prof. ali m. niknejad berkeley wireless research center...

UNIVERSITY OF CALIFORNIA, BERKELEY Prof. Niknejad: Multiband and Multimode VCO Design

Multi-Mode and Wideband VCO Design

Prof. Ali M. NiknejadBerkeley Wireless Research CenterUniversity of California, Berkeley


Outline

● Introduction● Oscillator Start-up ● Basic Oscillator Topologies● Simple Theory of Phase Noise● Varactors (MOS, PN Junction, Switch)● Switching LC Resonators● Design Example: Wideband CMOS VCO


Introduction

● Multi-band synthesizer requires VCOs at multiple frequencies● Simple solution: Build multiple VCOs for each band and switch between

bands ● Multiple VCOs can be physical large due to passives● Good frequency planning can re-use a single VCO by changing PLL divide

ratios● To accommodate various standards and to simplify frequency planning, a

wide tuning range is desirable ● To keep noise low in PLL, the gain of the VCO should be small


Oscillator Architecture

● Oscillators are non-linear circuits:

● Input: DC Power, Initial Condition● Ideal output: Sinusoidal oscillation ● Real output: Harmonics, Phase Noise, Spurious Signals● Oscillators have inherent amplitude stability ● Oscillators do not have phase stability (unlocked)

● Linearized Picture:

● In steady-state, infinite gain (pos FB with loop gain = 1)● At start-up, the osc is excited by noise ● Poles in RHP (unstable) cause perturbation to grow● Amplitude will grow until limiting mechanism kick in ● Stable steady state amplitude is obtained


Oscillator Start-Up: Feedback Perspective

● Positive feedback places poles at start-up in RHP● The loop gain determined by g

m, feedback factor, tank impedance

● Large signal Gm has limiting characteristics

● Amplitude grows until loop gain is unity (infinite gain)● In steady-state, poles on jw axis● Any amplitude perturbation is rejected

Al ,0=gmR

n1

Al=GmR

n=1


Oscillator Start-Up: Negative Resistance

● An oscillator is composed of a lossy tank and a regeneration circuit that has net negative resistance

● At start-up the negative resistance is larger than positive resistance for start-up (RHP pole)

● Steady-state negative resistance cancels the positive resistance of tank (zero net loss)

● Amplitude determined by large signal limiting of resistance● Equivalent to FB picture for 2-port devices● Possible to use 1-port “active” devices (Gunn Diodes)


Oscillator Topologies

● Ring Oscillators● Tuned Ring Oscillators● Distributed Oscillators● LC Tank positive feedback circuits:

● Transformer feedback● Capacitive transformer feedback● Tapped inductor feedback● LC feedback

● Single-ended versus differential● Grounding options● FET versus BJT (1/f noise, amplitude of osc)


Oscillator Topologies (2)

● Single ended● Colpitts Oscillator has capacitive feedback

● Common base/gate: capacitor feedback has no phase inversion ● Hartley and Pierce (dual of Colpitts)● Clap, Armstrong, ...



● Differential● Cross coupled diff pair (MOS can be better than BJT)● Colpitts (capacitor feedback for higher swing in BJT)● Colpitts with built-in buffer (take output at collector)

● PMOS versus NMOS (lower 1/f noise since PMOS device is not a surface device)

● Advantage is disappearing in ultra-short channel devices (0.13mm)



● Current source inject 1/f noise into “mixer”● DC and all even harmonics can form mixing products at fund. ● Use a large PMOS device or even a resistor● Use filter at current source to suppress noise● Double-differential ... (PMOS and NMOS cross-coupled pair)


Resonators Quality Factor

● The quality factor for a resonant system is defined as the product of the resonant frequency times the energy stored per cycle over the power loss.

● From Poynting's Theorem we can find the power in the electromagnetic field in a volume of space

● From circuit theory

Q= Av. Energy StoredPower Loss

=U mU e

P l

P= P0powercrossing surface

P lpower loss

2 jU m−U epower stored

Z i=VI=VI∣I∣2=2P

∣I∣2R=

PoP l

12∣I∣2

X=4U m−U e

12∣I∣2


Simple Phase Noise Theory

● Since any real system has noise, the “input” to an oscillator is not zero but finite (very small)

● The noise spectrum is shaped by tuned positive feedback amplifier● Signals near tank resonance see very large gain due to positive feedback

with loop gain < 1● The actual loop gain never reaches unity but is very close to one● Integrate spectral power density to find loop gain


Phase Noise Theory (2)

● Compute transfer function for input referred voltage noise ● Integrate expression to obtain total oscillator power

● Loop gain is not unity (but nearly so):

v2, rms2 =

vn2 Al

2n2

1−Al240

2

Q2

∫−∞∞ d

1a2=/a

Posc=vn

2

Rn2

21RC

Al2

1−Al

1−Al=

vn2

RPosc

2

1RC


Phase Noise Theory (3)

● This simple theory does not account for non-linear and noise mixing effects● 1/f noise from current source is mixed to RF (even harmonics)● Gain compression (use steady-state gm)● Oscillator can be approximated as a cyclostationary system (time of

noise injection is important [Kaertner] [ Hajimiri])● But it's a good first-order theory (Leeson equations) that highlight the

importance of tank Q● Oscillator Figures of merit can be defined accordingly● More Discussion of this approach can be found:

Phase noise in LC oscillators Kouznetsov, K.A.; Meyer, R.G.; Solid-State Circuits, IEEE Journal of , Volume: 35 Issue: 8 , Aug 2000 Page(s): 1244 -1248


Multi-Mode Resonators

● On-chip spiral inductor have multiple resonance frequencies (shorted T-line resonates at odd multiples of /4)

● Why not use second harmonic for second band?● Transformer has two fundamental resonant modes (in phase and

differential):

● High frequency mode has lower Q (energy storage)

U m=12L1 I 1

2L2 I 22±M I 2 I 2

Leff =L1L2±2M


Wideband VCOs

● Challenge of realizing wide tuning range ● Loop gain must be high enough over entire range● Must design for worse case (high current consumption)● Amplitude of oscillation a function of frequency

● Amplitude control loop (ACL) can provide just enough feedback to keep loop gain = 1 over entire range

● ACL subject to noise issues

V osc≈2 I bias RT

RT≈Q L∝2

V osc ∝a


Varactors for RF Applications

● Common technique for frequency variation is to vary the cap ● PN junction diodes are ubiquitous, MOS capacitors good alternative● MOS capacitors have larger tuning range (2:1) but also higher “gain”

(achieve tuning range over a narrow voltage swing)● Many options for MOS varactors:

● n-type or p-type, triple well for isolation● inversion mode versus accumulation mode● body bias (inversion only or accumulation only)

● Noise on control line and substrate reception an important consideration


Variable Inductors?

● Transformer technique: sense primary current and amplify secondary● Active circuit sets linearity and noise limits ● Active circuit must handle resonant current in secondary!● Resonant circuit current is Q times larger than oscillator current● Phase delay in secondary current can create loss

vs= j L1 i1 jM i2= jL1K M i1

Variable current gain

Leff =L1K M


Varactors: PN Junction Diodes

● Forward bias issues limits swing● Biasing and noise requires AC isolation and filtering● High tuning voltage for wideband operation● Need extra process steps to optimize performance (high doping to

minimize series resistance due to substrate loss)


Varactors: MOS Capacitors

● Accumulation or inversion Mode ● Accumulation mode preferred (higher electron mobility)● Tuning range is very large due to fast charge build-up● CV equation follows from solution of Poisson's equation:

Cg

Cox=

W0 2Vt

e−Vgb−Vfb

2Vt

1W0 2Vt

e−Vgb−Vfb

2Vt (W0 is product-log function)


Varactors: Switched-Capacitors

● MOS device is a pretty good switch (parasitic on resistance and off capacitance)

● PN Junction can also be switched between “low” and “high” cap ● Why not switched inductor? Low inductor Q prevents use unless switch

has very low on-resistance


MOS Switched-Capacitor Topologies

● Binary weighted array of capacitors and switches● Can select discrete sub-bands and tune with variable capacitor● Band overlap by some safety margin● Tuning range limited by parasitic off capacitance● Quality factor limited by on-resistance● Device size chosen large enough such that the overall tank Q dominated by

inductor ● Differential topology also possible


Switched-Capacitor Design Equations

● Size does matter:● Series loss goes down with W● Parasitic capacitance goes up with W● Tuning Range and Q tradeoff

● Max/min frequency of oscillation

● Frequency overlap inequality:

max :1

0,max2 L

=C ,min2n−1 1

Cdd

1Ca−1

C p

min :1

0,min2 L

=C ,max2n−1CaC p

C ,max−C ,minCa− 1Cdd

1Ca−1


Switched Capacitor Equations...

● Let k > 1 be the safety margin ● Overlapping tuning ranges provide robustness against process ● In terms of overlap and capacitance ratio

=C ,maxC ,min

C ,min=k−1 [Ca− 1

Cdd

1Ca−1]≈ k

−1Ca−Cdd

Ca=

1

0,min2 L

−Cp

k−1

2n−1C ,max=

k−1 [ 1

0,min2 L

−Cp

k−1

2n−1−C dd ]=Cox=

oxtox

W⋅L


Switched Capacitor Q Factor

● The on-resistance of a FET switch in triode region:

● The channel resistance of a MOS accumulation mode varactor (Factor of 12 due to distributed effects):

● Switch-capacitor Quality Factor (independent of n)

Ron=LW

1nCox V gs−V t

Rc=LW

112 pCox V gs−V t

Qc=0 1

0RonCa21 Ron2n−1

2n−1Ca

Qc≃1

0RonCa


Example: CMOS Wideband VCO

4W/L

4C

2W/L

2C

1W/L

C

B2 B1 B0

Vtune

Vo-

LB

M3

M1 M2

M4

IB

Vo+ Vo

-

Vtune

● All PMOS to reduce 1/f noise● Only 2 gain devices to minimize

cap loading.● Large area tail device since main

1/f contributor● P+/Nwell varactors● Very compact integrated varactor

bias chokes ● LB = 100nH at only 100μm/side!!

Ref: Axel Berny et al. (to appear at CICC '03)


CMOS Wideband VCO Die Photo

● Dimensions:

1600 x 1500 mm2

● Technology: IBM 0.25mm RF CMOS process

● 5 Al metal layers● To appear at CICC '03

VCO core

chokes

output buffer

P+/nwellvaractor

Cap array

Tail device


Measured Performance

● Measured tuning range:1.06-1.41 GHz or 28.3%● Simulated tuning range: 1.06-1.46 GHz or 31.7%

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

0.0 0.5 1.0 1.5 2.0 2.5 3.0

000

001

010

011

100

101

110

111

Tuning Voltage (V)

Fre

que

ncy

of O

scil

lati

on (

GH

z)


Measured and Simulated Phase Noise

VDD = 2 V, Vtune = 0|1.5 V, Icore = 3.6 mA

-135

-130

-125

-120

-115

-110

-105

1.10 1.15 1.20 1.25 1.30 1.35 1.40Frequency of Oscillation (GHz)

Pha

se N

oise

(dB

c/H

z) L(f=100 kHz)

L(f=1 MHz)

104

105

106

107

108

-160

-150

-140

-130

-120

-110

-100

-90

-80

L (d

Bc/H

z)

Frequency Offset (Hz)

Vtune=1.5V, B2B1B0=011

Vtune=0.0V, B2B1B0=000


Performance Summary

Technology

Supply Voltage 2 V

Current (VCO Core) 3.6 mA

Tuning Range 28.00%

< 75 Mhz/V

-111 dBc/Hz

-127 dBc/Hz

-131 dBc/Hz

.25 μm CMOS

Tuning Sensitivity (KVCO)

Phase Noise (f = 1.244 Ghz, Δf = 100 kHz)

Phase Noise (f = 1.244 Ghz, Δf = 600 kHz)

Phase Noise (f = 1.244 Ghz, Δf = 1 Mhz)


Summary

● VCO design is a careful tradeoff between power, noise, and passive element design and optimization

● Multi-band voltage controlled oscillators can be realized easily with a switched capacitor array

● Quality factor of switched capacitor array only a function of technology (low on-resistance for fixed parasitics)

● MOS varactors offer wide tuning range over small voltage swings

● Switch capacitor arrays decouple VCO gain K from achievable tuning range

prof. ali m. niknejad berkeley wireless research center...

Documents