02_basic rfic concepts

Bhaskar Banerjee, EERF 6330, Sp2013, UTD

Basic Concepts for RF Design

Prof. Bhaskar Banerjee

EERF 6330- RF IC Design


Non-linearity

Each circuit block in a system is not perfectly linear

Non-linearity causes spurious signals at frequencies other than those desired

Linearization of circuits needs heavy feedback which causes Instability issues Noise due to excess components Decreasing in gain Decreasing frequency response

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y1(t) = f [x1(t)]

y2(t) = f [x2(t)]

=) ay1(t) + by2(t) = f [ax1(t) + bx2(t)]

y(t) = f [x(t)]

=) y(t ) = f [x(t )]

Non-Linearity and Time Variance

A system is linear if its output can be expressed as a linear combination of its individual inputs.

A time-invariant system gives the same time-shift to the output as it sees in its input.

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Non-Linearity and Time Variance

Non-linearity and Time Variance depends on how you define the system

vin1(t) = A1 cos!1t

vin2(t) = A2 cos!2t

Nonlinear Time Variant

Linear Time Variant

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Gain Compression Harmonics

In single-ended circuits: In differential circuits:

Gain compression P1dB

vout(t ) 1 vin(t ) + 2 vin2 (t ) + 3 vin

3 (t ) +

vout(t ) 1 vin(t ) + 3 vin3 (t ) +

Harmonics

Vin

Vout

Pin(dBm)

Pout(dBm)

1dBOP1dB

IP1dB

Psat

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Gain Compression

http://en.wikipedia.org/wiki/List_of_trigonometric_identities

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y(t) =2A2

2+

1A+

33A3

4

cos!t+

2A2

2cos 2!t+

3A3

4cos 3!t+ . . .

Gain Compression

DC Fundamental Harmonics

Observations Even order harmonics result from j with even j, and vanish for

systems with odd symmetry (e.g. fully-differential systems - in ideal case)

nth order harmonics amplitude is proportional to An and higher powers of A

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Gain Compression

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Gain Compression: Effect on the signal

FM signal: No information on the amplitude - OK with gain compression

AM signal: Information contained in the amplitude - Distorted with gain compression

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Desensitization and BlockingConsider a strong interferer in the band of our desired signal which is considerably weaker.

Hence the large signal from the interferer desensitizes the receiver and acts as a blocker.

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Example on Gain Compression A 900-MHz GSM transmitter delivers a power of 1 W to the antenna. By how

much must the second harmonic of the signal be suppressed (filtered) so that it does not desensitize a 1.8-GHz receiver having P1dB = -25 dBm? Assume the receiver is 1 m away and the 1.8-GHz signal is attenuated by 10 dB as it propagates across this distance.

Solution: The output power at 900 MHz is equal to +30 dBm. With an attenuation of 10 dB, the second harmonic must not exceed -15 dBm at the transmitter antenna so that it is below P1dB of the receiver. Thus, the second harmonic must remain at least 45 dB below the fundamental at the TX output. In practice, this interference must be another several dB lower to ensure the RX does not compress

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y(t) =h1 +

323A2

21 + m

2

2 +m2

2 cos 2!mt+ 2m cos!mti

A1 cos!1t+ ...

Cross-Modulation Consider an AM signal as the interferer: The output signal becomes:

Clearly, the desired signal at the output picks up an amplitude modulation.

A2(1 +m cos!mt) cos!2t

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y(t) = 1(A1 cos!1t+A2 cos!2t) + 2(A1 cos!1t+A2 cos!2t)2 + ...

1A1 +

343A

31 +

323A1A

22

cos!1t+

1A2 +

343A

32 +

323A2A

21

cos!1t

33A21A24

cos(2!1 + !2)t+33A21A2

4cos(2!1 !2)t

33A1A224

cos(2!2 + !1)t+33A1A22

4cos(2!2 !1)t

Intermodulation Let us consider a two tone input: Going through the non-linear system we get:

Expanding an combining terms, gives us the following products:

x(t) = A1 cos!1t+A2 cos!2t

Fund:

IM Terms:

and other harmonics ...13


Intermodulation

Intermodulation Applying the appropriate trigonometric identities gives the following

frequencies While the 2nd and 3rd harmonics are outside of the passband, 2f1-f2

and 2f2-f1 are close to f1 and f2

Amplitude

Frequency

f2-f1 2f2-f12f1-f2 f1 f2 2f1 2f2f1+f2 2f2+f12f1+f23f1 3f2

Narrowband system

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NonlinearSystem

Harmonic Multiples of fundamental frequency

Intermodulation (IM) Unwanted harmonic caused by multiple inputs to a nonlinear system 3rd IM can be very close to the fundamental frequency: Hence, can be very difficult to filter out!

FundamentalFrequency

890, 900

Harmonic

1780 (2*890), 1800 (2*900),2670 (3*890), 2700 (3*900)

2nd IM1790 (890 + 900),

10 (900 - 890)

3rd IM

2680 (2*890 + 900),2690 (890 + 2*900),880 (2*890 - 900), 910 (2*900 - 890 )

Effects of Intermodulation

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Intermodulation

Intermodulation These products, 2f1-f2 and 2f2-f1, affect the desired signal

2f2-f12f1-f2 f1 f2

Desired channel

Preselect filter response

Frequency

Rx band

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POUT

As POUT increases assuming no saturationINTERCEPT!

IP3 (3rd Order Intercept Point) 3rd Order means 3x slope in log scale Assuming Signal power does not saturate, as POUT increases, IM3 Power increases 3x faster. At some point, intercept occurs! IIP3(Input IP3), OIP3(Output IP3) IP3 is an important figure of merit in specifying linearity.

Intermodulation

Actual Signal Power

Signal PowerAssuming Linear

IM3 Power

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Intermodulation

Hence, to the 1st order, the difference in the P1dB and IIP3 of a system ~ 10 dB

(IIP3 is higher than the P1dB)

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IIP3 (dBm) =P (dB)

2+ Pin (dBm)

Intermodulation: Estimation Inter-modulation

Third-order intercept point (IP3) IIP3: Input IP3 OIP3: Output IP3

2f2-f12f1-f2 f1 f2

P

Pin

Pout

IIP3

OIP3

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1

3

Main signal power

IM power

P

P/2

Pi

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Intermodulation

-20 dBm

+10 dBm

-40 dBm

Non-linear block

IIP3 = Pin + P/2 = (-20 dBm) + (50 dB)/2 = 5 dBm

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Intermodulation

-15 dBm

+15 dBm

-25 dBm

Non-linear block


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Intermodulation

-10 dBm

+20 dBm

-10 dBm

Non-linear block


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Intermodulation

-5 dBm

+25 dBm

+5 dBm

Non-linear block


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Intermodulation

+5 dBm

+35 dBm

Non-linear block

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Intermodulation

Intermodulation Effective IIP3 of cascaded stages

G1 G2

IIP31 IIP32

Gn

IIP3n

1IIP32eff

=1

IIP321+

G21IIP322

+ ...+G21G

22...G

2n1

IIP32n

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Non-linearity

Harmonic Distortion: Signal by itself(P1dB)

Signal + Interferer: Blocking/Desensitization

Intermodulation: IIP3

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Noise Thermal Noise in resistors

k = 1.38 1023(J/K)T = Absolute Temperature in KelvinB = Bandwidth of the channel in Hz

*

*

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v2nB

= 4kT R (V 2/Hz)

i2nB

=4kT

R(A2/Hz)


Noise Shot Noise at p-n Junctions

Flicker Noise (1/f noise or Pink Noise)

N2 = Kfn BN : rms noise (voltage or current)

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i2nB

= 2q IDC (A2/Hz)


Noise

Input referred Noise

- All the noise in a noisy two-port network can be referred to the input as a voltage noise source and current noise source, which are, in general, correlated

vn can be calculated by shorting the inputin can be calculated by opening the input

NoisyCircuitinput output Noiseless

Circuit

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Signal to Noise Ratio (SNR)

Noise factor (F)

Noise figure (NF)

Noise

NF = 10log10F = 10log10SNRinSNRout

Noise Factor (F ) =SNRinSNRout

SNR =Signal Power

Total Noise Power (Over the signal bandwidth)

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F =Si/NiSo/No

=SiNi NoSo

Noise Figure

Si

Ni

So

NoGain, G

Noise Factor, FSo = G Si

No = G Ni +NA

F =SiNi G Ni +NA

G Si

=) F = 1 + NAG Ni

=) NA = G Ni (F 1)

Noise added by the amplifier

Note: F is defined with respect to the same input referred thermal noise 31


Noise: Cascaded Stages

Si

Ni

So

NoG1F1

G2F2

S1

N1

So = G2 S1 = G1 G2 Si

No = G2 N1 +G2 Ni (F2 1)N1 = G1 Ni +G1 Ni (F1 1) = G1 F1 Ni

=) No = G1 G2 F1 Ni +G2 Ni (F2 1)

Feff =SiNi

NoSo

=SiNi

G1 G2 F1 Ni +G2 Ni (F2 1)G1 G2 Si

=) Feff = F1 + F2 1G1

Friis Formula

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Ftot = 1 + (F1 1) + F21G1 + F31G1G2 + ...+ Fm1G1G2...Gm1

Cascaded Stages

Noise factor of cascaded stages Assumption: each stage is conjugately matched Friis equation

G1 G2

F1 F2

Gm

Fm

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Cascaded Stages

Noise factor and noise figure with a passive lossy stage Passive lossy stage with loss (Pin/Pout), L , has a noise factor

of L Effective noise factor of the following two stages cascade is

loss=L F1

lossystage

Feff = L+F1 11L

= L F1

NFeff = 10log10(L F1) = 10log10(L) +NF1 = L|dB +NF1

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PRS = kT = 174 dBm/Hz at 300K

PRS is the source resistance Noise Power (per unit bandwidth)Psig is the Signal Power

B is the channel bandwidth

Psig|dBm = PRS |dBm/Hz + NF |dB + SNRmin|dB + 10log10B

SNRin =Psig

PRS BNF =SNRinSNRout

Sensitivity and Dynamic Range

Psig = PRS NF SNRout B

Pin,min|dBm = 174 dBm/Hz + NF |dB + SNRmin|dB + 10log10B

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Pin,min|dBm = 174 dBm/Hz + 10log10B + NF |dB + SNRmin|dB

DR = Max Tolerable SignalMin Detectable Signal


Noise Floor (F) of the system (referred to the input)

Dynamic Range (DR)

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Sensitivity and Dynamic RangePout

PinPIIP3Pin,max

POIP3

Fo (Output Noise)

Fundamental

IM31

3

Po

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The Power level at which the IM3 term becomes large enough as the Noise Floor - and we start getting the spurious modulation signals at the output - determines our maximum spur-free tolerable power.

In last figure,

And if G is the power gain of the circuit, then at the IP3 point,POIP3 = PIIP3 + G, and the output noise floor FO = F + G.

This gives,


POIP3 FoPIIP3 Pin,max = 3

Pin,max =2PIIP3 + F

3

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Pin,max = 2PIIP3+F3Pin,min = F + SNRmin

BDR = P1dB F SNRmin


Hence,

SFDR = Pin,max Pin,min= 2(PIIP3F )3 SNRmin

Spurious Free Dynamic Range

Blocking Dynamic Range (BDR)Here we assume, Pin,max = P1dB,

Hence,

(NB: theoretically, P1dB ~ PIIP3 - 10 dB)

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Example: Dynamic Range

Consider an amplifier with the following specification

Gain BW NF P1dB IIP3

30 dB 200 MHz 6 dB 30 dBm 40 dBm

MDS is 6 dB above thermal noise power level

Blocking Dynamic Range = ?Spurious Free Dynamic Range = ?

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Example: Dynamic Range

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Example: Isolation requirement in duplexer

FDD Front-end

Leakage Signal from PA desensitizes the LNA

Require HIGH ISOLATION at the Duplexer

BDR = 100 dB, MDS = -125 dBm PA output power = 0.5 W

Required isolation = ?

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Example: Isolation requirement in duplexerP1dB,LNA = BDR+MDS = 100 dB 125 dBm = 25 dBm

Leakage power from the PA should be (significantly) less than P1dB of the LNA!

Required Isolation = Pout,PAP1dB,LNA = 27 dBm(25 dBm) = 52 dB

Pout,PA = 10log500 mW1 mW

= 27 dBm

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Example: NF of a Receiver Chain

Overall Noise Figure = ?

Diplexer

LNAPre-select

Filter

Image

Rejection

Mixer

IF SAW

Filter

I.L.=4dBConversion

Gain=5dB

NF=8dB

Gain=18dB

NF=2dB

I.L.=1.5dBI.L.=1dB

Rx

Tx

Antenna

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Diplexer

LNAPre-select

Filter

Image

Rejection

Mixer

IF SAW

Filter

I.L.=4dBConversion

Gain=5dB

NF=8dB

Gain=18dB

NF=2dB

I.L.=1.5dBI.L.=1dB

Rx

Tx

Antenna

Example: NF of a Receiver ChainMethod 1: Brute force Friis Formula

G1 = -1 dBNF1 = 1 dB

G2 = -1.5 dBNF2 = 1.5 dB

G3 = 18 dBNF3 = 2 dB

G4 = 5 dBNF4 = 8 dB

G5 = -4 dBNF5 = 4 dB

Ftot = F1 +F2 1G1

+F3 1G1 G2 +

F4 1G1 G2 G3 +

F5 1G1 G2 G3 G4

Ftot = 10110+

10 1.510 110

110

+10 210 1

10110 101.510 +

10 810 110

110 101.510 10 1810 +

10 410 110

110 101.510 10 1810 10 510

Ftot = 2.98 => NFtot = 10logFtot = 4.7 dB45


Diplexer

LNAPre-select

Filter

Image

Rejection

Mixer

IF SAW

Filter

I.L.=4dBConversion

Gain=5dB

NF=8dB

Gain=18dB

NF=2dB

I.L.=1.5dBI.L.=1dB

Rx

Tx

Antenna

Example: NF of a Receiver Chain

G1 = -1 dB -1.5 dB + 18 dB = 15.5 dBNF1 = 1 dB + 1.5 dB + 2 dB = 4.5 dB

G2 = 5 dBNF2 = 4.5 dB

G3 = -4 dBNF3 = 4 dB

Method II: Combine Lossy stage and active stages, then Friis formula

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02_basic rfic concepts

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