ECE 665 (ESS)
LC Voltage Control Oscillator AAC
A Stable Loss-Control Feedback Loop to Regulate the
oscillation Amplitude of LC VCO’s
Problem: Previously reported AAC loops use a
conditionally stable negative feedback loop
Motivation: To propose a practically stable
negative feedback loop
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1
VCO Amplitude Control
• More on VCO AAC loop
– Fast and reliable start up.
– Optimal bias point in terms of phase noise
performance.
– Adequate amplitude over wide oscillation frequency
range.
– Variations of oscillation amplitude could be fast when
other digital blocks pull the ground or the power
supply rails.
– VCO-based Q-tuning.
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ECE 665 (ESS
LC Filters
• Active LC filters
The advent of highly integrated wireless
communication transceivers.
Persistent effort to improve the quality of on-chip
spiral inductors.
Superior dynamic range performance.
However,
Reactive elements integrated on silicon are more
non-ideal than corresponding discrete parts.
Automatic tuning is a major challenge.
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LC Filters: Q-Tuning
• Tuning techniques
– Direct tuning: Self-tuning
• Filter is the plant in the tuning
system
• Tuning accuracy doesn’t rely on
matching.
Signal Input
Tuning Input
reference
– Indirect tuning: master-slave
• VCF-based : Master is a filter
• VCO-based : Master is a VCO
Tuning
Control
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Tunign Output
Tuning
Control
Input
reference
Signal Output
Slave
Filter
Slave
Filter
Output
Master
Filter
4
LC Filters: Q-Tuning
• VCF-base tuning
– A reference signal with low harmonic content.
– A phase detector having low offsets.
– Since output amplitude varies with frequency thus Q-tuning loop
heavily relies on frequency tuning loop.
• VCO-base tuning
– No reference signal is needed.
– Amplitude and phase of the VCO are independent, theoretically,
thus the Q-tuning and frequency tuning loops are not affecting
each other.
– Leakage of the VCO output to signal path.
– Inherent nonlinearity of VCO and its effect on Q-tuning accuracy.
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VCO-Based Q-Tuning
• Principle of Operation
Slave Filter
 Gin
– VCO: Large signal
vin
i
G
neg
Ccoupling
a v
 a v3 ; a  0, a  0
1 out
3 out
1
3
 Gneg
 Gneg
L
L
C
C
RL
RL
d 2vout  a1  GP 3a3 2  dvout
1


vout 

vout  0
dt 2
C
C
dt
LC


If vout  As sin( ω0t ), the steady state
 Gneg
oscillatio n amplitude As can be found as :
As  2
a1  GP
3a3
, for a1  GP
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L
C
RL
Master VCO
Amplitude
Control
Loop
6
VCO-Based Q-Tuning
Slave Filter
Ccoupling
 Gin
vin
 Gneg
 Gneg
L
L
C
C
RL
RL
For the slaved filter,
operating in small signal regime :
Qslave filter
4

3a3 As2
C
L
 Gneg
L
C
RL
Master VCO
Amplitude
Control
Loop
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VCO-Based Q-Tuning
• Experimental results
TSMC 0.35 m
Area : 0.144mm
Supply :1.8V
Current :15mA
2
Q=50, 75, 115, 160
3- F. Bahmani, E. Sanchez-Sinencio, ”VCO-based quality factor tuning of a second-order
LC filter at 2.25GHz” Under revision of IEE Electronics Letters, 2006.
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Loss-Control Feedback
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Loss-Control Feedback
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Loss-Control Feedback
Oscillatio n amplitude :
I bias
A(t ) 
Gtank  Gneg
• Control the overall
LC tank’s loss by
changing Gneg
Vdd
Gtank
Vo (t )  A(t ) cos(0t )
 Gneg
Envelop
Venv
I bias
VC
1
s Int
detector
( env )
Aref
As
2 Int
A( s)
H ( s) 

Aref ( s) s 2  As ENV s  As
2 Int
2 Int
• Different signs of the denominator: unstable!
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How can we stabilize the LCF loop?
• Use a local feedback loop (F)
VCO
A( s ) 
s2 
As
AREF ( s )
2 Int
As ENV 
1 
 Int
F 

2
As
s 
 2 Int
Vo (t )  A(t ) cos(0t )
1
VC
s Int
Venv

Aref
Envelop
detector
F
Stability requiremen t : F  Fcritical 
As ENV
2
For a typical LC VCO : Fcritical  1.3
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Transient Behavior of the Proposed LCF
• Step Response
• Trade-off between power and settling
time
d  A  1  A  Gm1
VCO
  
  
 A(t )  A02   0
dt  A   Int  A 
2Cloop
 Gneg
Envelope
Detector
L
C
Rloss
vc
Cloop
venv (t )
Gm1
ve

vref
1
Gm 2
Gm 2
F
Gm1
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Loss-Control Feedback: Implementation
• Experimental results
Vdd
Vdd
Vout  or Aref  
ME1
Vout  or Aref  
ME 2
Venv or Vref 
I bias
L
L
CENV
ME 4
ME3
Vf
Vout
Vout 
C
C
Envelop
detector
LPF
Venv
F
Gm1
M3
M4
Mtail
Aref
VC
Envelop
detector
Gm 2
Gm1
Cloop
Vref
Gm 2
TSMC 0.35m
Area : 0.046mm 2
Supply : 2.8V
Current : 8mA
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Loss-Control Feedback: Experimental Results
• Phase noise
F 2
F=2
Stable
F=0
Unstable
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Loss-Control Feedback: Experimental Results
• Stability over the amplitude tuning range
-25
-100
-27
-105
-29
-110
-31
-115
-33
-35
-120
1.4
1.6
1.8
2
2.2
2.4
- 42
- 44
- 46
- 48
- 50
2.6
Bias voltage of the VCO tail current source [V]
Measured oscillation amplitude (■)
Phase noise (●)
HD3 (▲)
4- F. Bahmani, E. Sanchez-Sinencio,”A stable loss-control feedback Loop for amplitude
regulation
of LC Oscillators” IEEE Transactions on Circuit and Systems I, 2006.
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HD3 [dB]
 40
- 40
-95
Phase noise @ 1MHz [dBc/Hz]
 30
Oscillation amplitude [dBm]
-23
A New Q-Tuning Scheme: Why?
• To tune the quality factor of an LC filter
– VCO-based approach is the best choice
• Needs perfect match between the LC filter and LC VCO
• Needs a stable amplitude control loop for VCO
• The tuning range of Q depends on the VCO amplitude and
nonlinearities of the Gneg:
Qslave filter 
4
3a3 As2
C
L
• Is there any way to tune Q to an arbitrary
value?
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LC Filters Q-Tuning
An Accurate Automatic Quality Factor Tuning
Scheme for Gigahertz Range LC Filters
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LC Filters Q-Tuning
• Basics of 2nd order LC filter
V (s)
H (s)  o
Vin ( s )
 A0
s 
2
0
Q
0
Q
Vdd
s
L
L
Vout
s   02
2 m V gm  VT 
Gm
A0 

G P  Gneg G P   q Vq  VT 
C
Vin 
M4
C
Vf
M6
M5
Vin 
Vgm
M3
M2
M1
Vq
C
1
Q
L GP   q (Vq  VT )
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LC Filters Q-Tuning
• Basics idea:
A0
H ( j L ) 
(1  j )
2
H(jω 0 )  A 0
H(jω L )  H(jω H )  A 0 / 2
- 3dB BW

1 

 L   0 1 
 2Q 
1 1
Q

2
1 L
0
ω L ω0 ω H
• Two amplitude locked loop: one at ω0 and the
other one at ωL.
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LC Filters Q-Tuning
• Proposed Scheme
A0VL
2 cos Lt  sin Lt 
A0V0 cos 0 t
Vf
V0 cos 0 t
V L cos  L t
Vg
Vq
m
Vf 0

V02
2
LPF
A0V02
2 Ad
Loop 2
Q - Tuning
1 / Ad
Loop 1
Amplitude Tuning
Vq
Vf 0

m
errorq
errora
LPF
Vg
Vf
FB
VL2
2
2
0 L
AV
2 Ad
2 / Ad
LPF
LPF
A0VL2  2
1

cos L t  sin 2L t 
2 
2

A0V02 cos 2 0t
Amplitude Tuning Loop
Quality Factor Tuning Loop
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LC Filters Q-Tuning
• Stability analysis via phase portrait
technique
4v
u   K L (
q K0
Ad u
2v
 1) 
(1 
)
C 1

K
A
u
m L
d
1
2
2
LQd u
v  K 0 (1 
2v
)
Ad u
Equilibriu m point :
1 
1 C

Vq 0  VT   GP 
q 
Qd L 
A
Vgm0  VT  d GP   q (Vq 0  VT ) 
2 m
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LC Filters Q-Tuning: Implementation
• One filter is used to overcome
the mismatch problem
Vf
OFF
CHIP
Vq
Vg
m

LPF
TSMC 0.35 m
1 / Ad
Area : 0.073mm
Supply :1.3V
Current : 5mA
LPF
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LC Filters Q-Tuning: Multiplier
• Self-multiplier
– Linearized Gilbert cell
LPF
C
R1
LPF
R
M 11
M7
Vin 
Vin 
Vbias
M1
M2
M b1
R
M 12
I bleeding
vout 
R2
M8
M4
M5
M b2
R3
R4
Mb 3
Circles :
Measurement
M 10
M9
A2
2
C
vout 
M3
Vin 
A cos(t )
Vin 
M6
line :
Simulation
Mb4
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LC Filters Q-Tuning: Experimental
Results
• Independent tuning of Q and A0
A0(dB)={-15, -10, -5, 0}
Q={60, 80, 120, 220}
Q={50, 60, 70, 120}
A0(dB)=0.
5- F. Bahmani, T. S. Gotarredona, E. Sanchez-Sinencio, ”An accurate quality factor and amplitude tuning scheme
for high frequency LC bandpass filters ” submitted to the IEEE Transaction on Circuit and System I, 2006.
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Conclusion
• A stable amplitude control feedback loop
for LC VCO’s is proposed and its
application in the VCO-based Q-tuning of
LC filters are demonstrated
• An accurate Q-tuning scheme for 2nd order
active LC filters is presented.
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References
•
•
•
F. Bahmani, and E. Sánchez-Sinencio, "A Stable Loss
Control Feedback Loop for VCO Amplitude Tuning",
IEEE Transaction on Circuits and Systems I: Regular
Papers: Volume: 53, Issue 12, pp. 2498-2506, Dec.
2006.
F. Bahmani, E. Sánchez-Sinencio, ”VCO-based quality
factor tuning of a second-order LC filter at 2.25GHz” in
dissertation
F.Bahmani, T. Serrano-Gotarredona, and E. SánchezSinencio, "An Accurate Automatic Quality Factor Tuning
Scheme for 2nd-Order LC Filters", IEEE Transaction on
Circuits and Systems I, pp745-756, Vol 54, Issue
4, April 2007.
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Publication
7.
F. Bahmani, E. Sanchez-Sinencio, ”A Low THD, 10.7 MHz Tuned Oscillator Using
Positive Feedback And Multilevel Hard Limiter” submitted to the IEE Transaction on
Circuits, Devices and Systems, 2006.
8.
F. Bahmani, E. Sanchez-Sinencio, ”A highly Linear 3rd order CMOS Pseudo-Differential
Low Pass Filter” to be submitted to the Journal of Solid State Circuit, 2006.
9.
S. W. Park, F. Bahmani, E. Sanchez-Sinencio, ”A 10.7 MHz Linearized SwitchedCapacitor Based Oscillator Using the Multilevel Hard Limiter” To be submitted to the
IEEE Journal of Solid State Circuit, 2006.
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