Date post: | 08-Sep-2015 |
Category: |
Documents |
Upload: | jatayu2011 |
View: | 51 times |
Download: | 6 times |
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
Basic Concepts for RF Design
Prof. Bhaskar Banerjee
EERF 6330- RF IC Design
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
2
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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.
3
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
4
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
5
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
Gain Compression
http://en.wikipedia.org/wiki/List_of_trigonometric_identities
6
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
7
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
Gain Compression
8
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
9
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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.
10
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
11
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
12
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
14
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
15
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
16
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
17
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
Intermodulation
Hence, to the 1st order, the difference in the P1dB and IIP3 of a system ~ 10 dB
(IIP3 is higher than the P1dB)
18
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
11
1
3
Main signal power
IM power
P
P/2
Pi
19
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
Intermodulation
-20 dBm
+10 dBm
-40 dBm
Non-linear block
IIP3 = Pin + P/2 = (-20 dBm) + (50 dB)/2 = 5 dBm
20
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
Intermodulation
-15 dBm
+15 dBm
-25 dBm
Non-linear block
IIP3 = Pin + P/2 = (-15 dBm) + (40 dB)/2 = 5 dBm
21
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
Intermodulation
-10 dBm
+20 dBm
-10 dBm
Non-linear block
IIP3 = Pin + P/2 = (-10 dBm) + (30 dB)/2 = 5 dBm
22
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
Intermodulation
-5 dBm
+25 dBm
+5 dBm
Non-linear block
IIP3 = Pin + P/2 = (-5 dBm) + (20 dB)/2 = 5 dBm
23
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
Intermodulation
+5 dBm
+35 dBm
Non-linear block
24
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
Intermodulation
Intermodulation Effective IIP3 of cascaded stages
G1 G2
IIP31 IIP32
Gn
IIP3n
1IIP32eff
=1
IIP321+
G21IIP322
+ ...+G21G
22...G
2n1
IIP32n
25
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
Non-linearity
Harmonic Distortion: Signal by itself(P1dB)
Signal + Interferer: Blocking/Desensitization
Intermodulation: IIP3
26
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
Noise Thermal Noise in resistors
k = 1.38 1023(J/K)T = Absolute Temperature in KelvinB = Bandwidth of the channel in Hz
*
*
27
v2nB
= 4kT R (V 2/Hz)
i2nB
=4kT
R(A2/Hz)
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
Noise Shot Noise at p-n Junctions
Flicker Noise (1/f noise or Pink Noise)
N2 = Kfn BN : rms noise (voltage or current)
28
i2nB
= 2q IDC (A2/Hz)
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
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
29
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
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)
30
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
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
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
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
32
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
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
33
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
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
34
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
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
35
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
Pin,min|dBm = 174 dBm/Hz + 10log10B + NF |dB + SNRmin|dB
DR = Max Tolerable SignalMin Detectable Signal
Sensitivity and Dynamic Range
Noise Floor (F) of the system (referred to the input)
Dynamic Range (DR)
36
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
Sensitivity and Dynamic RangePout
PinPIIP3Pin,max
POIP3
Fo (Output Noise)
Fundamental
IM31
3
Po
37
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
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,
Sensitivity and Dynamic Range
POIP3 FoPIIP3 Pin,max = 3
Pin,max =2PIIP3 + F
3
38
Bhaskar Banerjee, EERF 6330, Sp2012, UTD
Pin,max = 2PIIP3+F3Pin,min = F + SNRmin
BDR = P1dB F SNRmin
Sensitivity and Dynamic Range
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)
39
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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 = ?
40
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
Example: Dynamic Range
41
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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 = ?
42
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
43
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
44
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
Bhaskar Banerjee, EERF 6330, Sp2013, UTD
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
46