analog and telecommunication electronics: mini-project€¦ · mini-project design of a single...

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Noise definitionOrigin of noise and modelization of components

Low-Noise AmplifierEquivalent input noise of BJT in CE

Design of a LNA

Analog and telecommunication electronics:Mini-project

Design of a single stage bipolartransistor low-noise amplifier

L. Nyssens

Polytechnic University of Turin

May 31, 2016

L. Nyssens Analog and telecommunication electronics: Mini-project

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Design of a LNA

Table of contents

1 Noise definition

2 Origin of noise and modelization of componentsSource of noiseModelization of components

3 Low-Noise AmplifierParametersLNA in a receiver chain

4 Equivalent input noise of BJT in CEInput current and voltage noise generator of a BJT

5 Design of a LNAProcedureExample


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Design of a LNA

Noise definition

• ”Any unwanted disturbance that obscures or interferes with adesired signal”

• Random process with a zero average value but carrying non zeropower

2 origins of noise Interferences from an external source

Intrinsic noise


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Design of a LNA

Source of noiseModelization of components

Table of contents

1 Noise definition






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Design of a LNA


Thermal noise

• Thermal noise is due to carrier velocity fluctuations→ Proportional to the absolute temperature (zero at 0 K)• Power spectral density:

p(w) = kBT

⇒ Flat spectrum, thus white noise (actually until ≈ 100 GHz)


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Design of a LNA


Shot noise

Shot noise is present in a pn junction.

• Direct current fluctuation depending on carrier’s energy andvelocity direction that crosses the potential barrier of the junction.• Depends on the bias point: direct current ID .• Spectral density constant up to the gigahertz region, thendecreases with 1/f 2. Here consider only the flat region:

Si = I 2 = 2qID


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Design of a LNA


Flicker noise or 1/f noise

Carrier population fluctuations are related to the Flicker noise.• Flicker noise is dominant at low frequencies.• Current spectral density:

Si = I 2 = K1I γDf b

ID the direct current

K1 constant, fits a particular device

γ and b constants

• In general b ' 1, therefore it is often called 1/f noiseDominant sources of noise in the megahertz region: thermal, shotand 1/f noise.


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Design of a LNA


Noise model of a Resistance

Actual value of the resistance is an average value R andfluctuations due to thermal noise modeled by:

Series voltage noise generator en

Sen = E 2n = 4kBTR

Shunt current noise generator in

Sin = I 2n = 4kBTG

• Capacitance and inductance noiseless in itself, but parasiticresistance contains noise.


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Design of a LNA


Bipolar transistor

Active forward region, Cµ neglected : valid up to fβ = fT/√β0.

Sinc = 2qIC Sinb = 2qIB Sif =2qfLI

γB

fSex = 4kBTrx Sens = 4kBTRS

• The other resistances rπ, ro are not physical, thus not noisy.


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Design of a LNA

ParametersLNA in a receiver chain

Table of contents

1 Noise definition






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Design of a LNA


Parameters

The purpose of a low-noise amplifier is to amplify a signal with alow Signal-to-Noise ratio (S/N).Noise is a low power signal as well as the useful signal.→ Amplifier is considered to be working in its linear region for itsnoise analysis (small-signal region).

Figures of merit: general amplifier and specific low-noise:

Gain, bandwidth, 1 dB compression level, IP3.

Noise Figure.

Noise Temperature (equivalent to noise figure).

Minimum Detectable Signal.


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Design of a LNA


Noise Figure and Noise Temperature

The Noise Figure (F or NF ) represents the total available noisepower generated by the device itself. It can be defined as:

F =(S/N)in

(S/N)out

⇒ F > 1 and F must be as close as possible to 1.

Noise Temperature (Tn) is equivalent to the Noise Figure.

Tn = T0(F − 1)

Generally, T0 = 290 K. Tn is a normalized quantity useful tocharacterize very low-noise devices.


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Design of a LNA


LNA in a receiver chain

First element (afterfilter, transceiver)

Good gain

Low NF : NF < 3dB

Friis formula:

Ftot = 1 + (F1 − 1) +F2 − 1

G1+

F3 − 1

G1G2+

F4 − 1

G1G2G3+ ...


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Design of a LNA

Input current and voltage noise generator of a BJT

Table of contents

1 Noise definition






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Design of a LNA


Equivalent input noise of a BJT

Inside the shot noise region:Sen = E 2

n = 4kBTrx + 2qIC r2e

Sin = I 2n = 2qIB


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Design of a LNA


Equivalent input noise of a BJT in CE

The optimal noise figure and source resistance:

Fopt = 1 +

√2rxreβ0

+1

β0R0 =

√0.05

rxβ0

IC+ (0.025)2 β0

I 2C

In a common-emitter configuration:

Seni = EniE ∗ni ' E 2ns + E 2

n ·(RS+RD

RD

)2

+I 2n

∣∣∣RS+ 1jωCC

∣∣∣2 + I 2DR

2S

+E2E

1+(ωRECE )2 +E2C

|G ′v |2


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Design of a LNA

ProcedureExample

Table of contents

1 Noise definition






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Design of a LNA

ProcedureExample

Procedure

Procedure of LNA design

Optimize noise performances: select the device and its biaspoint (for a specified RS and Bandwidth).

Chose a configuration (CE, CB, ...) to meet the specifications:gain, bandwidth, impedance. Add feedback if necessary.

Make an analysis without noise and check if all thespecifications are met. If not, change bias point or device andstart from the beginning.


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Design of a LNA

ProcedureExample

Example’s Specifications

Specifications:

RS = 10[kΩ].

F as low as possible with F < 3 dB at T = 290 [K].

A gain Vout/Vin = 50[V /V ] with maximum 0.5 dB ofdeviation inside the bandwidth.

A bandwidth from 1 [kHz] to 100 [kHz].


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Design of a LNA

ProcedureExample

Device selection

⇒ Select BJT

Frequency [kHz] Noise figure [dB]2N4124 2N4403

range of IC [µA] range of IC [µA]1 < 1 [2;30] [4;20]

10 < 1 [4;200] [3;200]100 < 1 [5;250] [10;100]

1000 < 1 [15;250] no

⇒ Select 2N4124


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Design of a LNA

ProcedureExample

Bias point

• Need to operate in the shot noise region ⇒ IC ∈ [10; 100]µA.

R0 '

√(0.025)2β0

I 2C

= RS

With β0 ≈ 100⇒ IC = 25µA.


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Design of a LNA

ProcedureExample

Select configuration

• Common-Emitter: high gain, relatively small bandwidth.

RE bias point.

RD trade-off.

RC fixes the gain.

CE sets fc,low .

Ccc sets fc,high.

CC and CC2 couplingcapacitances: large.


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Design of a LNA

ProcedureExample

References

P.R. GRAY, P.J. HURST, S.H. LEWIS and R.G. MEYER,Analysis and Design of Analog Integrated Circuits, John Wileyand Sons, 2009, USA, 5th edition, pp. 736-795.

G. GHIONE and M. PIROLA, Notes from the courseMicrowave Electronics, 2014.

C.D. MOTCHENBACHER and J.A. CONNELLY, Low-NoiseElectronic System Design, John Wiley and Sons, 1993, USA.

A. KONCZAKOWSKA and B.M. WILAMOWSKI, Noise inSemiconductor Devices, Chapter 11, CRC Press, 2011, 2ndedition.


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Design of a LNA

ProcedureExample

Noise performances

Shot noise region: OK1/f noise underestimated (too low corner frequency).High frequency noise underestimated (too large fβ).


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Design of a LNA

ProcedureExample

Gain, bandwidth

fc,low fc,high in-band gain Gain at 1 [kHz] Gain at 120 [kHz]

240 [Hz] 320 [kHz] 52.4 [V/V] 51.2 [V/V] 49.7 [V/V]Zin at 3 [kHz] Zout at 3 [kHz] MDS= enirms enorms ensrms

90 [kΩ] 56 [kΩ] 4.34 [µV ] 184 [µV ] 4.05 [µV ]

rms values computed only inside the bandwidth (1 kHz to 100 kHz).


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Design of a LNA

ProcedureExample

Sensitivity to RS

NF in blue, gain in green.

RS from 10 kΩ to 500 Ω. RS from 10 kΩ to 200 kΩ.NF = 3dB for RS ≈ 500Ω or 120kΩ.


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