08 Noise Fundamentals

Bhaskar Banerjee, EERF 6330, Sp2013, UTD

Noise Fundamentals

Prof. Bhaskar Banerjee

EERF 6330- RF IC Design


Outline

Noise as a statistical quantity Noise Power Spectral Density

Input Referred Noise Noise in Transistors, Resistors Noise Figure Calculation Noise Parameters

Reading: RF Microelectronics, B. Razavi

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Noise as a Random Process

The avg current = VB/R but cannot estimate/calculate instantaneous value.

Estimate the avg power over long enough time.

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Measurement of Noise Spectrum

To measure the energy content at a given frequency, we filter out everything else and measure the power over 1 Hz bandwidth at the frequency of interest.

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Power Spectral Density (PSD) of Noise

Total area under Sx(f) represents the avg power carried by x(t)

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Two-sided One-sided


Example of Noise Spectrum

A resistor of value R1 generates a noise voltage whose one-sided PSD is given by

where k = 1.38 10-23 J/K denotes the Boltzmann constant and T the absolute temperature. Such a flat PSD is called white because, like white light, it contains all frequencies with equal power levels.(a) What is the total average power carried by the noise voltage?(b) What is the dimension of Sv(f)?(c) Calculate the noise voltage for a 50- resistor in 1 Hz at room temperature.

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Example of Noise Spectrum

(a) What is the total average power carried by the noise voltage?The area under Sv(f) appears to be infinite, an implausible result because the resistor noise arises from the finite ambient heat. In reality, Sv(f) begins to fall at f > 1 THz, exhibiting a finite total energy, i.e., thermal noise is not quite white.(b) What is the dimension of Sv(f)?The dimension of Sv(f) is voltage squared per unit bandwidth (V2/Hz)(c) Calculate the noise voltage for a 50- resistor in 1 Hz at room temperature.For a 50- resistor at T = 300 K:

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Effect of Transfer Function on Noise

Define PSD to allow many of the frequency-domain operations used with deterministic signals to be applied to random signals as well.

Noise can be modeled by a series voltage source or a parallel current source

Polarity of the sources is unimportant but must be kept same throughout the calculations

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Example of Device NoiseSketch the PSD of the noise voltage measured across the parallel RLC tank depicted in figure below.

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Modeling the noise of R1 by a current source and noting that the transfer function Vn/In1 is, in fact, equal to the impedance of the tank, ZT , we write

At f0, L1 and C1 resonate, reducing the circuit to only R1. Thus, the output noise at f0 is simply equal to 4kTR1. At lower or higher frequencies, the impedance of the tank falls and so does the output noise.


Resistor as an Energy Source? What happens if both are at the same temperature? Suppose R2 is held at T = 0 K

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This quantity reaches a max if R2 = R1(Maximum Power Transfer Theorem)

Then, PR2,max = kT (Available Noise Power) = -173.8 dBm/Hz @ 300 K


Theorem about Lossy Circuit

If the real part of the impedance seen between two terminals of a passive (reciprocal) network is equal to Re{Zout}, then the PSD of the thermal noise seen between these terminals is given by 4kTRe{Zout}

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An example of transmitting antenna, with radiation resistance Rrad

Bhaskar Banerjee, EERF 6330, Sp2013, UTD 12

Noise Figure of Lossy Circuits

LC-filter, needs to have well-defined resistive input/output impedances

A Linear Time Invariant passive with real input and output impedance can be represented using a Thevenin equivalent circuit with the PSD given by 4kTRout.*

*cf. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed., New York: McGraw Hill, 1991.


Noise in MOSFETs

Thermal noise of MOS transistors operating in the saturation region is approximated by a current source tied between the source and drain terminals, or can be modeled by a voltage source in series with gate.

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Induced Gate Noise At very high frequencies thermal noise current flowing

through the channel couples to the gate capacitively to generate gate-induced noise current.

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Example: If W = 1 m, L = 45 nm, and sheet resistance = 15 , then the gate resistance, RG = 333 .


Flicker Noise

A MOSFET having a small-signal voltage source of magnitude V1 in series with its gate is equivalent to a device with a current source of value gmV1 tied between drain and source.

Thus,

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Noise in Bipolar Transistors

Bipolar transistors contain physical resistances in their base, emitter, and collector regions, all of which generate thermal noise. Moreover, they also suffer from shot noise associated with the transport of carriers across the base-emitter junction.

In low-noise circuits, the base resistance thermal noise and the collector current shot noise become dominant. For this reason, wide transistors biased at high current levels are employed.

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Input Referred Noise

Noise of a 2-port system can be modeled by 2 correlated noise generators:

- a series voltage source (vn)- a parallel current source (in)


Input Referred Noise

To find the equivalent noise sources, we evaluate the output noise $ power by shorting and opening the input.

* *


Input Referred Noise: Example

Calculate the input-referred noise of the common-gate stage depicted in figure below (left). Assume I1 is ideal and neglect the noise of R1.

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Noise Voltage Noise Current


Importance of Impedances in NF

The output noise of a circuit depends on the output impedance of the preceding stage.

Modeling the noise of the circuit by input-referred sources, we observe that some of noise current flows through Z1, generating a noise voltage at the input that depends on |Z1|. Thus, the output noise, Vn,out, also depends on |Z1|.

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NF =SNRinSNRout

NF = 1 +(Vn + InRS)2

4kTRS

NF =V 2n,outA2

14kTRS


Calculating Noise Figure

For simulation purposes, we can rewrite NF as:where, A = total voltage gain from Vin to Vout and Vn,out is the total output noise voltage



NF must be specified with respect to a source impedance-typically 50 Reduce the right hand side to a simpler form:

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NF =V 2n,outA2

14kTRS



Either of the following: Calculate the output noise due to the amplifier, divide it by the

gain, normalize it to 4kTRs and add 1 to the result. Divide total output noise by the gain from Vin to Vout and

normalize the result to the noise of Rs.

Valid even if no actual power is transferred. So long as the derivations incorporate noise and signal voltages, no inconsistency arises in the presence of impedance mismatches or even infinite input impedances.

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V 2n,out = 4kT (RS ||RP ) A =RP

RS +RP

NF = 4kT (RS ||RP ) (RS +RP )2

R2P 14kTRS

= 1 +RSRP


Calculating Noise Figure - Example: A Resistor

To minimize NF, RP should be large.To maximize power transfer RP = RS => NF = 2 ~ 3 dB!


Calculating Noise Figure - Example: Amplifier Determine the noise figure of the common-source stage shown in below (left)

with respect to a source impedance RS. Neglect the capacitances and flicker noise of M1 and assume I1 is ideal.

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This result implies that the NF falls as RS rises. Does this mean that, even though the amplifier remains unchanged, the overall system noise performance improves as RS increases?!


Noise Figure of Lossy Circuits

L =PinPout

=V 2inV 2TH

RoutRS

V 2n,out = 4kTRout R2L

(RL +Rout)2

Av =VTHVin

RLRL +Rout

NF = 4kTRout V2in

V 2TH 14kTRS

= L


Source Resistance

For RS = 0, the voltage noise is the important component.

For RS = , the current noise is the important component.

For large RS, prefer low current noise (MOS), for small RS select low voltage noise (Bipolar).

For a given RS, there is an optimal ratio of voltage to current noise for low noise figure.


Classical Noise Theory

Lets assume that in and vn are uncorrelated.Total output Noise Voltage:



All noise represented as single noise source:

Noise Figure:



Define:

which gives,

Optimum RS:

Minimum Noise Figure for ROPT:



Hence, under the assumption that the in and vn noise sources are uncorrelated, the minimum noise figure, Fmin:



Rn basically the noise sensitivity parameter

Rate of deviation from Fmin is governed by the Rn term. We want Rn to be as small as possible as then we can tolerate impedance mismatch at the input with lesser effect on Fmin.

Ropt is dependent on Frequency, Bias and Device Size. Very important to optimize that with respect to all of them.


Noise Parameters Four Noise Parameters:

Minimum Noise Figure (NFmin) Noise Resistance (Rn) Optimum Source Conductance (Gs,opt) Optimum Source Susceptance (Bs,opt)

NF

Gs

BsGs,opt

Bs,opt

NFminRn

08 Noise Fundamentals

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