E3 237 Integrated Circuits for Wireless Communication

Lecture 15: Oscillators

Gaurab BanerjeeDepartment of Electrical Communication Engineering,

Indian Institute of Science, Bangalorebanerjee@ece.iisc.ernet.in

Outline

• Basic Concepts

• Feedback Based

• One Port View

• Ring Oscillators

• Basic Oscillator Topology

• Voltage Controlled Oscillators• Voltage Controlled Oscillators

• Negative gm Oscillators

• Phase Noise

Voltage Controlled Oscillators

Basic idea : Vary the resonant frequency of the tank using a varactor.

Vcntrl

Vcntrl

• In ring oscillators, the frequency is varied by changing the delays of invertors (e.g., by changing power supply voltage.)

• Mathematical model:

• An ideal VCO generates a periodic output, whose frequency is a linear function of the control voltage (Vcont).

• ωωωωout = ωωωωFR + kVCO Vcont

• ωωωωFR = “Free running” frequency

• KVCO = “gain” of the VCO -> measure of sensitivity -> rad/s/V

• Vcont creates a change around ωωωωFR -> often used in feedback loops to stabilize frequency -> PLLs

Voltage Controlled Oscillators

• Phase is the integral of frequency w.r.t time -> output of the VCO can be expressed as:

• If V cont = V0 ,

• If V cont = Vm cos ωωωωm t ,

• If ,

the signal can be approximated narrowband FM

-> main components of output spectrum at

Initial value of phase

High frequency components on the

control input are rejected

Outline

• Basic Concepts

• Feedback Based

• One Port View

• Ring Oscillators

• Basic Oscillator Topology

• Voltage Controlled Oscillators• Voltage Controlled Oscillators

• Negative gm Oscillators

• Phase Noise

Negative-gm Oscillators

Instead of an impedance transformer, use a buffer.

• Use a source follower as a buffer.

• Note that the gate of Q1 is connected to VDD to make the biases on Q1 and Q2 symmetric.

• Differential implementation : Make loading on Q1 and Q2 symmetric.

Negative-gm Oscillators : 1-port view

• For a cross coupled oscillator, Rin = -2/gm• For a cross coupled oscillator, Rin = -2/gm

• Resonant Frequency:

• Output is differential

• Biasing possible from the top (PMOS) or bottom (NMOS)

• Flicker noise from biasing circuits can get up-converted due to mixer action

• Parasitic capacitors can “eat into” the tuning range.

Complementary Architecture

• Current reuse provides extra -2/gm from PMOS

• (W/L)p = 3(W/L)n for better rise/fall time symmetry -> similar to invertors

• Output amplitude = 2X of NMOS VCO

• To calculate output, assume that:

• The two cross coupled devices commutate the tail current very fast (square wave).

• All harmonics and DC are filtered out by the tank, only ωωωω0 survives.

• At resonance, tank resistance = Rtank

• NMOS cross-coupled VCO : Vout = 2/ππππ Ibias Rtank

• NMOS/PMOS VCO : Vout = 4/ππππ Ibias Rtank

Outline

• Basic Concepts

• Feedback Based

• One Port View

• Ring Oscillators

• Basic Oscillator Topology

• Voltage Controlled Oscillators• Voltage Controlled Oscillators

• Negative gm Oscillators

• Phase Noise

Phase Noise in VCOs

Noise injected into an oscillator by constituent devices or external means -> Influences the amplitude and phase of the output signal.

• Random deviation in phase (or equivalently, frequency) is called phase noise.

• Time domain -> random variation in period or zero crossing points.

Consider, x(t) = A cos [ ωωωωc t + φ φ φ φ n (t)]

φ φ φ φ (t) = random excess phase representing variations in period ���� Phase noiseφ φ φ φ n (t) = random excess phase representing variations in period ���� Phase noise

If φ φ φ φ n (t) << 1 rad (small variations),

x(t) = A cosωωωωct - A φ φ φ φ n (t) sin ωωωωc t

Multiplication --> Spectrum of φ φ φ φ n (t) is translated to +/- ωωωωc

Phase Noise in VCOs

• Typically quantified by measuring noise power in unit bandwidth at an offset ∆ω∆ω∆ω∆ω

with respect to the carrier at ωωωωwith respect to the carrier at ωωωωc

e.g. -100 dBc/Hz @ 1 MHz offset. (dBc = dB w.r.t carrier power)

• Example: carrier power = -2 dBm

noise power measured in 1 kHz BW @ 1 MHz offset = -70 dBm

noise power in 1 Hz BW = -70 dBm – 30 dBm = -100 dBm

noise power referred to carrier = (-100 dBm) - (-2 dBm) = -98 dBm

Phase noise = -98 dBc/Hz @ 1 MHz offset

Effects of Phase Noise

-> RX systems: The “tail” of the LO spectrum picks up the interferer and down-converts it to -> RX systems: The “tail” of the LO spectrum picks up the interferer and down-converts it to IF/Baseband degrading SNR -> known as reciprocal mixing

-> TX systems: Weak desired signal at ωωωω2 corrupted by the tail of the strong interferer at ωωωω1.

GSM Example: Reciprocal Mixing

I. Ngompe, “Computing the LO Phase Noise Requirements in a GSM Receiver”, Applied Microwave and Wireless.

• GSM 3 MHz blocker can be 76 dB above the desired signal• For a reference sensitivity of -102 dBm -> desired signal can be 3 dB above this

power level.• Strong blocker + High Phase noise from LO -> high interference

Modelling Phase Noise

���� A slightly different definition of “Q”

• Q is usually defined as the “sharpness” of the magnitude response

⇒ Resonant frequency divided by the two-sided 3 dB Bandwidth

• Another definition of Q, useful in feedback system • Another definition of Q, useful in feedback system analysis:

• Circuit modeled as a feedback system

• Phase of the open loop transfer function φ(ω)φ(ω)φ(ω)φ(ω) examined at resonance

• Large phase slope -> significant change in phase shift with small change in frequency

• Feedback loop forces the system to return to ωωωω0 -> High Q system

Phase Noise Mechanisms

H(s)+

Noise

x(t) y(t)

vcont

H(s)

+Noise

y(t)

vcont

Phase Noise in signal path Phase Noise in control path

Phase Noise in Signal Path • Noise x(t) affects output y(t)

• Represent O.L.T.F. as :

• Around the frequency of oscillation, ω = ωω = ωω = ωω = ω0000 + ∆ω. + ∆ω. + ∆ω. + ∆ω. Using an approximate Taylor expansion,

• Since

• Noise component “x” at ωωωω0000 + ∆ω + ∆ω + ∆ω + ∆ω is multiplied by –(∆ω ∆ω ∆ω ∆ω dH/dωωωω)-1 when it appears at the oscillator’s output.

• Noise spectrum is shaped by:

Phase Noise in Signal Path Also,

=>

=>

In LC oscillators, around resonance.

Also, |H| is approximately 1 for oscillators =>

=>

=>

Q

• Leeson’s equation

• Inverse square dependence on Q

• Increases as centre frequency increases

• Larger for small offsets

Phase Noise in Control Path • Noise in the signal path -> mixes with the carrier.

• Noise in the control path -> changes the physical property of the oscillator -> changes the resonant frequency (LC) of the tank.

� Basic Idea:

• Variations on the control voltage line result in frequency modulation of the carrier.

• Noise power at ωωωω0000 +/- ωωωωm , w.r.t carrier power =

• As ωωωωm decreases, phase noise gets worse from the above expression.

• As ωωωωm decreases, 1/f noise also increases -> phase noise degrades further.