PHASE NOISE MECHANISMS

BY

Bharath Kumar R

1RN12LVS06

Mtech 3rd Sem (VLSI)

SEMINAR

ON

 

Agenda and Q’ns 

• What is Phase noise

• What are source of phase noise

• How Q factor Related to Phase noise

• Where phase noise occur

• Mechanisms of phase noise

 

What is Phase Noise• Phase noise is the frequency domain representation of

rapid, short-term, random fluctuations in the phase of awaveform, caused by time domain instabilities

• Example :- All real oscillator have phasemodulated noise components, the phase noise componspread the power of a signal to adjacent frequencies,resulting in noise sidebands

Random variation in the period or deviation of the zero crossing poifrom their ideal position

Consider the noise free signal:

v (t ) =  Acos(2π f 0t )

PH noise is added to this signal by adding a stochasticprocess represented by φ

v (t ) =  Acos(2π f 0t  + φ(t ))

 

• Phase noise is a type of cyclostationary noise and isclosely related to jitter

• A particularly important type of phase noise is thatproduced by oscillators

• Phase noise is typically expressed in units of dBc/Hz

• it represents the noise power relative to the carriercontained in a 1 Hz bandwidth centered at a certainoffsets from the carrier

• For example, a certain signal may have a phasenoise of -80 dBc/Hz at an offset of 10 kHz and -95 dBc/Hz at an offset of 100 kHz. Phase noise canbe measured and expressed as single sideband ordouble sideband values. the IEEE has adopted thedefinition as one-half of the double sideband PSD

 

Source of Phase Noise

• Oscillator noise performance is characterized as

 jitter in the time domain and as phase noise in the

frequency domain

• Noise injected onto an oscillator by constituent

devices or by externals means both freq and amp of

o/p signal or supply voltage etc

 

How Q-factor related to Phase Noise

• Q is an indication of how much of the energy is lost

as it is transferred from the capacitor to the

inductor and vice versa

• Defined as the resonance frequency divided by the

two sided -3db bandwidth

Q =(1/PHASE NOSIE)

 

Phase Noise Mechanisms

• Effects such as nonlinearity and periodic variation of

the circuit parameters ia a cause of Phase Noise and

analysis of this quite difficult

• Oscillators Phase Noise is generated primarily

through two mechanisms distinguished by the path

into which the noise is injected

-- Feedback Oscillation signal path

-- Frequency control path

Ex:- A VCO Includes both oscillation path and

frequency control path

 

H(S)NOISE

x(t)

Vcont

+

+

Y(t)

SIGNAL PATH

H(S)

NOISE

Vcont

Vout

CONTROL PATH

The Noise x(t), appearing in these paths gives rise to distinctly

different effects

 

• Noise in signal Path :- Noise is injected into theoscillation signal path

How is y(t) Affected by x(t) ?

Representing the open loop circuit by a linear transferfunction H(s), we can Write

In the vicinity of the frequency of oscillations, ,we can approximate with the first terms in itsTaylor expansion

 

• since and typically , y(s)/x(s)

reduces to

Implying that a noise component at is

multiplied by when it appears at the output

of the oscillator. In other words the noise spectrum is

shaped by

Let us consider the term . Expressing in

polar form ,we have

 

• Equation 7.20 is called Leeson’s Equation”, this

expression reveals the dependence of the output

noise upon the Q of the tank, the center frequency

and the offset frequency

• Also includes the effect of noise on the amplitude

and the phase of the carrier the phase noise is

typically half the value given by 7.20

• Overall phase noise power with respect to carrier

depends on two other parameters as well : the

noise generated by the devices that is the

magnitude of X(jw). 

 

• The noise shaping function become sharper

• The power dissipation decrease and

• The noise injected by active devices decreases….  

• Oscillators usually experience amplitude limiting andhence nonlinearity thus “folding” the noisecomponents as shown below

Effect arises when odd order nonlinearity in theamplitude leads to intermodulation between an injectednoise components at Wn and the carrier, creating anothercomponent at 2Wo-Wn

 

• In order to represent the effect of noise folding due

to nonlinearity, leeson’s equation can by multiplied

by a factor

Were A is the actual small signal loop gain. This

relation indicate that the loop gain must be chosen as

close to unity as possible while ensuring reliable start

up. A typical value is between 2 and 3

 

Noise in Control Path :-

• The noise injected injected into the signal path mixes with

the carrier. By contrast, noise injected into the control path

affects the frequency by changing the physical properties of

the oscillator

Ex:- if a varactor is used to tune the VCO, noise on the DC

voltage applied across the diode varies the tank capacitances

and hence the resonant frequency.

In analog frequency modulation, this effect translates low

frequency noise components in the control path to the region

around the carrier

 

• To quantify the FM noise Mechanism as Shown

below

• We represent the noise per unit bandwidth as a

sinusoid with the same average power

• Denoting the gain of the VCO by Kvco and using the

narrowband FM approximation we have

•  

 

• Thus noise power at with respect to carrierpower is equal to

• In practice Kvco is proportional to the carrierfrequency

• Because for a given control voltage range, the tuningrange must be a constant percentage of the centerfrequency so as to compensate for process andtemperature variations

• The effect of this type of noise become moreprominent as Wm decrease, making 1/f noise incontrol path particularly detrimental

• The phase noise decreases indefinitely as ∆wincreases. In reality the noise reaches a relatively flatfloor because the loop does not shape the noise ofthe devices at high frequency offsets

 

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