Download - Rf Lna Slides

Dr. Ahmed Bassyouni 1

Dr. Ahmed M. BassyouniDr. Ahmed M. Bassyouni Research ProfessorResearch Professor

Electrical and Computer Engineering DepartmentElectrical and Computer Engineering DepartmentBoise State University, IdahoBoise State University, Idaho

On-chip RF On-chip RF Transceiver CircuitsTransceiver Circuits


A Design Approach for Sub-micronCMOS Low Noise Amplifier

Electrical Engineering Department

Boise State University, Boise Idaho


Receiver channel


RF Receiver Sensitivity

Receiver sensitivity Sx is the minimum RF signal at matched impedance input that LNA can amplify to adequate SNR at the Rx output.

Sx = 10 Log [ Pin / 1 mw ] dBm


RF input signal

Calculate RF input voltage signal Vin

knowing receiver sensitivity Sx in dBm

Sx = 10 Log [ P / 1mw ]

P = 10[(Sx/10) - 3]

P = Vin2 / R (R = 50)

Vin = ( 50 P)1/2

Vin = 7.07 [ 10[(Sx/10) - 3] ]


RF input & sensitivity

Rx Sx (dBm) Vin (V)

DECT - 83 15.8

Bluetooth - 85 12.57

GSM - 102 1.8


Noise Power

Matching Rs = Rin

Vin(rms) = (1/4) Vrms2

N = k T f


Noise Floor

Noise Floor = 10 Log ( k Tf ) dBmNoise Floor = - 173.8 dBm / Hz + 10 Log (f )

More sensitive Rx is required for narrow band.


Continue…

Parameter DECT GSMBW 1.7 MHz 200 kHz

Noise Floor - 111.5 dBm -120.8 dBm(SNR)in 28.5 dB 18.8 dB(SNR)out 10.5 dB 9 dB

BER 10-3 10-3

Required NF 18.5 9dB


Sensitivity Equation

Pin (min) = Sensitivity Sx

Sx = -174 dBm / Hz + SNR out (min)

+ NF + 10 Log (f)


Bluetooth Standard Specifications

Sx = - 70 dB

SNRout (min) = 21 dB for BER<10-3

f = 1MHz

NF = 174 dBm / Hz - SNRout(min)-10Log(f ) + Sx

NF = 23 dB


Noise Figure Definition

Noise Factor F = [ SNRin / SNRout ]

NF = 10 Log F dB


NFRx

NFRx = NFLNA + [(NFMXR - 1) / GLNA]

+ [(NFIF - 1) / GLNA . GMXR]


Dynamic Range Equation

Dynamic Range = P-1dB - Noise Floor

= P-1dB + 174 - NF - GLNA - 10 Log f


Spurious Free Dynamic Range

SFDR = (2/3) [P3IP + 174 - 10 Log (f)] - NF -GLNA


Linearity Linearity of the receiver determines the

maximum allowable signal level to its input.

Nonlinear system V0 = f (V0)

V0 = a0 + a1 Vi + a2 Vi2 + a3 Vi3

a0 dc……. offset term

a1 Vi……. linear term

a2 Vi2…... quadratic term

a3 Vi3…... 3th order term


Gain of Two-Tones Input

Apply Vi = A1 cos 1t + A2 cos 2t

At: A1 = A and A2 = 0 (neglect Harmonics)

V0 = [a1 + (3/4) a3 A2] cos 1t

Gain = a1 + (3/4) a3 A2

If: a3 < 0Then: the gain approaches zero for sufficiently large input signals.


1-dB Compression Point

20 Log [ a1 + (3/4)a3A2-1dB] =20 Log (a1) - 1dB

A-1dB = [ 0.145 |ai/a3| ]1/2


Intermodulation IP3

IP3 is determined by applying a two-tone test

to the amplifier two equal sinusoidal signals

with 1, 2

V0 = a1 A[cos 1t + cos 2t] +

(3/4)a3A3 [cos(2 1- 2)t + cos(2 2 - 1)t]


3th Order Components


OIP3:3rd order of Distortion

The theoretical output level where 3th

order distortion components

(21 - 2) & (2 2 - 1) equal

the desired output signal level is called

the 3th order output intercept.


Distortion Condition

OIP3, IIP3: 3rd order output, and input intercept.

Distortion occurs at the applied input level

Ain = IIP3 a1 AIIP3 = (3/4) a3 A3IIP3

AIIP3 = [(3/4) |a1/a3|]


Spurious-Free Dynamic RangeSFDR


SFDR Equation

SFDR- the maximum relative level of interference that a receiver can tolerate.

Nfloor = -174 dBm/Hz + NF + 10 Log (f)

Pin max = (1/3) ( Nfloor + 2IIP3 )

SFDR = (2/3) ( IIP3 - Nfloor ) - SNRmin


Basic LNA Functions

1. Provide gain and receiver dynamic range.

2. Establish receiver noise figure (NF<2dB.

3. Provide receiver linearity.

4. Provide receiver sensitivity, and selectivity.

5. Provide 50 input impedance.

6. Minimum power dissipation.

7. Provide receiver stability.


LNA as a Nonlinear System

Si(t) S0(t)

S0(t) a1Si(t)+a2Si2(t)+a3Si

3(t)

LNA


Output HarmonicsConsider Si(t) = S1 cos 1t

Sa(t)= a1S1 cos 1t + a2S12 cos2 1t + a3S1

3 cos31t

= a1S1 cos 1t (Desired output from linear system)

+ a2S12 (1/2) (cos 2 1t + 1) (DC Shift)

+ a3S13 (1/4) (cos 3 1t + 3 cos 1t) (Gain Compression)

+ a4S14 (1/8) (cos 4 1t + 4 cos 2 1t + 3)


Desensitization and Blocking

Si(t) = S1 cos 1t + S2 cos 2t

S0(t) = (a1S1 + (3/4) a3S13 + (3/2)a3 S1S2

2) cos 1t + …..

If S2 >> S1

S0(t) = (a1 + (3/2) a3S22) S1 cos 1t + ….

If a3 is negative, the Gain decreases .


MOSFET EquationsN MOSFET drain saturation current effected by mobility

degradation

ID = 0.5 Cox.(W/L) (VGS - VT)2 / [1 + (VGS - VT)]

The transconductance

gm = dID/dVGS = 2ID/ (VGS - VT)

(gm / I) = 2/ (VGS - VT)


The Unity Current Gain Frequency

fT = gm / [2 (CGS - CGD)] gm/ 2 CGS

The 3rd order IP3 caused by mobility degradation

IP3 2 [ 2/3(VGS - VT) / ]1/2


CMOS Noise Model


CMOS Noise Model(Id

2/f) = 4kT gdo + (k/f) (gm2 / WLCox

2)

Vg2 = 4kT Rg , Rg = (1/ 5gdo)

= a bias dependant factor.

(2/3) < <1 (Long channel) >1 (Short Channel)

gdo zero-bias drain conductance.

gate noise-factor.

= 4/3 (Long channel) =2 (Short Channel)


Factor for Short Channel CMOS


LNA Design Considerations

• The Gain is typically 10 dB < Gain <10 dB Sufficient gain to minimize

the influence of noise, but not too

high, otherwise interfering signals will exceed mixer’s linearity.

• NF must be as little as possible, up to the application. Bluetooth NF < 4 dB.

• Good linearity to accommodate large signals without distraction.

• Zin = 50 to ensure high quality gain-frequency for narrow band.

• Minimum power dissipation (can be achieved with scaled CMOS).


MOSFET Small Signal Model • Assuming rg = Cgd = 0 ,

r0 = << T

• Noise Factor


Impedance Matching for LNA

inductor degeneration Topology

Matching criteria


Effective transconductance Gm

Iin = Vs / Zin

Iout = Iin . 1/ (S Cgs) . gm

Gm eff = T / [ (Rs + T Ls) ]

where

T = gm / Cgs


The Q factor of LNA input Resonance

Q = Vout / Vin

= 1/ [ 1 - 2 LC + j R C]

Vgs = Q . Vs

Gmeff = Q . gm

NF = 1 + ( / Q2 Rs gm )


LNA Design ProcedureCMOS LNA cascode with

L degeneration topology is selected.

1. Choose Ls smallest technological value Ls ~ ( 0.7 to 3 nH)

2. Find MOSFET unity gain frequency T

T = gm / Cgs = Rs | Ls


Continue…LNA Design Procedure

3. Calculate the parameter = 2 / 5

4. Determine the optimal quality factor

Q = [ 1 + (1/ ) ]1/2

5. Calculate Lg

Lg = [Q Rs / 0] - Ls

6. Find Cgs

Cgs = 1 / [ 02 (Lg + Ls) ]



7. Choosing the possible value of CMOS Length ‘L’ [ m ] , the device Width ‘W’ is obtained as

W = 3/2 Cgs / Cox L

8. Find the CMOS transconductance gm

gm = T Cgs

9. Find the device voltage Veff

Veff = VGs - VT

= gm L / n Cox W



10 . Find the device drain current

ID = 0.5 gm Veff

11. Calculate the noise factor F



12. LNA voltage gain equation

Q is the quality factor of drain load parallel resonance Ld and Cd

Assume 0 = 1 / (Ld Cd)Tip: Ld ~ 7 nH , and Q 4 for gain 20 dB


Single Ended LNA


LNA Spec’s

f = 2.4 G Hz IIP3=-3dBm

NF = 3.2 dB

S21 = 20 dB

Power = 0 dBm

Vdd = 1.5 V

Tech 0.1 m CMOS