EE 647: Radio Frequency Integrated Circuits Module 1 ...

EE 647: Radio Frequency Integrated Circuits

Module 1: Fundamentals of RF

Circuits and Systems

Nagarjuna Nallam

Department of Electronics and Electrical Engineering,

Indian Institute of Technology Guwahati,

Guwahati, Assam 781039

Transceiver specification: Frequency

EE 647: Radio Frequency Integrated Circuits Nagarjuna Nallam, IIT Guwahati

Tx Rx

f =?

88.1 M 108.1 M 890 M 960 M

GSM 900FM

1710 M 1880 M

GSM 1800

freq

Transceiver specification: Duplexing


Tx Rx

f =?

TxRx

Duplex: Two way/One way communication?

Transceiver specification: Duplexing


BPFft

BPFfr

BPF

ft

BPF

fr

Tx

Rx

Base stationf t

ft

f r fr

Tx

Rx

Tx

Rx

Tx

Rx

Tx

Rx

Tx

Rx

f c fc

fcf c

at time t1 at time t2

Time Division Duplexing (TDD): Only half duplex

Frequency Division Duplexing (FDD):

(a) (b)

(c)

Full duplex at the cost of 2-channels/link

Single wide-

band antenna

DiplexerDiplexer

Two narrow-band antennas

or

Transceiver specification: Multiple Access in FDD


1 2 3 4 N

frequency

Frequency band for the standard

frequency

GSM 900 uplink GSM 900 downlink

890-915 MHz 935-960 MHz

GSM 1800 uplink GSM 1800 downlink

1805-1880 MHz1710-1785 MHz

Channel spacing = 200 KHz

Duplex spacing = 45 MHz

Channel spacing = 200 KHz

Duplex spacing = 95 MHz

Transceiver specification: Power


Ptx Prx

TX RX

Ptx =?(Prx)min =?→ Defines the sensitivity of the receiver

(Prx)max =?→ Defines the dynamic range of the receiver

Dynamic range:(Prx)max

(Prx)min

Speaking about the power


Usually expressed in dBW or dBmW.

Power in dB = 10log(power in W1 W

)

Power in dBm = 10log(power in mW1 mW

)

dB is used in general to express the ratio of two similar quantities in

the log domain.

Examples:

Speaking about the gain


Power gain in dB = 10log(Pout

Pin) = Pout|dBm − Pin|dBm

Voltage gain in dB = 20log(Vout

Vin)

Vin Rload

DUT

Rin

Power gain in dB = 10log(Pout

Pin) = 10log(

V 2out/Rout

V 2

in/Rin

)

Power gain in dB = Voltage gain in dB⇔ Rout = Rin

Typical sensitivity of a receiver


Receiver minimum input sensitivity:

The packet error ratio (PER) shall be 10% or less when the PSDU length is 1000 octets and the rate- dependent input level

is as shown in below Table. The minimum input levels are measured at the antenna connector (noise factor of 10 dB and 5

dB implementation margins are assumed).

Alternate Minimum Minimum Minimum

Coding Adjacent Adjacent sensitivity sensitivity sensitivity

Modulation rate (R) channel channel (dBm) (dBm) (dBm)

rejection rejection (20 MHz (10 MHz (5 MHz

(dB) (dB) cha. spa.) cha. spa.) cha. spa.)

BPSK 1/2 16 32 -82 -85 -88

BPSK 3/4 15 31 -81 -84 -87

QPSK 1/2 13 29 -79 -82 -85

QPSK 3/4 11 27 -77 -80 -83

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

Receiver specification: ACR and AACR


1 2 3

f

A.C.

rejection

rejection

Alternate A.C.

Desired Channel

frequency

uplink downlink

Channel spacing = X KHz

Duplex spacing = Y MHz

Noise factor


+

Amp

Pi Po

Ni No

SNRi =Pi

Ni; SNRo =

Po

No= Gain.Pi

Gain.Ni+NA;

Noise factor = SNRi

SNRo= Pi

Ni.No

Po= 1 + NA

Gain.Ni> 1

If expressed in dB, Noise factor is referred as Noise figure and is

always > 0 dB.

Noise factor


+

Amp

Pi Po

Ni No

Noise factor = SNRi

SNRo= Pi

Ni.No

Po= 1 + NA

Gain.Ni> 1

= 1 + NA/GainNi

Noise factor


+

Amp

Pi Po

Ni

+

NA

G

NF− 1 = Input referred amplifier noisesource noise

=

Noise factor of a cascaded system


+

Po

Rs

G2, F2G1, F1

Ps

P1

+

Fcas =Pi

Po.No

Ns= 1

G1G2.G1G2Ns+G2.NA1+NA2

Ns

Fcas − 1 = NA1

G1Ns+ NA2

G1G2Ns

= (F1 − 1) + F2−1G1

Noise factor of a cascaded system


+

Po

Rs

G2, F2G1, F1

Ps

P1

+

Generalized expression:

Fcas − 1 = (F1 − 1) + F2−1G1

+ F3−1G1G2

+ F4−1G1G2G3

+ . . .

Noise figure of the receiver


IFprocessingPA LNA

PTx PRx

RF source RF source

Data

(NF)Rx is dominated by (NF)LNA

frequency

PowerSets up the Noise floor

Only the signals whose

amplitudes are greater

than the noise floor of

the Rx can be detected.

Sensitivity of the receiver


(NF)Rx =(SNR)in(SNR)out

=(P)in/(N)Rs

(SNR)out⇒ Pin = NRs . (NF)Rx . (SNR)out (1)

Usually, both Pin and NRs are expressed in W/Hz or dBm/Hz.

If the receiver bandwidth is B then,

⇒ Pin = NRs . (NF)Rx . (SNR)out. B (2)

Psen|dBm =

Integrated noise of the Rx or Noise floor︷︸︸︷

NRs|dBm/Hz + (NF )Rx|dB + 10logB + (SNR)out,min|dB(3)

For a 50 Ω source at 300K and a matched LNA,

NRs = −174 dBm/Hz

Example: Sensitivity of the receiver


A radio receiver needs to be designed to have a sensitivity of -105

dBm and a minimum SNR of 10 dB. The bandwidth of the channel

is 200 KHz. Assume a 50 Ω antenna impedance. What is the NFrx

needed?

−105|dBm = −174|dBm/Hz +NFrx|dB + 53|Hz + 10|dB

⇒ NFrx = 6 dB

(4)

Large input signals


IFprocessingPA LNA

PTx PRx

RF source RF source

Data

How large Prx can be?

Large input signals


IcID

Vbe Vgs

I = f(Vin)⇒ I +∆I = f(Vin +∆Vin) (5)

I +∆I = f(Vin) + f ′(Vin)∆Vin +f ′′(Vin)

2∆V 2

in + . . .

i = c1vin + c2v2in + c3v

3in + . . .

For a single tone input vin = Acosωt, (considering upto third order

terms)

i = c2A2

2+

(

c1A+ 3c3A3

4

)

cosωt+ c2A2

2cos2ωt+ c3A3

4cos3ωt

Large input signals: HD


i = c2A2

2+

(

c1A+ 3c3A3

4

)

cosωt+ c2A2

2cos2ωt+ c3A3

4cos3ωt

• Harmonics

ith Harmonic distortion, HDi=ith Harmonic signal levelfundamental signal level

If we assume c1A≫3c3A3

4, then HD2 ≈

c2A3c1

and HD3 ≈c3A2

4c1

Total Harmonic Distortion, THD =√

∑∞i=2HD

2i

Large input signals: Gain compression


i = c2A2

2+

(

c1A+ 3c3A3

4

)

cosωt+ c2A2

2cos2ωt+ c3A3

4cos3ωt

• Harmonics

• Bias point can change due to the even harmonics ( c2A2

2).

• Fundamental gets affected by the odd harmonics (3c3A3

4).

Gain of the amplifier = c1 +3c3A2

4⇒ depends on the signal

amplitude.

vin vin

Gain expansion Gain compression

i ic1c3 > 0 c1c3 < 0

1dB compression point


vin vin

Gain expansion Gain compression

i ic1c3 > 0 c1c3 < 0

1 dB

20log(A

out)

20log(Ain)Ain,1dB

20log|c1 +3c3A2

in,1dB

4| = 20log|c1| − 1

Ain,1dB =√

0.145| c1c3|

Strong interferer: Desensitization, Blocking


Desired

Interferer

frequencyω0 ωi

Let the input to a (memoryless) nonlinear circuit is

A0cosω0t+ Aicosωit.

Fundamental at the output =(

c1 +3c3A2

0

4+

3c3A2

i

2

)

A0cosω0t

If the interferer is large compared to the desired, i.e. if Ai ≫ A0 then

gain of the circuit is ≈ c1 +3c3A2

i

2← decided by the interferer!

If c1c3 < 0, then for a particular Ai, gain of the circuit can be 0! ←blocker.

Strong interferer: Cross modulation


Desired

Interferer

frequencyω0 ωi

Let the input be A0cosω0t+ Ai(1 +mcosωmt)cosωit︸︷︷︸

Interferer is an AM signal

.

Fundamental at the output =[

c1 +3c3A2

i

2(1 + m2

2+ m2

2cos2ωmt+

2mcosωmt)]

A0cosω0t︸︷︷︸

Transfer of modulation from interferer to fundamental ⇒ cross modulation

Inter-modulation


Desired

Interferer 1

frequencyω0 ω1

Interferer 2

ω2

Consider the case of two interferers, at ω1 and ω2 (both are close to

the desired signal at ω0), present at the input of a receiver.

ω2ω1ω2ω1

If either 2ω2 − ω1 = ω0 or 2ω1 − ω2 = ω0then the inter-modulation of

the interferers can corrupt the desired signal (overlaps with ω0).

IM3, IIP3


ω2ω1ω2ω1

Assuming equal amplitude, A, for the tones at ω1 and ω2,

IM3 =Amplitude of the tone at 2ω1−ω2

Amplitude of the tone at ω1= 3c3

4c1A2 = 3HD3

20log(Aout)

20log(Ain)AIIP3

AOIP3

fund

amen

tal

IM3

Expression for IIP3


20log(Aout)

20log(Ain)AIIP3

AOIP3

fund

amen

tal

IM3

At AIIP3, magnitude of the fundamental at the output = magnitude

of the IM3 at the output

c1AIIP3 =3

4c3AIIP33 (6)

⇒ AIIP3 =

√

|4c13c3| =

√

4

0.435A1dB

⇒ AIIP3|dBm ≈ A1dB|dBm + 9.6 dB

One point measurement of IIP3


ω2ω1ω2ω1

AIM3 Af

ω2 − ω1 ω2 + ω1

A A

Af

AIM3

= 4|c1|3|c3|A2 =

A2

IIP3

A2

20log(AIIP3) = 1

2[20log(Af )− 20log(AIM3)] + 20log(A)

IIP3 =Pf−PIM3

2+ Pin ←all quantities in dBm

Note:

IIP3 =A2

IIP3

2Rs

IIP3 of a cascaded network


ω2ω1

ω2ω1ω2 − ω1 ω2 + ω1

ω2ω1ω2 − ω1 ω2 + ω1

(∆)2

(∆)1

y1 y2x

y1 = a1x+ a2x2 + a3x

3 y2 = b1y1 + b2y21 + b3y

31

AIIP3 =√

43| a1b1a3b1+2a1a2b2+a3

1b3|

1A2

IIP3

= | 1A2

IIP3,1

+ 3a2b22b1

+a21

A2

IIP3,2

|

If every stage in the cascade has a gain > 1, then

1A2

IIP3

≈ 1A2

IIP3,1

+G2

1

A2

IIP3,2

+G2

1G2

2

A2

IIP3,3

+ . . .

NF-IIP3 trade-off in a cascaded network


ω2ω1

ω2ω1ω2 − ω1 ω2 + ω1

ω2ω1ω2 − ω1 ω2 + ω1

(∆)2

(∆)1

y1 y2x

y1 = a1x+ a2x2 + a3x

3 y2 = b1y1 + b2y21 + b3y

31

1A2

IIP3

≈ 1A2

IIP3,1

+G2

1

A2

IIP3,2

+G2

1G2

2

A2

IIP3,3

+ . . .

Fcas − 1 = (F1 − 1) + F2−1G1

+ F3−1G1G2

+ F4−1G1G2G3

+ . . .

Large input signals


PTx PRx

Tx Rx

How large Prx can be?

Magnitude of the IM3 products at the output should not exceed the

integrated noise floor.

Spurious-free dynamic range


ω2ω1

Rx

SFDR

ω2ω1

Rx integrated noiseSensitivity

SFDR

Pin,max

Pin,max +GRx

Sensitivity + GRx

Rx integrated noise + GRxSNRmin

SNRmin

Magnitude of the IM3 products at the output should not exceed the

integrated noise floor.

Spurious-free Dynamic Range


ω2ω1

Rx

SFDR

ω2ω1

Rx integrated noiseSensitivity

SFDR

Pin,max

Pin,max +GRx

Sensitivity + GRx

Rx integrated noise + GRxSNRmin

SNRmin

PIIP3 = Pin +Pout − PIM,out

2(7)

= Pin +Pin +G− PIM,in −G

2

=3Pin − PIM,in

2

⇒ Pin =2PIIP3 + PIM,in

3

Spurious-free Dynamic Range


Pin,max =2PIIP3 +

= Integrated noise floor︷︸︸︷

PIM,in

3(8)

=2PIIP3(

= Sensitivity−SNRout,min︷︸︸︷

−174 dBm+NF + 10logB)

3

⇒ SFDR = Pin,max − Sensitivity (9)

=2[PIIP3 − (−174 +NF + 10logB)]

3− SNRout,min

Note:

For Linear Dynamic Range, one can consider P1dB as Pin,max.

Transceiver specifications


PTx PRx

Tx Rx

How much Ptx can we transmit?

Radio standards will define this (Ptx,max) value along with a

worst-case spectrum profile.

Transmitter specification: Spectral mask


ff1 f2 f3 f4 f5−f5 −f3 −f1

Center frequency of the channel

Permitted level (0 dBr)

Power spectral density (dB)

Pf2

Pf4Pf3

RBW = X KHz

V BW = Y KHz

Power spectral density = Power measured within the RBW of the measurement deviceResolution Bandwidth (RBW) of the measurement device

dBr → Relative (or normalized) amplitude

Transmitter specification: Spectral mask


ff1 f2 f3 f4 f5−f5 −f3 −f1

Center frequency of the channel

Power spectral density (dB)

Valid Tx specta

Transceiver specifications: Summary


Rx specifications

Tx specifications

Frequency related Power related

Channel spacing

Duplex spacing

Prx,min Prx,max

Noise figure

Sensitivity

Limited by P1dB

Limited by PIIP3

SFDR

Linear DR

Ptx,max

Spectral mask

EE 647: Radio Frequency Integrated Circuits Module 1 ...

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