MICROWAVE OVER FIBERApplications and Performance
IEEE North Jersey LEOSNovember 12, 2012
John A. MacDonald
Linear Photonics 1
John A. MacDonaldVice President of Engineering
Linear Photonics, [email protected]
Dr. Allen KatzPresident, Linearizer Technology, Inc.
Professor, The College of New [email protected]
OUTLINE
1. MICROWAVE LINKS: ANALOG / DIGITAL
2. INTENSITY MODULATION & DETECTION
3. PRACTICAL LINK STRUCTURES
– DIRECT MODULATION
– EXTERNAL MODULATION
– PHOTORECEIVERS–
– TRANSMISSION MEDIUM
4. PERFORMANCE LIMITATIONS
– LINEAR EFFECTS
– NONLINEAR EFFECTS
5. NONLINEAR PERFORMANCE IMPROVEMENT/LINEARIZATION
6. SUMMARY
2Linear Photonics
Analog / Digital
• The bulk of fiber optic communications uses digital
modulation
– Fast switching and low pulse distortion determine link fidelity
• Certain applications not suited to digital:
– Bandwidth too high to be digitized– Bandwidth too high to be digitized
– System complexity favors a broad pipe
• Primary distinction between digital and analog is linearity
– Analog/Microwave links depend upon low distortion to achieve high
fidelity
3Linear Photonics
Microwave Fiber Optic Link
Ideally, the output is a linear copy of the input
E to O
transducerRF Input
O to E
transducer RF OutputOptical Fiber
– E/O transducer modulates the RF information onto an optical carrier
– O/E transducer reverses the operation
– Transducers must effectively transfer RF power (information)
• 50 Ω impedance to RF environment
– Modern Microwave Link technology is dominated by:
• Intensity modulation of semiconductor lasers
• Envelope detection using PIN or APD photodiodes
4Linear Photonics
Microwave Link Applications• Radar
– Low weight, complexity
– Beamsteering and Direction-finding
• Antenna and Signal Remoting
– Direct-RF over longer distances (many km)
– Reliable alternative to wireless in fixed services
• Electronic Warfare / SIGINT / ELINT
– Secure Comms (EMI hard)
– Towed Decoys– Towed Decoys
• Space-based
– Mass advantage
– Deployed fiber: can be radiation hard; less thermally sensitive
• Precise Time and Frequency Distribution
• High RF and Magnetic EMI Environments– Fiber is almost completely EMI-proof, and non-metallic
• High Voltage Environments– Fiber will not conduct
5Linear Photonics
Practical Intensity Modulation
• Direct
– Laser diode is modulated directly
• External
– Laser source drives a separate optical – Laser source drives a separate optical
component
6Linear Photonics
Direct Modulation
Bias
Modulating
Signal
SemiconductorLaser
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140 160
Optical Intensity
Mean Offset + Modulation
Slope Efficiency
ηL
IL
im
PDiode Laser
Power vs. Current
7
0 20 40 60 80 100 120 140 160
Laser Modulation Current
DC Bias + RF
ITH
)()( mTHLLm iIIiP +−=η
IL
Linear Photonics
• A CW optical signal is intensity modulated
via a field-dependent optical medium
• µwave / mm-wave modulation speeds can
be achieved with 2 major methods:
External Modulation
be achieved with 2 major methods:
– Electro-Optic Modulation
• Field-dependent change in optical index (electo-
optic effect)
– Electro-Absorption Modulation
• Field-dependent change in optical attenuation
8Linear Photonics
• Mach-Zehnder Interferometer
– Index of refraction is dependent on applied
field (modulating signal)– Electro-Optic effect can be realized in Lithium Niobate (LiNbO3),
InP, and other crystal structures, i.e. KDP (KH2PO4)
Electro-Optic Modulation
InP, and other crystal structures, i.e. KDP (KH2PO4)
9
Vm (RF + Bias)
Optical
Vector • Propagation constant of the beam in
the lower leg is retarded due to applied
electric field – experiences less phase
shift than upper leg.
• Optical intensity (power) is
modulated by the applied RF signal
due to summation of out-of-phase
vectors.Diffused Optical Waveguide
on LiNbO3 substrate
Linear Photonics
0
0.5
1
-15 -10 -5 0 5 10 15
Vm
Inte
nsi
tyMach-Zehnder
Optical Intensity
Mean Offset + Modulation
10
Vm
• Optical Output power follows cos2 function o Vector phase summation
• Vππππ is DC voltage that causes 180° phase rotationo Depends on crystal physics and electrode length o Corresponds to “min” and “max” output powero Digital Modulation: variation between min and max
• Analog Modulation: Bias at Quadrature (shown)o Results in linear intensity modulationo Slope = 1 at quadrature pointo Even order distortions are balanced (zero)
Linear Photonics
Modulation Voltage
DC Bias + RF
• Absorption of optical signal dependent on applied bias
• Transmission follows exponential relationship with applied field
• Generally not as linear as MZM
Electro-Absorption
1
Vm
transmitted
11
0
0.25
0.5
0.75
1
0 0.5 1 1.5 2 2.5 3
)()( Vmf
m eVP−=
N
P
ia
Pin Pout
Linear Photonics
Modulation Voltage
DC Bias + RF
Transmitted Optical Intensity
Mean Offset + Modulation
absorbed
transmitted
• P-I-N diodes are most common
Photodetection
iout
VDC
Iave
PRPI ⋅=)(
R = responsivity (amps/watt)
= ηq / hω
– Intrinsic bandwidth limited by diode capacitance
– Package and launch considerations may also limit
performance
• ~30 GHz bandwidth from lateral PIN
• ~100 GHz from waveguide PIN
12Linear Photonics
Transmission Medium
• Fiber is Optical Waveguide
• Fiber has very low loss
cladcore nn >
< 0.25 dB/km at 1550 nm
• High-fidelity Microwave Links
require Single-Mode fiber
13Linear Photonics
Singlemode
Qualitative Link Measures
E to O
transducer
RF Input
O to E
transducer
RF Output
Optical Fiber
Gain (Loss)
Added Noise
Linear Photonics, LLC 14
• Gain
– Broadband links are lossy
– Gain Slope / Ripple important to system design
• Noise Figure
– Generally higher than the link loss
• Third-Order Intercept
– Intercept of fundamental and 3rd-order IMD curves
• Spur-Free Dynamic Range (SFDR)
– Power Range over which the intermodulation distortion is below the noise floor
– Useful Quality Factor – incorporates Noise and Third-order Distortion
Nonlinear Distortion
Linear Factors affect the Gain and Noise of the output signal
– Microwave Launch– Inherent Bandwidth
• Limited by device and package reactances– Noise– Fiber Medium
• Absorptive Loss• Dispersion (Chromatic, Polarization Mode)
Performance Limits
• Dispersion (Chromatic, Polarization Mode)
Nonlinear Factors affect the shape of the output signal
– Distortion (Harmonic, Intermodulation, …)– Fiber Medium
• Stimulated Brillouin Scattering• Raman Scattering• Four-wave Mixing
15Linear Photonics
Linear Impacts: Microwave Launch
Primary source of microwave loss is input/output matching
DC
10 GHz
RL
RS
C
RS
C
• Narrow band links can be reactively tuned• Limited Bandwdith
• Fano’s rule: (BW)(Reflection Coefficient) < c
• However: Many or Most links require Broadband• Must use lossy matching – affects link gain
RLCL
Forward Biased Laser Diode
• Small real resistance RL
• Junction Capacitance and Ohmic Resistance
Reverse Biased Photo Diode
• Large reactive impedance dominated by junction
capacitance
• Ohmic Resistance adds dissipative loss
CJ
16Linear Photonics
Linear Impacts: Noise
• Laser Relative Intensity Noise (RIN)– Caused by spontaneous emission
• Laser is not a perfect oscillator
• 100 THz carrier is spread over 100’s of GHz
– Receiver detects as microwave noise
– Noise Power follows detection square-law: No ~ I2∙RIN
• Receiver Shot Noise• Receiver Shot Noise– Random arrival of photon quanta
– Output Noise power is white and follows the optical power: No ~ I
• Thermal Noise– Ubiquitous Johnson Noise
– Output Noise Power is constant and white
17Linear Photonics
Noise power delivered to the RF load is the sum of 3 independent sources
Output Noise of F/O Link
-180
-175
-170
-165
-160
-155
-150
-10 -8 -6 -4 -2 0 2 4 6 8 10
Optical Receive Power (dBmo)
No
ise
Po
we
r D
en
sit
y (
dB
m/H
z)
Thermal
Shot
RIN
Total
Gain of F/O Link
-60
-50
-40
-30
-20
-10
0
-10 -8 -6 -4 -2 0 2 4 6 8 10
Optical Receive Power (dBmo)
Ga
in (
dB
)
Noise Figure of F/O Link
0
10
20
30
40
50
60
-10 -8 -6 -4 -2 0 2 4 6 8 10
Optical Receive Power (dBmo)
No
ise
Fig
ure
(d
B)
Noise Figure
• Output noise depends • Gain also depends on • Noise Figure
18
• Output noise depends
on optical power
2:1 in RIN region
1:1 in shot regionconstant in thermal region
• Gain also depends on
optical powerAlways 2:1
• Noise Figure
decreases with optical
powerAsymptotic
Link Noise Figure and Dynamic Range vary with optical power – defined in
conjunction with the operational system
Linear Photonics
Linear Impacts: Fiber Medium
• SM Fiber Attenuation
– Due primarily to Rayleigh (elastic) Scattering
– 0.25 dB/km (1550 nm)
– 0.5 dB/km (1310 nm)
• Chromatic Dispersion
– Wavelength dependent propagation velocity
– Sidebands arrive out-of-phase: gain nulling– Sidebands arrive out-of-phase: gain nulling
• Polarization mode Dispersion
– Orthogonal Polarization Modes different
propagation velocities
– Non-uniform through fiber length• concentricity defects
• mechanical and thermal perturbations
• laser spontaneous emission
– Nondeterministic
– Affects pulsed (digital) systems
– Affects Time/Freq Distribution systems
19
Chromatic Dispersion
Polarization Mode Dispersion
FAST AXIS
SLOW AXIS
Linear Photonics
Nonlinear Impacts:
Modulator Transfer Function
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140 160
Bias Current
Optical Power
Direct Modulation
• Gain Compression• Even and Odd order amplitude distortion
• Phase distortion due to laser chirp (FM to PM)• Laser wavelength = function(drive level, temperature)
Bias Current
0
0.5
1
-15 -10 -5 0 5 10 15
Vm
Inte
nsi
ty
MZM External Modulation
• Gain Compression• Primarily Odd order amplitude distortion
• Very little phase distortion
20Linear Photonics
Linearity Measures
• Third-Order Intercept (IP3)– (Imaginary) point where two-tone third-order intermodulation products (IMD3) are equal to the fundamental
• Spur-Free Dynamic Range– Range of power over which the fundamental is above the noise floor and the IMD3 are below the noise floor
Pout
[ ])()(3)(1743
2)( 3
2
3 dBBWdBmIIPdBNFHzdBSFDR ++−=⋅
21
Pin
Output Noise Floor
IIP3SFDR-3
Linear Photonics
Nonlinear Impacts: Fiber
• Stimulated Brilluoin Scattering (SBS)
– Vibrational/Acoustic oscillations generated by high energy photons
– Forward wave energy is converted to acoustic backward wave (phonons)
– Threshold Effect
– Reduced forward gain; Increased noise floor
• Stimulated Raman Scattering (SRS)
– Inelastic photon scattering Nonlinear fiber effects must be – Inelastic photon scattering
– Wavelength translation
– Reduction in gain
• Self-Phase Modulation
– AM-PM conversion of a single signal
• Cross-Phase Modulation
– AM-PM Transfer from one signal to another (WDM systems)
• 4-Wave Mixing
– Intermodulation Distortion (WDM systems)
22
Nonlinear fiber effects must be
considered during link design phase.
Linear Photonics
Intensity Modulation Summary
TYPE COMPLEXITY SIZE
WEIGHT
POWER
PRACTICAL
MODULATION
FREQUENCY
LINEARITY COST
DIRECT Low: one optical
component
(laser)
Lowest 15 GHz Poor 2nd and
3rd-order
performance
Lowest
ELECTRO- Moderate: Similar to 40 GHz Poorest Higher,
23
ELECTRO-
ABSORPTION
Moderate:
requires separate
source laser and
small modulator
Similar to
direct mod
40 GHz Poorest Higher,
comparable
to EOM
ELECTRO-
OPTIC (MZM)
Highest: requires
source laser,
large modulator,
plus optical and
electrical
controls for bias
locking
Highest > 60 GHz Well-defined
(sin curve).
Operation at
quadrature
provides 2nd-
order null.
Highest
Linear Photonics
Closing the Link
LINK
• Directly Modulated Laser / PIN Receiver
/ Postamplifier
• Reactively Tuned 3.25 – 4.00 GHz
LINK
• E-O Modulator (MZM) / Waveguide
PIN Receiver
• Broadband Response to 40 GHz
PHOTORECEIVER
Broadband O/E Response to 20 GHz
and Output Return Loss
24
Link Type
Centerband
Gain Input IP3 Noise Fig SFDR3
dB dBm dB dB Hz^2/3
4 GHz
Direct Mod-20 32 28 118
20 GHz
MZM-25 31 38 111
30 GHz
EAM-30 18 40 101
40 GHz
MZM-30 25 43 104
“Typical” Link
Gain, Noise, Dynamic Range
Linear Photonics
Trade-Offs, or Why Use Fiber?
• What are the System Engineer’s Tradeoffs?
• Should I consider fiber?
– Tradeoff performance, cost, weight vs. other options
• If fiber, then what do I need to know?
– Direct Mod vs. Ex-Mod (Decision Needed)– Direct Mod vs. Ex-Mod (Decision Needed)
• Direct Mod (usually < 12 GHz)
– Weight, Cost, Loss, Dynamic Range, DC Power
– Often Comparing directly to Coax
• Ex-Mod
– Must evaluate system impact for linearity, G/T, etc
25Linear Photonics
Direct Mod Comparison to Coax
• At Direct Mod frequencies, choice of Fiber vs.
Copper often made on basis of performance as a
function of link length
• Primary System Trades include:
– Attenuation– Attenuation
– Noise Figure
– Weight
– Cost
26Linear Photonics
Direct Mod vs. Coax: Attenuation
25
30
35
40
45
50A
tte
nu
ati
on
(d
B)
Direct Mod Link
27Linear Photonics
0
5
10
15
20
0 200 400 600 800 1000
Att
en
ua
tio
n (
dB
)
Distance (meters) 2000 MHz
Direct Mod vs. Coax: Noise Figure
25
30
35
40
45
50N
ois
e F
igu
re (
dB
)
Direct Mod Link
28Linear Photonics
0
5
10
15
20
0 200 400 600 800 1000
No
ise
Fig
ure
(d
B)
Distance (meters) 2000 MHz
Direct Mod vs. Coax: Weight and Cost
WEIGHT (pounds) 1 m 100 m 1000m
RG8 .32 32 320
LDF6 .21 21 210
Direct Mod Link .14 1.1 10.1
29Linear Photonics
COST 1 m 100 m 1000m
RG8 $3 $300 $3,000
LDF6 $38 $3,800 $38,000
Direct Mod Link $5,000 $5,100 $6,000
Crossover Lengthwhen DM performance exceeds that of coax
Attenuation Noise Figure Weight Cost
RG8 110 m 180 m 30 cm 1800 m
Heliax LDF6 560 m 900 m 50 cm 125 m
Direct Mod Comparison to Coax
• Other factors may influence choice of Fiber vs. Copper:– Linearity (link dynamic range is less than coax)
– EMI immunity (may trump performance)
– Safety, Reliability, etc.
Example: Crossover Lengths at 2 GHz
30Linear Photonics
• Linearization Techniques
– Linearization improves nonlinear distortion, increases dynamic range
– Major techniques under study include optical, electrical, and combinatorial approaches
Performance Improvement
electrical, and combinatorial approaches
• Electrical: aim is to cancel distortion products– Feedforward/Feedback: Inject out-of-phase distortion
products to cancel
– Predistortion: Nonlinear circuits with opposing distortion characteristics
• Optical: generally more complex– Operates in optical domain – inherently wide-band
31Linear Photonics
Electrical Predistortion
• Predistortion Linearization has long history in
Broadcast Power Amplifiers; SSPAs, TWTAs, Space
and Ground Station equipment
– Generally less complex than optical or combinatorial
systemssystems
• Does not rely on sampled waveforms
• Bandwidth is the major challenge
– The aim is to compensate for the gain and phase
compression of the nonlinear system by providing a
cascaded element function that has the opposite gain
and phase characteristic: gain and phase expansion
Electrical Predistortion
• PERFORMANCE OF LINK IS PRIMARILY LIMITED BY THE DISTORTION INTRODUCED BY OPTICAL MODULATION.
• PREDISTORTION (PD) LINEARIZATION ELIMINATES THIS DISTORTION BY GENERATING A FUNCTION WITH OPPOSITE MAGNITUDE AND PHASE OF THE MODULATOR
Predistortion Linearization
-5
-4
-3
-2
-1
0
1
2
3
-5 -4 -3 -2 -1 0 1
1
2
3
4
Input Power
Output Power
Phase
34
• Nonlinear Device exhibits Gain and Phase Compression
-2
-1
0
1
-5 -4 -3 -2 -1 0 1Input Power
Linear Photonics
Predistortion Linearization
-5
-4
-3
-2
-1
0
1
2
3
-5 -4 -3 -2 -1 0 1
1
2
3
4
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5 -4 -3 -2 -1 0 1
1
2
3
4
Input Power Input Power
Output Power Output Power
Phase Phase
35
• Nonlinear Device exhibits Gain and Phase Compression
• Precede it with another nonlinear device that exhibits gain and phase expansion, in
conjugate with the device to be linearized (the linearizer)
-2
-1
0
1
-5 -4 -3 -2 -1 0 1
-2
-1
0
1
-5 -4 -3 -2 -1 0 1Input Power Input Power
Linear Photonics
Predistortion Linearization
-5
-4
-3
-2
-1
0
1
2
3
-5 -4 -3 -2 -1 0 1
1
2
3
4
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5 -4 -3 -2 -1 0 1
1
2
3
4
-5
-4
-3
-2
-1
0
1
2
-5 -4 -3 -2 -1 0 1
-1
0
1
2
3
Input Power Input Power Input Power
Output Power Output Power Output Power
Phase Phase Phase
36
-2
-1
0
1
-5 -4 -3 -2 -1 0 1
-2
-1
0
1
-5 -4 -3 -2 -1 0 1
-5
-4
-3
-2
-1
-5 -4 -3 -2 -1 0 1Input Power Input Power Input Power
• Nonlinear Device exhibits Gain and Phase Compression
• Precede it with another nonlinear device that exhibits gain and phase expansion, in
conjugate with the device to be linearized (the linearizer)
• The desired outcome is an ideal limiter
– The linearity of an ideal limiter cannot be improved
Linear Photonics
Wideband Predistorter
• Functions from 1.5 to > 20 GHz
• Target: ΔGain = 2.5 dB
• ΔФ < 5 degrees (Ach. to 13 GHz) (Ach. to 13 GHz)
• Flatness ± 0.5 dB (Ach. to 12 GHz)
• Feel can achieve <1GHz to <30GHz
• LPL generic predistorter is very broadband
Linearized Microwave Link
Preamp PredistorterPostamp/
Equalizer
MZM
1550 nm
Source Laser
MPR0020
Photoreceiver
LINEARIZER NONLINEARIZED LINK
RF IN RF OUT
38
• Nonlinearized MZM Link:
– Commercial modulator biased at quadrature
– 20 GHz flat receiver driven at 0 dBmo
• Linearizer:
– Includes broadband gain stages
– Predistorter is single-chip GaAs circuit (proprietary design)
• Signal levels adjusted to match gain expansion of predistorter to gain compression of MZM
– Postamp stage includes slope equalizer to match levels over frequency
LINEARIZER NONLINEARIZED LINK
LINEARIZED LINK
MZM Linearization
• Demonstration of IMD improvement from
predistorting an MZM link
MZM Microwave Link
Linearized IMD Products
120
Non Linearized
Linearized
• Results at 8 GHz
• Measured improvement
0
20
40
60
80
100
0.01 0.10 1.00
Optical Modulation Index
Th
ird
-Ord
er
IMD
(d
Bc
)
21 dB IMD improvement
(yields 5 dB SFDR3)
• Measured improvement
>14 dB (minimum)
from 4 to 12 GHz
Predistortion Linearizer Performance
Pout
• Linearization Results of EAM Link at 14 GHz
• Non-Linearized 4 dB Gain Compression at
Ref. Input Power
0-12
Input Power Backoff (IPBO) in dB
Gain Pout Gain
Pout
Input Power Backoff (IPBO) in dB
0-20
• Linearized Predistortion linearizer
effectively compensates the
gain compression
Predistortion Linearizer Performance
• Intermodulation Distortion Improvement EAM– Measured at 6 dB IPBO
Non-Linearized Linearized
• 15 dB improvement in IMD equates to 5 dB
improvement in SFDR3
THIRD ORDER
AM COMPRESSION TERMS
F1 F2
FOR WB OPERATION (> OCTAVE BW) FOR WB OPERATION (> OCTAVE BW) FOR WB OPERATION (> OCTAVE BW) FOR WB OPERATION (> OCTAVE BW) ---- EVEN & ODD EVEN & ODD EVEN & ODD EVEN & ODD ORDER DISTORTION MUST BE CONSIDEREDORDER DISTORTION MUST BE CONSIDEREDORDER DISTORTION MUST BE CONSIDEREDORDER DISTORTION MUST BE CONSIDERED
Multi-Octave Problem
• IM AND HARMONIC DISTORTION A PROBLEMIM AND HARMONIC DISTORTION A PROBLEMIM AND HARMONIC DISTORTION A PROBLEMIM AND HARMONIC DISTORTION A PROBLEM• 2F1, F22F1, F22F1, F22F1, F2----F1, 2F2F1, 2F2F1, 2F2F1, 2F2----F1 AND 2F1F1 AND 2F1F1 AND 2F1F1 AND 2F1----F2 PRODUCTS OF MOST CONCERNF2 PRODUCTS OF MOST CONCERNF2 PRODUCTS OF MOST CONCERNF2 PRODUCTS OF MOST CONCERN• MOST PREDISTORTERS CORRECT ONLY ODD ORDER DISTORTIONMOST PREDISTORTERS CORRECT ONLY ODD ORDER DISTORTIONMOST PREDISTORTERS CORRECT ONLY ODD ORDER DISTORTIONMOST PREDISTORTERS CORRECT ONLY ODD ORDER DISTORTION
F2-F1 2F1-F2 2F2-F1 2F1
F1 F2
FREQUENCY
EMISSION LIMIT
Multi-Octave Linearization
• MZMs produce minimal 2nd harmonic distortion with bias voltage control
• Predistorters can generate 2nd in addition to 3rd order nonlinearities
43
3 order nonlinearities
– 2nd order terms may worsen performance for > octave bandwidth
– Even terms not in the proper phase to cancel
• Developed predistorters that generate only 3rd-order components and operate over multi-octave bandwidth
Multi-Octave Linearizer
• A multi-octave broadband with even order cancelation
- operating from 1 to 20 GHz
- with single linearizer providing both IM and harmonic
distortion correction using push-pull NLG
Balu
n
NLG
NLG
Pre-Distortion Linearizer Circuitry
NLG
NLG
AttenB
alu
n
Optical & Electro-Optical Linearization
• Dual Series MZM Modulators
– Proper biasing of series MZMs may result in linearization of sinusoidal transfer
• Has been shown to approximate ideal limiter response
• Inherently wideband
• Difficult to tune/align
• Feedforward
– Nonlinear response is sampled (electrically) and re-injected to fundamental path in order to cancel undesired frequency products
• Limited bandwidth due to need for electrical delay in feedforward path
Optical Linearization Example
• Optical Feedforward Coupled linearization of
Mach-Zehnder modulator
– Third-order cancellationOMI
0.2(OMI)^3
split
Vrf
MZMbiased at Vpi/2
AC coupled
-0.5sin(piOMI/2)
a2
MZMbiased at Vpi/2
a1
0.2(a2)(OMI)^3
opticaloutput
delay
Potential for even greater cancelation (> SFDR)
Description
• First MZM generates distortion products
• Amplitudes of distorted detected outputs are:
• 2-tone 3rd-order amplitudes (IMDs) were found by eval. Fourier Series of the output
• Note that Fundamental and IMD products are always out of phase
⋅−=
2sin
2
1 OMIV fund
π 32.0 OMIVIMD ⋅=
• Note that Fundamental and IMD products are always out of phase
• RF signal is delayed and added to the distorted output• Level is set to “just cancel” the carriers of the detected signal, leaving just the
distortion
• Distortion products are re-modulated, and summed with the first modulator
output.• Summation must be noncoherent
• Dual lasers or sufficient delay
• Fiber Optic Links are increasingly being deployed for linear microwave transport applications
– Radar/Antenna remoting where weight and loss are critical
– Sensor Systems
– Precise Time and Frequency Distribution
– High EMI environments
Summary
• Photonic microwave links beneficial alternative to coax or wireless in many applications
– Size, Weight, Cost, Performance, EMI, Safety, …
• Practical intensity modulation links were presented
– Typical Performance, Limitations, and Methods of Improvement
• Linearization can offer dramatic improvement in dynamic range
Linear Photonics 48