enable M1 M2 Vo1ʼ VDD M1 M2 I1 I2 Vo2ʼ Vo1ʼ NMOS latch PMOS latch The inputs are initially applied to the outputs of the latch. Vo1’ = initial input applied to vo1 CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-22 Step Response of a Latch (Enable) Circuit: Ri and Ci are the resistance and capacitance seen to ground from the i-th transistor. Nodal equations: gm1Vo2+G1Vo1+sC1 VDD VDD I1 I2 vo2 M1 M2 vo1 + + Vo2 Vo1 gm1Vo2 R1 C1 Vo1' s - - gm2Vo1 R2 Vo1’ s = gm1Vo2+G1Vo1+sC1V o1-C1Vo1’ = 0 Vo1- gm2Vo1+G2Vo2+sC2 Vo2’ s = gm2Vo1+G2Vo2+sC2V o2-C2Vo2’ = 0 Vo2- Solving for Vo1 and Vo2 gives, Vo1 = R1C1 sR1C1+1 Vo1’ - gm1R1 sR1C1+1 Vo2 = 1 s1+1 Vo1’ - gm1R1 s1+1 Vo2 Vo2 = R2C2 sR2C2+1 Vo2’ - gm2R2 sR2C2+1 Vo1 = 2 s2+1 Vo2’ - gm2R2 s2+1 Vo1 Defining the output, Vo, and input, Vi, as Vo = Vo2-Vo1 and Vi = Vo2’-Vo1’ C2 Vo2' s + Vo2 - Fig. 8.5-4 CMOS Analog Circuit Design © P.E. Allen - 2010
  • 16. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-23 Step Response of the Latch - Continued Solving for Vo gives, Vo = Vo2-Vo1 = s+1 Vi + gmR s+1 Vo or Vo = Vi s+(1-gmR) = Vi 1-gmR s 1-gmR+1 = ’Vi s’+1 where ’ = 1-gmR Taking the inverse Laplace transform gives vo(t) = Vi e-t/’ = Vi e-t(1-gmR) / egmRt/Vi, if gmR 1. Define the latch time constant as L = |’| gmR = C gm = 0.67WLCox 2K’(W/L)I = 0.67Cox WL3 2K’I if C Cgs. Vout(t) = et/L Vi CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-24 Step Response of a Latch - Continued Normalize the output voltage by (VOH-VOL) to get Vout(t) VOH-VOL = et/L Vi VOH-VOL which is plotted as, The propagation delay time is tp = L ln VOH-VOL 2Vi Note that the larger the Vi, the faster the response. 1 0.8 0.6 0.5 0.4 0.3 0.2 0.1 0.05 ΔVi VOH-VOL 0.03 ΔVout VOH-VOL 0.01 0.4 0.2 0 0.005 0 1 2 t 3 4 5 τL Fig. 8.5-5 CMOS Analog Circuit Design © P.E. Allen - 2010
  • 17. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-25 Example 320-3 - Time Domain Characteristics of a Latch. Find the propagation time delay for the NMOS if the W/L of the latch transistors is 5μm/0.5μm and the latch dc current is 10μA when Vi = 0.1(VOH-VOL) and Vi = 0.01(VOH-VOL). Solution The transconductance of the latch transistors is gm = 2·120·10·10 = 155μS The output conductance is 0.6μS which gives gmR of 93V/V. Since gmR is greater than 1, we can use the above results. Therefore the latch time constant is found as L = 0.67Cox WL3 2K’I = 0.67(60.6x10-4) (5·0.5)x10-24 2·120x10-6·10x10-6 = 0.131ns Since the propagation time delay is the time when the output is 0.5(VOH-VOL), then using the above results or Fig. 8.5-5 we find for Vi = 0.01(VOH-VOL) that tp = 3.91L = 0.512ns and for Vi = 0.1(VOH-VOL) that tp = 1.61L = 0.211ns. CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-26 Comparator using a Latch with a Built-In Reference† How does it operate? 1.) Devices in shaded region operate in the triode region. 2.) When the latch/reset goes high, the upper cross-coupled inverter-latch regenerates. The drain currents of M5 and M6 are steered to obtain a final state determined by the mismatch between the R1 and R2 resistances. 1 R1 = KN W1 L (vin+-VT)+ W2 L (VREF--VT) and 1 R2 = KN W1 L (vin--VT)+ W2 L (VREF+-VT) φ1 φ1 Latch /Reset Latch /Rese φ1 φ1 vout- M9 M3 R1 R2 M1 M7 M5 M8 M2 M2 M1 M10 M4 M6 vin+ vin-vout+ VREF- VREF+ 3.) The input voltage which causes R1 = R2 is vin(threshold) = (W2/W1)VREF W2/W1 = 1/4 generates a threshold of ±0.25VREF. VDD Fig. 8.5-6 Performance 20Ms/s 200μW † T.B. Cho and P.R. Gray, “A 10b, 20Msamples/s, 35mW pipeline A/D Converter,” IEEE J. Solid-State Circuits, vol. 30, no. 3, pp. 166-172, March 1995. CMOS Analog Circuit Design © P.E. Allen - 2010
  • 18. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-27 Simple, Low Power Latched Comparator† VDD φ1 φ1 φ1 φ1 vout- M9 M3 M7 M5 M10 M4 M8 M6 vin+ vin-vout+ M1 M2 Fig. 8.5-7 Dissipated 50μW when clocked at 2MHz. Self-referenced † A. Coban, “1.5V, 1mW, 98-dB Delta-Sigma ADC”, Ph.D. dissertation, School of ECE, Georgia Tech, Atlanta, GA 30332-0250. CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-28 Tail-Referenced Latch The previous two latches experience poor input offset voltage characteristics because the input devices are working in the linear region during the latch phase. The latch below keeps the input devices in the sat-uration region. The resulting larger gain of the input devices reduces the input offset voltage as shown. The input offset voltage of the tail referenced latch is compared between two latches with the referenced latch for 100 samples. The x-axis is the deviation from the mean of the first latch and the y-axis is the deviation of the mean of the second latch. Latch vout - + vin M1 M2 Latch 070511-01 VDD Latch vout + - + Vref Vref - vin All transistors are 3.5μm/0.4μm excep M1 and M2 CMOS Analog Circuit Design © P.E. Allen - 2010
  • 19. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-29 CMOS Latch Circuit: M6 M3 M4 M8 VREF vin vout- vout+ VDD φLatch M1 M2 M7 φLatch M5 Fig. 8.5-8 Input offset voltage distribution: 20 10 L = 1.2μm σ = 5.65 (0.6μm Process) 0 -15 -10 -5 0 5 10 15 Number of Samples Input offset voltage (mV) Fig. 8.5-9 CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-30 CMOS Latch with Different Inputs and Outputs Latch Outputs M5 M6 M1 M2 M7 M3 M4 060808-10 VDD Latch_bar Latch Inputs When Latch_bar is high, M5, M6 and M7 are off and the latch is disabled and the outputs are shorted together. When Latch_bar is low, the input voltages stored at the sources of M1 and M2 will cause one of the latch outputs to be high and the other to be low. The source of M1 and M2 that is higher will have a larger source-gate voltage resulting in a larger transconductance and more gain than the other transistor. CMOS Analog Circuit Design © P.E. Allen - 2010
  • 20. Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-31 Metastability Metastability is the condition where the latch cannot make a decision in the time allocated. Normally due to the fact that the input is small (within the input resolution range). Metastability can be improved (reduced) by increasing the gain of the comparator by preceding it with an amplifier to keep the signal input to the latch as large as possible under all conditions. The preamplifier also reduced the input offset voltage. Latch Outputs 060808-11 VDD Latch_bar VNB1 Preamplifier Comparator Inputs Latch Latch Inputs CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 320 – Improved Open-Loop Comparators and Latches (3/28/10) Page 320-32 SUMMARY • Discrete-time comparators must work with clocks • Switched capacitor comparators use op amps to transfer charge and autozero • Regenerative comparators (latches) use positive feedback • The propagation delay of the regenerative comparator is slow at the beginning and speeds up rapidly as time increases • The highest speed comparators will use a combination of open-loop comparators and latches CMOS Analog Circuit Design © P.E. Allen - 2010