E3 237 L15.ppt - ece.iisc.ac.in
Transcript of E3 237 L15.ppt - ece.iisc.ac.in
E3 237 Integrated Circuits for Wireless Communication
Lecture 15: Oscillators
Gaurab BanerjeeDepartment of Electrical Communication Engineering,
Indian Institute of Science, [email protected]
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.