LC Tank Voltage Controlled Oscillator Tutorial

1 lc tank Voltage Controlled OscillatorTutorialbyProfessor John Starr HamelIntroduction byRyan Norris,Presented to the UW ASIC Analog Group and edited byRyan Norris,Waterloo, Ontario, Canada, 2005c 2005 This Tutorial was created from a set of hand written notes that were preparedby Professor John Starr Hamel at the University of Waterloo, Ontario, Canada foruse in E&CE 439, an undergraduate course in Analog Integrated Tutorial provides an introduction to the fundamentals of lc tank voltagecontrolled Oscillator analysis and would like to thank Professor John Starr Jamel for allowing the UW ASICA nalog Group to utilize his Tutorial within the UW ASIC Analog Tutorial is dedicated to the students of the UW ASIC Analog Introduction12 lc tank Voltage Controlled Oscillator Voltage Controlled Oscillator Analysis and Design.

2 Small Signal ( ) Analysis .. Design Constraints .. Transistor Non-Idealities .. Determining Transistor Width W .. VCO Design Procedure .. Oscillator Phase Noise .. Quality Factor Q of an Oscillator .. Dependence of Phase Noise on Q and Offset frequency .. MOS Varactors .. MOSFET Models .. 33 Bibliography42viList of lc tank .. Balanced NMOS VCO.. Balanced NMOS VCO with each tank represented by a series im-pedance.. VCO of Figure .. Bandwidth of an lc tank Oscillator .. MOSFET parasitic elements.. lc tank parasitic elements.. MOSFET I-V characteristics.. Illustration of phase noise in the time domain.

3 Illustration of phase noise in the frequency domain.. Calculation of Q from the frequency response.. lc tank VCO open-loop transfer function.. lc tank and phase function.. Phase noise in the signal path.. Noise shaping in an Oscillator .. Nonlinear mixing.. Tuning characteristic for PMOS capacitor where Body, Drain andSource are connected together.. MOS internal capacitors.. Fingered MOSFET gate.. IMOS C-V characteristic.. MOSFET transistor cross section and symbols.. MOSFET energy band diagram.. 3D MOSFET.. Detailed 3D MOSFET, and MOSFET output Drain characteristics. MOSFET small signal equivalent circuit.

4 NMOS depletion capacitance.. NMOS capacitances.. Gate-Drain overlap region.. 40viiiList of List of ideal VCO specifications.. 2ixChapter 1 IntroductionThe Analog Group, of the UW ASIC Group, has decided to concurrently designtwo different VCO ( Voltage Controlled Oscillator ) topologies. This introductionprovides some of the reasoning for why the Analog Group has chosen to designVCOs that have the ring Oscillator and the lc tank are two types of VCOs that one may choose to design:1) waveform oscillators2) resonant oscillators :1) ring Oscillator topology2) relaxation Oscillator (which has poor phase noise performance).Resonant oscillators :1) lc tank Oscillator topology2) crystal Oscillator (which is neither integrated nor tunable).

5 Ideally a given VCO topology would be able to meet all of the specifications listedin Table 1: Introduction2 Table : List of ideal VCO ) low noise2) low power3) integrated4) wide tuning range5) small die area occupancy6) high frequency (GHz)As discussed below, it is unlikely that either the ringVCO (ring Oscillator VCO) orLCVCO ( lc tank VCO) topologies can meet all of these a comparison of ringVCOs and LCVCOs, the following advantages anddisadvantages may be advantages:1) highly integrated in VLSI2) low power3) small die area occupancy4) wide tuning disadvantages:1) As frequency increases phase noise and jitter performance advantages:1) outstanding phase noise and jitter performance at high disadvantages:1) contains an inductor and a varactor (variable capacitor) which are large areacomponents, and thus is not as suitable for VLSIC hapter 1: Introduction32) high power consumption3) occupies a large die area4) small tuning , the ringVCO is most suitable for low power, highly integrated applicationsthat require a large tuning range and a low die space area.

6 In contrast, the LCVCOout performs the ringVCO in low noise mobile wireless applications one desires low power, hence the ringVCO maybe of choice. However, wireless applications require outstanding noise (phase noiseand jitter) performance at high frequency , hence the LCVCO may be of said that, there may be specific applications where either the ringVCO orthe LCVCO topology may be optimized to perform sufficiently aforementioned advantages and disadvantages should hold true for the fabri-cation technologies ( m CMOS, etc) that are predicted, by IRTS road map,to be in use in the future. Hence, a design decision - to utilize either a ringVCOor a LCVCO - that is based on the above advantages and disadvantages shouldbe a valid decision in the future when silicon CMOS fabrication technologies scalefurther into the deep deep sub-micron analysis illustrates that to be able to target the most diverse range of appli-cations, one should be knowledgeable in the design and optimization of both theringVCO and LCVCO forthcoming Tutorial provides fundamental information on the analysis anddesign of a Norris.

7 2005 UW ASIC Analog Group leaderChapter 2LC Tank Voltage ControlledOscillator TutorialPlease see the Section entitled Bibliography at the end of this document for a listof useful references [1] [2] [3] [4]. Voltage Controlled Oscillator Analysis andDesignAn lc tank VCO can be thought of as two 1-port networks connected : LC 1-port represents the frequency selective tank where the oscillations occurand the other 1-port represents the active circuit that cancels the losses in the can occur when:4 Chapter 2: lc tank Voltage Controlled Oscillator Tutorial5i) the negative conductance of the active network cancels out the positive conduc-tance (loss) of the tankii) the closed loop gain has zero phase i) & ii) above amount to a closed loop gain greater than or equal tounity magnitude with no imaginary first step in designing an Oscillator is to choose a circuit topology or this example a balanced NMOS VCO will be : Balanced NMOS only losses being assumed in Figure are those associated with the induc-tor.

8 In reality there would also be losses associated with the variable capacitors(varactors) and the MOSFETs (the active devices).In practical integrated VCOs the inductors are on-chip spiral inductors with lowquality factor that dominates the losses of the VCO quality factorQLof the inductor is given byChapter 2: lc tank Voltage Controlled Oscillator Tutorial6QL= oLR( )where ois the oscillation frequency [rad/s]Lis the value of the inductance [H]Ris inductor s equivalent series resistance [ ].QLin practical silicon RF IC processes ranges from 5 to of on-chip inductances range from nH to 10 mH in practical RF can be shown that the oscillation frequency of the circuit shown in Figure ,assuming ideal varactors and MOSFETs is given by o=12 LC2 1 R2CL( )It can also be shown, under the same set of assumptions that thegmof eachMOSFET must begm RCL( )for oscillation to Small Signal ( ) AnalysisThe Oscillator is essentially a differential pair that have been cross-coupled in apositive feed back 2: lc tank Voltage Controlled Oscillator Tutorial7 Figure.

9 Balanced NMOS VCO with each tank represented by a series input of each transistor in the differential pair has been connected to the outputof the opposite output voltagevo=v1 v2is a differential output is the input signal toM1is also the single ended output individual transistor in the pair is essentially a common-source amplifier witha complex, tuned load comprised of a lossy inductor in parallel with a is called a tank circuit since it holds the oscillating energy like atank at the oscillation two separate tanks form a differential load to the differential pair where node A remains, to first order, at the same potential during A is a virtual ground point in the same manner as the virtual groundthat exists in a normal differential 2: lc tank Voltage Controlled Oscillator Tutorial8 Node A is not a complete short, however, since, ideally, there should be aninfinite impedance between this node and the power supply proper active current source must be designed to provide the biasing to node A and henceM1andM2as well as maintaining a high impedance betweennode A and the supply the impedance between node A andVDDis not high, then RF energy will leak out of the tanks into the supply rail destroying the.

10 VCO of Figure small signal ( ) analysis the current source of Figure behaves as an opencircuit. The VCO of Figure can then be represented by Figure as two 1-portnetworks. Assuming ideal MOSFETs ( no parasitic resistances or capacitances),the entire differential amplifier can be modeled as a negative resistance R(ornegative conductance Gm= gm2).The two tank circuits appear in series whereZT= 2Zs=RT+jXT= 2(Rs+jXs)( )The oscillation condition requires that the closed loop gain (around the two 1-ports)be of at least unity magnitude and zero phase angle. The zero closed loop phasecondition implies that at the frequency of oscillation, o,XT( o) = 2: lc tank Voltage Controlled Oscillator Tutorial9 The magnitude of the amplifier negative resistance must be at least as large asRT( o), the total resistive or real loss of the two tanks .