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IEEE JOURNAL OF SOLID-STATE CIRCUITS
1
A Distributed Low-Noise Amplifier for Broadband
Linearization of a Silicon Photonic
Mach–Zehnder Modulator
Navid Hosseinzadeh , Member, IEEE, Aditya Jain , Roger Helkey, Senior Member, IEEE,
and James F. Buckwalter , Senior Member, IEEE
Abstract— RF photonic components suffer from poor
spurious-free dynamic range (SFDR) due to the high noise and
distortion generated by a silicon photonic (SiP) Mach–Zehnder
modulator (MZM). This work demonstrates a distributed silicon–
germanium (SiGe) heterojunction bipolar transistor (HBT)-based
low-noise amplifier (LNA) co-designed for linearization with a
SiP MZM for a broadband radio-over-fiber (RoF) link. The
SiGe LNA incorporates a distributed, tunable predistortion
scheme that is inherently wideband and improves the thirdorder intercept point over an 18-GHz range. The assembled SiGe
LNA and SiP MZM prototype demonstrates an SFDR as high
as 120 dB · Hz2/3 at 9 GHz, a 14-dB improvement over previous
SiP RF components or RoF links.
Index Terms— Analog predistortion, distributed amplifier, driver, linearization, Mach–Zehnder modulator (MZM),
microwave photonics, RF photonics, silicon–germanium (SiGe),
silicon photonics (SiP), spurious-free dynamic range (SFDR),
third-order intermodulation (IM3).
Fig. 1. Top: block diagram of an RoF link with a SiGe LNA driving an
MZM. Bottom: recently published SFDR results for SiP MZMs in RoF links.
I. I NTRODUCTION
R
ADIO-OVER-FIBER (RoF) has the potential to support
microwave and millimeter-wave communication with
remote antenna heads. Remote antennas can improve wireless
network reliability in environments with poor signal coverage;
typically in situations with high RF path loss or blockage.
In addition, RoF links are capable of capturing signals over a
large instantaneous frequency range and transporting signals
with low loss over optical fiber. RoF links are typically
characterized by spurious-free dynamic range (SFDR), defined
by (2/3) (IIP3-MDS), where IIP3 is the third-order input
intercept point and MDS is the minimum detectable signal
assuming 1-Hz bandwidth (BW). To support wideband RF
Manuscript received May 5, 2020; revised August 30, 2020; accepted
November 5, 2020. This article was approved by Guest Editor Daniel
Friedman. This material is based on research conducted under AIM Photonics
and sponsored by Air Force Research Laboratory via agreement number
FA8650-15-2-5220. This article was presented at the IEEE Radio Frequency
Integrated Circuit Symposium (RFIC 2019), Boston, MA, USA, June 2–7,
2019. (Corresponding author: Navid Hosseinzadeh.)
Navid Hosseinzadeh and James F. Buckwalter are with the Department of
Electrical and Computer Engineering, and Institute for Energy Efficiency,
University of California at Santa Barbara, Santa Barbara, CA 93106 USA
(e-mail: navid@ece.ucsb.edu; buckwalter@ece.ucsb.edu).
Aditya Jain was with the Institute for Energy Efficiency, University of
California at Santa Barbara, Santa Barbara, CA, USA. He is now with Seagate
Technology, Edina, MN, USA.
Roger Helkey was with the Institute for Energy Efficiency, University
of California at Santa Barbara, Santa Barbara, CA, USA. He is now with
Evidation Health, Santa Barbara, CA, USA.
Color versions of one or more figures in this article are available at
https://doi.org/10.1109/JSSC.2020.3038448.
Digital Object Identifier 10.1109/JSSC.2020.3038448
and microwave communications applications, where complex
modulation schemes are employed, the RoF link requires
an SFDR exceeding 120 dB · Hz2/3 , compatible with RF
receivers [1], [2].
Fig. 1 shows a conventional RoF link consisting of a lownoise amplifier (LNA) followed by an electro-optical (E/O)
conversion using a Mach–Zehnder modulator (MZM). The
RF-modulated optical signal is transported over fiber with little
loss and converted back to the electrical domain through a
photodetector. The linearity of the RoF link—as characterized
by IIP3—is typically limited by Vπ , the voltage required
to change the optical carrier phase by 180◦, of the MZM.
While high Vπ improves IIP3, it reduces the RF link gain and
increases the noise figure (NF) resulting in no overall SFDR
improvement of the RoF link [3].
Optoelectronic materials offer different fundamental limits
on the Vπ L product of the MZM, where L is the length of
the MZM arms. For instance, InP MZMs typically exhibit
4 V·mm, whereas SiP MZMs exhibit 15 V·mm due to the
weaker change in the index of refraction induced by plasma
dispersion. Larger Vπ L of the SiP modulator requires long
arms (L) to increase gain and reduce NF at the expense of
frequency-dependent loss. Prior work illustrates that the SiP
MZM has an SFDR of around 110 dB · Hz2/3 at 1 GHz
that reduces at higher frequency [4], as shown in Fig. 1(b).
Therefore, a 20-dB SFDR gap exists between current SiP
MZMs [5]–[27] and the 120-dB · Hz2/3 target, particularly in
microwave bands extending to 18 GHz.
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IEEE JOURNAL OF SOLID-STATE CIRCUITS
Fig. 2. Loaded and unloaded transmission line and corresponding lumped
model for a small section.
While SiP MZMs have higher Vπ L, Si processes offer
integration of the E/O RoF receiver in a monolithic platform
for larger scale RF systems. Consequently, this work attempts
to overcome the physical IIP3 limits of the broadband MZM
with an electronic linearization scheme. Prior optical linearization techniques include optical-based approaches, such
as feedforward modulators and ring-assisted MZMs. While
these approaches have demonstrated a 112-dB · Hz2/3 SFDR
at 1 GHz and 94-dB · Hz2/3 SFDR at 20 GHz for a LiNbO3
MZM [22], they typically also require discrete electronic
components [28]–[30]. Prior work [31]–[33] proposed predistorter drivers as a radio frequency integrated circuit (RFIC)
for linearization of commercial LiNbO3 and electroabsorption
modulators and reported up to 19.5-dB third-order intermodulation (IM3) distortion suppression. These improvements were
limited to a maximum operation frequency of 1 GHz and
did not explore linearization of SiP modulators, which require
significant compensation to rival III–V optical modulators.
Here, we present a broadband linearization approach based
on electronic predistortion using the second-order intermodulation (IM2) products injection within a distributed amplifier
to compensate for the nonlinearity of the SiP MZM and
improve the SFDR to compete with LiNbO3 or InP MZMs.
Three innovations are presented in this work. First, a distributed high-gain LNA is presented that covers 0.5–20 GHz
to drive the MZM. Second, a distributed IM2 injection is
demonstrated to reduce IM3 and linearize the cascade of the
silicon–germanium (SiGe) LNA and MZM. Third, a co-design
procedure for a segmented MZM (S-MZM) is described that
predicts the broadband IIP3 and NF and supports the broadband linearization of the MZM. Prior work presented the circuit and initial measurements of the RoF link [34]. This article
extends this earlier presentation with analysis of the linearity
of the co-integrated SiP MZM and SiGe LNA to calculate the
IIP3 of the RF photonic receiver. We also present new circuit
analysis that is corroborated with measurement to describe the
power consumption of the linearization approach given the
IM3 reduction. A record 120-dB · Hz2/3 SFDR at 9 GHz and
a response above 110 dB·Hz2/3 –18 GHz is demonstrated. The
measured SiGe/SiP RoF indicates that the IIP3 improvement
exists over more than 18 GHz, demonstrating the potential for
broadband linearization.
II. S-MZM S FOR B ROADBAND RF R ESPONSE
SiP MZMs produce optical response through a change in
the charge concentration in a p-n or p-i-n junction along the
Fig. 3. IL of a loaded transmission line as a function of frequency for
different diode resistances.
optical waveguide. The MZM absorbs the reverse-biased
depletion capacitor into a transmission line that can generally
be modeled as a lumped circuit network where the LC
ladder network predicts microwave propagation characteristics.
In order to model loss, series resistance and shunt conductance
are added to the LC network, where the former represents conductor loss and the latter represents substrate loss. Fig. 2 shows
the unloaded and loaded transmission lines in the MZM and
the corresponding lumped model unit cell, considering both
conductor and dielectric loss. A small section of transmission
line (z) is incorporated into the lumped model in Fig. 2,
where z is the length of unit section. The attenuation constant
per unit length and phase constant per unit length is
C
L
1
R
+G
(1a)
αRF ∼
=
2
L
C
and
√
βRF ∼
= ω LC.
(1b)
In an unloaded transmission line, the term Gz represents a
large resistor, which models the conductor loss. The RF phase
constant should be designed to match the optical travelingwave group velocity in a traveling-wave MZM (TW-MZM),
whereas the attenuation constant should be minimized to
reduce the losses along the length of the line.
When the transmission line is loaded with a reverse-biased
diode, we can use the RC network model in Fig. 2 to find the
new value for G z. The series resistor R j can be converted
into a shunt resistor using series-to-shunt conversion for RC
networks. Consequently, we can find (1/G ) = R j (1+ Q s 2 ) =
R j (1+(1/(ω2 C j 2 R j 2 ))), where Q s is the quality factor of the
series RC circuit. Here, R j is defined as the total resistance
that also includes the contact resistance and wiring (vias)
resistance. We can see that G is a function of frequency,
R j , and C j . With the new value of G z, Fig. 3 plots the
attenuation constant of a 1-mm long transmission line as a
function of frequency for different values of R j . Even a very
small series junction resistance, αRF induces a limited BW
and higher NF. Here, for simplicity, we assumed that R j is
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HOSSEINZADEH et al.: DISTRIBUTED LNA FOR BROADBAND LINEARIZATION
3
where C J 0 is the zero-bias junction capacitance, Vbi is the
built-in potential, and m is the grading coefficient of the
junction. C0 and C1 are polynomial coefficients for (2).
The capacitance nonlinearity is characterized by IIP2VQ and
IIP3VQ and has been reported in prior work [35].
B. β Nonlinearity
Fig. 4. Comparison of E/O integration strategies based on MZMs using
traveling-wave design (top) and segmented design (bottom).
independent of C j . This assumption is partially valid if the
wiring resistance is dominant. However, in general, doping
levels in the junction control the value of both R j and C j ,
where increasing doping levels will make R j smaller and C j
larger. While smaller R j is preferred, larger C j means obtaining simultaneous 50- matching and E/O velocity matching is
more difficult. Also, loss of the optical waveguides increases
with higher doping levels.
To improve the RoF link gain, a low Vπ demands long
MZM arms. However, the p-i-n junction loss suggests that each
arm should be under 1 mm to allow for a frequency response
of 18 GHz. Therefore, the MZM transmission line of length L
is broken into segments of less than 1 mm each. Consequently,
the LNA should be distributed to allow a single transmission
line input where the LNA buffers the signal as well as produces
a differential drive signal to the two arms of the MZM. The
LNA is a buffer between the transmission line and reverse bias
diodes. The insertion loss (IL) is improved, resulting in lower
NF for the system at high frequency.
A four-segment MZM shown in Fig. 4 is designed in
a 65-nm SiP technology, where each segment includes a
differential p-i-n optical phase shifter to confine the optical
field in the waveguide. While the SMZM improves the SFDR
at high frequencies compared to a TW-MZM, it does not
improve the SFDR beyond 110 dB · Hz2/3 [35]. Increasing
the SFDR further demands an active linearization approach to
improve IIP3 that does not penalize NF.
III. D ISTORTION A NALYSIS OF S I P E/O I NTERFACES
The optical carrier travels with propagation constant γopt =
αopt + jβopt , where βRF ∼
= βopt . To modulate the optical
carrier with the RF signal, the propagation constant has a linear
dependence on the applied voltage such that αopt = a0 + a1 Vi
and βopt = b0 + b1 Vi , where b1 = (1/Vπ L). We will examine
how the SiP MZM deviates from this model and produces
distortion in the following.
The change in the charge produced by the depletion capacitance produces a change in the phase shift through the
waveguide that is not necessarily linear but rather modeled by
a higher order polynomial. Rather than considering the voltage
dependence on the phase constant, a charge relationship is used
here to isolate the RF and optical sources of distortion
β(Q) =
m
2π
2π n eff ≈
qk Q k
λ
λ
(3)
k=1
where qk is polynomial coefficient for the nonlinear index of
refraction and λ is the light wavelength. The phase nonlinearity is characterized by IIP2 Qβ = |q1 /q2 | and IIP3 Qβ =
(|4q1/3q3 |)1/2 .
C. Vπ Nonlinearity
The optical transmission is determined by the differential
phase shift between the two MZM arms. In addition, a dc
voltage is applied to the electrode that results in a static phase
shift αDC = 2α0 + α1 (V A + V B ) [35]
Pout
e−αDC L
(cosh(2α(Q)L) + cos(2β(Q)L − φDC ))
=
Pin
2
(4)
m
k
where α(Q) =
k=1 αk Q is defined as the polynomial
modeling α as a function of charge. The generalized model
presented here characterizes the MZM by IIP2β P and IIP3β P
to incorporate the transfer function from the junction capacitance nonlinearity and phase nonlinearity of p-n-junction phase
shifters [35], [36]. If (4) is assumed to be ideal with linear
β with respect to the applied voltage and quadrature bias
point, distortion is caused by the sin(x) transfer of Vi to Pout
conversion. The output of optical transmission is modeled with
a third-order memoryless nonlinearity
Pout
π
1 π 3 3
3
−αDC L
= c1 v i − c3 v i = e
vi −
v i . (5)
Pin
Vπ
6 Vπ
Consequently, the√intermodulation distortion is characterized
from IIP3V π = 2 2(Vπ /π). For a 3-mm-long SiP, the equivalent IIP3 is 26 dBm. Therefore, if we are dominated by the sine
nonlinearity, the polynomial model is a memoryless, weakly
nonlinear function and linearization of this characteristic is the
primary role of broadband predistortion circuitry.
A. C–V Nonlinearity
Charge in the waveguide is modulated through a reversebiased depletion capacitance, Q = C(V )V , where
CJ0
(2)
C(V ) =
(1 − V /Vbi )m
D. Cascaded Nonlinear Analysis
The block diagram in Fig. 5 represents both the amplitude
and phase distortion in the MZM. Neglecting the amplitude
path, which primarily generates only even-order distortion
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IEEE JOURNAL OF SOLID-STATE CIRCUITS
Fig. 5. Block diagram representing a nonlinear model for distortion in the
SiP MZM.
Fig. 7. IIP3 and gain of the RC network using Volterra series for different
configurations, where L = Nseg × L seg , as a function of frequency.
If we also include the diode depletion capacitance, the short
length more significantly reduces the OIP3, particularly as the
frequency increases. While we conclude that OIP3 improves
for longer length, higher frequency loss also increases as
discussed in Section II, which results in a tradeoff between
linearity and BW.
IV. L INEARIZATION T ECHNIQUES FOR S I P C OMPONENTS
Fig. 6. OIP3 as a function of MZM length for various cases considering
different sources of nonlinearity, found from cascade analysis.
when biased at quadrature and driven differentially, a distortion
cascade analysis for IIP3 combines each source of nonlinearity
1
IIP32MZM
2
|A1 |2 C02 2π
|A1 |2 C02
|A1 |2
λ n1
=
+
+
2
2
IIP3VQ
IIP3Qβ
IIP3β P 2
2π
3 C1 |A2 | C02 |A1 |2 λ n 2 +C1 |A2 |
+
+
2 IIP2 Qβ
IIP2β P
2π
λ n1
(6)
where A1 ( j ω) and A2 ( j ω) are Volterra kernels found for
(2) and presented in the Appendix. The cascade analysis
indicates how the components interact to produce a frequencydependent distortion due to the capacitance of the waveguide.
Considering that the RF gain of the link is
G RF = sin φDC e−αDC L
Pin Ro ∼ Pin Ro
=
Vπ
Vπ
(7)
where is the responsivity in A/W of the photodetector and
Ro is the output resistance. The OIP3 is calculated from the
product of IIP3MZM and G RF and is plotted in Fig. 6. When
considering only the Vπ nonlinearity, the OIP3 is independent
of length since IIP3 increases with Vπ , but the gain reduces
with Vπ .
When adding the βopt nonlinearity, the OIP3 reduces for
shorter MZM arms since a much larger voltage must be produced across the MZM diode capacitance and the large voltage
produces a more nonlinear response in the phase constant.
We propose three distinct RF linearization techniques for
the O/E and E/O components specific to each source of
nonlinearity presented in Section III.
A. C–V Linearization
To mitigate the nonlinearity due to C–V variation in the
depletion capacitance, the segments of the MZM allow the
RC time constant of the segment to be tailored to reduce
the generation of distortion. First, the design incorporates
more fixed capacitance at each segment, which reduces the
contribution of the nonlinear C–V component. In addition,
a smaller resistance can be used to drive each segment to
reduce the large-voltage variation that results in intermodulation distortion. In addition, biasing the junctions at higher
reverse bias voltages will further reduce the capacitance and
improves linearity. In a TW-MZM, junction capacitance and
loading on the electrodes are optimized for E/O velocity
matching and matching the characteristic impedance to the
source impedance. These constraints move to other parts of
the design, the driver design, and hence, phase shifter loading
can be optimized for linearity. IIP3 due to C–V variation can
be characterized by [35]
IIP3CV =
1 + 5ω2 Ri2 C02 + 4ω4 Ri4 C04
4
2
4
3ω Ri C2 C2
1 + ω2 Ri2 C12 + 2C0
(8)
where Ri is the load resistance. Fig. 7 shows IIP3 and gain
due to capacitance nonlinearity found from (8) and compared
cases with one 4-mm segment with two 2-mm and four
1-mm segments. As expected, gain roll-off increases as we
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HOSSEINZADEH et al.: DISTRIBUTED LNA FOR BROADBAND LINEARIZATION
Fig. 8.
5
Concept of MZM linearization by third-order predistortion.
increase the segment length and, hence, capacitance. The
IIP3 improvement is due to fixed load resistance being used for
all three cases, which keeps voltage swings the same as well.
Increasing a number of segments furthermore and making
them shorter will lead to improved BW. However, at the
same time, power consumption of the driver chip is increased
proportional to a number of segments. Hence, we choose to
have a minimum number of segments for a specific BW. Here,
we targeted >20-GHz BW, and, based on simulation results
in Fig. 7, we chose four segments.
B. Kerr Effect Linearization
Prior work has demonstrated the linearization of the optical
phase shift with induced voltage through engineering of the
second-order optical response with respect to the electric field
induced in the p-n junction of the waveguide [37]. A p-i-n
junction diode is formed in the waveguide, which introduces
a Kerr effect (χ-2) dependence on the optical phase. Balancing
the plasma dispersion and Kerr effect modulation linearizes the
phase constant with applied voltage. Nonetheless, SiP DC Kerr
effect MZMs have reported only slight improvement of the
SFDR at low frequency and no improvement higher frequency
bands [4], [38], [39]. This is presumably due to the linearity
being limited by other sources of nonlinearity, such as MZM
transfer function and nonlinear junction capacitor.
C. Vπ Linearization
Since the arcsin(x) transfer function is frequency independent, a broadband predistortion circuit could linearize the
MZM. The system shown in Fig. 8 is a cubic predistorter for
linearization of the MZM. Here, a second path generates a
cubic term electronically, which is then weighted by w and
added back to the main signal before applying to the MZM.
The predistorted signal is
v x = v i + wv i3 = v i · 1 + wv i2 .
(9)
Applying this predistortion signal to the modulator results in
Pout
= c1 v i + (wc1 − c3 )v i3 − c3 wv i5 − c3 w2 v i7 − c3 w3 v i9 .
Pin
(10)
The third-order term is eliminated when w = (c3 /c1 ) and
the cubic polynomial generates a number of additional higher
order terms. The effectiveness of this cancellation is demonstrated in the OIP3 plot as a function of MZM length for
different values for w, represented in Fig. 9. For each device
Fig. 9. OIP3 as a function of MZM length when the system is limited by
different sources of nonlinearity (dashed line) and after applying predistortion
for different third-order component weights (solid line). Each solid line is
plotted for a different weight of injected IM3 component.
length, an optimum w produces OIP3 that exceeds the original
OIP3 (21 dBm) realized from the sine nonlinearity. Predistortion results in peaking for particular device lengths. Adding
other sources of nonlinearity discussed in Sections III-A and B
results in red and blue curves in Fig. 9. Comparing these two
figures indicates how secondary sources of nonlinearity, charge
and phase shift, affect the overall OIP3.
Designing a broadband cubic term generator is challenging
since the cubic nonlinearity generates signal components over
three times the original signal BW. Another approach to
IM3 generation is to mix IM2 with the original signal as
indicated in the final equality in (9) to imitate a cubic term
generator response, which we refer to as IM2 injection [40].
A broadband IM2 generator is realized from the intrinsic
nonlinearity of an heterojunction bipolar transistor (HBT)
device as is typically used in a frequency doubler. Since
the squaring of an RF signal at frequency ωRF generates
components at dc and 2ωRF , we eliminate the components
at 2ωRF with a low-pass filter. The remaining enveloped is
modulated with the original RF signal and weighted to produce
the desired IM3 term.
Fig. 10 shows a conceptual block diagram of the proposed
distributed, analog predistortion LNA. The first block is the
LNA with high gain to set the NF of the RoF and relax
constraints on the length of MZM. The signal is then split
between two paths. In one path, the RF signal is amplified,
while through an auxiliary path, the RF signal is squared and
filtered to generate a relatively low-frequency IM2 component.
Next, the IM2 component is mixed with the original RF signal
to generate an IM3 component that can be weighted and
added to the original RF signal to cancel the IM3 components
generated by the MZM. By adjusting the IM3 weight (w),
the RoF can reach an IIP3 higher than the inherent MZM
IIP3, as shown in Fig. 9.
V. C IRCUIT I MPLEMENTATION
The distributed predistortion stage shown in Fig. 10 is
realized in an HBT technology. Fig. 11 shows the schematic
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IEEE JOURNAL OF SOLID-STATE CIRCUITS
Fig. 10. Conceptual illustration of the broadband linearization scheme with
block diagram of distributed IM3 injection.
Fig. 12. Circuit schematic illustrating the highly linear differential driver
and IM2 generator block.
filter the IM2 products. The weighting and mixing function is
produced by mirroring the IM2 current into the bias current of
the high-voltage differential driver. The output current of the
IM2 generator block, which is based on a frequency doubler,
is composed of a dc and IM2 component
I B v id 2
(11)
IIM2 = I B + 2
VT 2
Fig. 11. Circuit schematic illustrating the specific components including the
single-ended LNA, wideband active balun, variable delay transmission line.
of the LNA, active wideband balun, and tunable delay input
transmission line. The wideband LNA is a resistively degenerated cascode stage with inductive peaking to extend the
BW. Resistive degeneration extends the broadband frequency
response [41]. Next, an active balun produces differential RF
signals with less than 1-dB amplitude imbalance and under 5◦
of phase imbalance up to 25 GHz [35]. To match the optical
traveling-wave velocity in the MZM with the RF traveling
wave, the transmission line delay is adjusted over a small
range with a varactor. The distributed design allows delay
control between the RF input traveling-wave line and the
IM2 generation between stages.
Fig. 12 shows the schematic of the linear, high-voltage
differential cascode driver, which amplifies the RF signal
to 2 Vpp to drive the p-i-n phase shifter segments in
the S-MZM along with the IM2 injection circuitry. The
IM2 injection circuitry taps the differential signals and uses
an inductively degenerated frequency doubler to square and
where I B is the dc bias current, VT is the thermal voltage, and
v id is the amplitude of differential input voltage. If we drive
the IM2 current generated with two closely spaced tones at
ω1 and ω2 , the current terms are produced at ω1 − ω2 and
ω1 + ω2 . Both IM2 components can be injected into the driver
to produce IM3 components. Filtering of the sum components
occurs due to the frequency response of the IM2 generator
circuit. In Fig. 13, the inset plot shows that the difference
frequency current is constant to 18 GHz. The sum frequency
is roughly 8 dB lower in the broadband IM2 generator.
The IM2 current is plotted in Fig. 13 for tones located at
approximately 2 and 20 GHz. The tone spacing is 100 MHz
for the simulation, and the dc bias current is 10 mA. The
maximum IM2 current under this bias is 4 mA.
The output voltage of a differential BJT amplifier as a
function of differential input voltage follows the tanh(x)
function. Therefore, predistorted output voltage for the circuit
in Fig. 12 is
2
I B v id
v id
.
(12)
tanh
Vout = R L IEE + I B + 2
4
2V
VT
T
Representing tanh(x) as a linear Taylor series equivalent
2
v id
I B v id
1 v id 3
Vout = R L IEE + I B + 2
−
2VT
24 VT
VT 4
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HOSSEINZADEH et al.: DISTRIBUTED LNA FOR BROADBAND LINEARIZATION
7
Fig. 13. Current at ω2 − ω1 and ω2 + ω1 for the IM2 generator as a function
of input power, at 2 and 20 GHz.
Fig. 14.
OIP3 of the driver as a function of frequency for different
IM2 injection currents.
where we ignored higher order terms generated by the tanh
function. The desired predistorted signal is
v id
VSW
v id 3
Vout = VSW
+ IB RL −
(14)
2VT
3
2VT
heater, and photodiode to capture the nature of the ideal and
nonlinear behavior. With accurate behavioral modeling of the
SiP MZM, the improvement in the OIP3 can be characterized.
Fig. 15 shows the co-simulation test bench, including the
driver and S-MZM. A four-segment optical model for the SiP
MZM is constructed in Cadence and is shown in Fig. 15. The
sources of distortion are presented in Sections III-A–III-C. The
nonlinear characteristics for the capacitance nonlinearity and
phase and amplitude nonlinearity are included for the p-i-n
phase shifters. The capacitance change per applied reverse bias
voltage is illustrated to the bottom left and was measured for
the SiP MZM with an LC R meter. The capacitance changes
from 0.7 to 1.14 pF/mm. In addition, the change in the index
of refraction and attenuation constant with charge stored in the
optical waveguide is plotted on the left of Fig. 15. To establish
the linearity in terms of an RF output power, the MZM
is connected to an ideal photodiode with the responsivity
of 1 A/W to produce an output current as terminated by
a 50-.
The circuit schematic of the four-stage SiGe distributed
IM2-injection LNA is shown in Fig. 15 based on the predistortion technique from Fig. 10. Each driver stage is co-designed,
specifically for the SiP S-MZM stages. The input transmission
line distributes the RF signal to the four LNA stages. The
complete circuit schematic includes the LNA, active balun,
driver, and IM3 generation.
We simulate the OIP3 of the RoF link in Fig. 16 to indicate
the benefit of the feedforward, distributed IM3 injection. The
OIP3 is calculated in terms of RF power at the output of the
photodiode found from E/O co-simulation of driver and MZM.
In the absence of any predistortion, the OIP3 is around 5 dBm
and rolls off around 10 GHz.
The use of predistortion with injection of IM2 components
into the same stage indicates that the OIP3 is improved
by 10 dB. However, the OIP3 is limited to under a few GHz
due to the timing mismatch between the RF signal and the
IM3 products.
By injecting the IM2 component to the consecutive distributed stage, the time delay can be adjusted to achieve
where VSW = R L (IEE + I B ). Note that I B is the desired
weighting control that allows selection of the expansive
IM3 products and can compensate for distortion generated
by the driver or the following MZM. Generally, we assume
IEE + I B ≈ IEE .
Examination of tanh indicates that it also produces undesirable third-order distortion. Consequently, by calculating gain
and IIP3 = ((4/3)|(a1/a3 )|)1/2 from (13), the OIP3 for the
driver stage as a function of IM2 injection dc current is
IEE + I B .
(15)
OIP3 = 2VSW IEE − 2I B The OIP3 is tuned through I B and can cancel the selfgenerated distortion for I B = IEE /2. The injected IM2 current
is relatively large suggesting high power consumption for the
IM2 generator. For instance, a 1-V maximum swing requires
15 mA of I B current. An alternative approach is to linearize
the output driver such that the OIP3 can be improved to
compensate for the MZM nonlinearity. To include the role
of R E
(IEE + I B )R E 3
1+
OIP3 OIP3
.
(16)
VT
Fig. 14 shows OIP3 of the driver as a function of frequency
for different IM2 injection current amplitudes demonstrating broadband improvement of OIP3. The average simulated
OIP3 of the driver is about 43 dBm, an increase of more than
14 dB in the absence of IM2 injection.
VI. C O -S IMULATION OF E LECTRICAL AND O PTICAL IC S
To co-simulate the RFIC and PIC, a Verilog-A library
was developed for optical components, including laser, silicon
waveguide, splitter and combiner, p-i-n-junction phase shifter,
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Fig. 15.
IEEE JOURNAL OF SOLID-STATE CIRCUITS
Electrooptic co-simulation test-bench based on Verilog-A models for SiP and BiCMOS process models.
Fig. 16. OIP2 and OIP3 found from electrooptic co-simulation of driver and
MZM for three different cases: 1) IM2 off; 2) IM2 on and injected to the
same stage; and 3) IM2 on and injected to the next stage.
Fig. 17.
Simulated OIP3 variation after employing IM3 injection: with
temperature (top) and with NPN corner parameter (bottom).
a broadband linearization. The OIP3 now remains above
15 dBm to 18 GHz. Consequently, the SFDR should be
improved by more than 6 dB using the distributed predistortion
scheme.
The co-simulated OIP2 is also plotted in Fig. 16. While
there is a reduction in the OIP2 due to the injection of
the IM2 term, all three cases indicate that the minimum
OIP2 remains greater than 30 dBm from 0.5 to 20 GHz.
Stability of the linearization technique to temperature variation as well as process variation is investigated. Fig. 17 (top)
shows the effect of temperature on the simulated OIP3, where
the temperature is varied from 0 ◦ C to 100 ◦ C with 25 ◦ C steps.
The result shows good thermal stability with low sensitivity to
temperature change. Moreover, Fig. 17 (bottom) exhibits the
effect of NPN transistors corner parameter variation on the
linearized OIP3. Increasing this parameter will result in higher
speed transistors with higher currents. The result here shows
low sensitivity up to 12 GHz. In the future, a closed-loop
system can be designed to control the bias of the IM2 generator
block based on the performance for real-time optimization
and calibration, which improves the stability furthermore.
While a one-time calibration for each module would work
well, a calibration that is running in the background can be
employed to monitor the power of the input signal and possible
blocker and adjust the bias of the IM2 generator blocks and
other stages according to the power levels and frequency.
Such a system will help to lower the power consumption and
maximize the performance at the same time.
VII. M EASUREMENTS R ESULTS
The SiP S-MZM is fabricated in the 65-nm AIM silicon
photonic (SiP) process and the broadband, low-noise driver
is fabricated in the GlobalFoundries 130-nm SiGe BiCMOS
technology. The SiP S-MZM area is 5.5 × 0.65 mm2 and
driver chip area is 3.95 × 1.38 mm2 and is shown in Fig. 18.
The SiGe RFIC was designed using RF output GSSG pads
with matching pitch to the MZM. The PCB assembly is shown
in Fig. 18 with the SiGe distributed LNA and SiP MZM chips
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HOSSEINZADEH et al.: DISTRIBUTED LNA FOR BROADBAND LINEARIZATION
9
Fig. 18. Measurement setups for link characterization with QAM signal
(top left) and linearity measurements (top right), micrograph of the assembly
(bottom left), SiP S-MZM (middle), and LNA chip fabricated in 130-nm SiGe
BiCMOS technology (bottom right).
along with two 1550-nm lensed fibers used for optical interface
with edge couplers. The two chips are assembled side-byside on a PCB to minimize chip-to-chip wirebond length.
The power consumption of the driver is 1.70 W (425 mW
per stage) without IM3 predistortion and increases by 60 mW
with the use of IM3 predistortion to provide the 10 to 20-dB
IIP3 improvement. Most of the power consumption is consumed in the segment driver, which is designed to produce
2 Vpp across the load resistor using a 3.3-V supply.
Fig. 18 shows a block diagram of the measurement setup
with PNA-X, photodetector, micro-positioners, microscope for
fiber alignment, and the PCB. Two different setups are used:
one for small-signal and large-signal characterizations using
PNA-X and one for link characterization with modulated signals using an arbitrary waveform generator and oscilloscope.
A 1550-nm low-RIN (−168 dB/Hz) laser drives the MZM in
all measurements followed by a manual polarization controller.
The measured loss for optical edge couplers is about 3 dB and
the total optical loss of MZM is less than 10 dB, including
light coupling loss. The output of the MZM is sent to a 50-GHz
dual-band 1310-/1550-nm photodetector, which generates an
RF signal to the PNA-X.
Fig. 19 plots the measured S-parameters for the RoF link
with an external high-linearity photodetector. The link gain is
plotted against the measurement of a similar SiP TW-MZM in
the same technology with the same length. The active driver
improves the gain by 26 dB at 3 GHz and improves the gain
by 40 dB above 15 GHz. This supports the advantage of the
segmented design to improve the high-frequency response.
The simulated and measured input return losses are also
shown in Fig. 19(middle), and the measured S11 is better
than 10 dB to more than 20 GHz. The measured group
delay is plotted in Fig. 19(bottom) and indicates a relatively
low variation up to 20 GHz, with a maximum of 0.24 ns
at 16–18 GHz.
Fig. 20 shows the measured output power spectrum for
two tones at 1.9 and 2 GHz with and without IM2 injection.
The two tones are generated by the PNA-X and combined
into the driver. After applying IM2 injection and tuning the
Fig. 19. Measured RoF link gain compared to a single TW-MZM (top),
simulated and measured input return loss (middle), and group delay as a
function of frequency (bottom).
Fig. 20. Measured power spectrum for two tones at 1.9 and 2 GHz at input
of the driver.
IM3 reduction manually in the driver, the IM3 components
decrease by more than 23 dB, whereas an IM2 term at 3.9 GHz
increases by 8 dB. In addition, the HD3 components are
reduced by 10 dB, which demonstrates that the IM3 predistortion operates over a wide BW.
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10
IEEE JOURNAL OF SOLID-STATE CIRCUITS
Fig. 22. Measured IIP2 versus frequency before and after IM2 injection
(top) and measured IIP3 versus frequency with and without IM3 injection at
two bias points (bottom).
Fig. 21. Input power sweep at 5 and 10 GHz with and without IM3 injection
for fundamental and IM3 components.
The IM3 measurement is also characterized by the fundamental and IM3 over a range of input powers. Fig. 21 shows
the input power sweep at 5 and 10 GHz and indicates the
predistortion improves the IIP3 by 10 and 14 dB, respectively.
The weight of the IM3 component is controlled by the bias
current of the IM2 generator and a slight increase in the
injected fundamental power is observed.
Fig. 22 plots the IIP3 with and without IM2 injection at
two different bias currents to demonstrate the linearization
BW. Over the entire 1–20-GHz range, the IIP3 is increased
relative to the LNA without IM2 injection by at most 17 dB.
The bias on the IM2 injection is adjusted to achieve higher
IIP3 improvement above and below 10 GHz. The bias current
of the IM2 generator block was 3.4 and 5.6 mA to get
maximum IIP3 improvement in the 1–10- and 10–18-GHz
bands, respectively.
For broadband (larger than an octave) systems, IIP2 is also
a relevant metric. Since the IM2 generator injects IM2 components, the IIP2 is plotted as a function of frequency with
and without IM2 injection. Notably, IIP2 does not substantially
change over the frequency range with the IM2 bias current.
Fig. 23 plots the measured NF compared to the estimated
NF of a Si-based TW-MZM. The LNA improves the NF by
more than 20 dB with a minimum 13.6 dB at 3 GHz. From
the measured IIP3 and NF, the SFDR is 120 dB · Hz2/3 at
9 GHz, a 19-dB improvement over earlier work and 22-dB
improvement at 17 GHz.
A3 ( j ωa , j ωb , j ωc ) =
Fig. 23. Measured NF of the RoF link compared to the estimated NF of a
Si-based TW-MZM (top) and calculated SFDR from measurement data and
comparison with [22] (bottom).
The RoF link is also tested with 2-Gbd QPSK, 16-QAM,
and 64-QAM modulated signals at a carrier frequency
of 11 GHz. For QPSK at 4 Gb/s, 16-QAM at 8 Gb/s, and
64-QAM at 12 Gb/s, the measured EVMs are 2.6%, 3.7%, and
6.5%, respectively, which are measured without employing any
digital predistortion.
This work is compared to earlier reported linearized MZM
components or RoF links in Table I. The presented work
demonstrates the best SFDR for a SiP RF photonic link over
the highest frequency range and puts silicon MZMs at a similar
j (ωa + ωb + ωc )Ri (C1 A12 + C32 A1 ( j ωa )A1 ( j ωb )A1 ( j ωc ))
1 + j (ωa + ωb + ωc )C Ri
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(17c)
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HOSSEINZADEH et al.: DISTRIBUTED LNA FOR BROADBAND LINEARIZATION
11
TABLE I
S TATE - OF - THE -A RT H IGH SFDR RF P HOTONIC M ODULATORS
ACKNOWLEDGMENT
Fig. 24. Measured QPSK (top), 16-QAM (middle), and 64-QAM constellations, all at 2 GS/s.
This material is based on research conducted under AIM
Photonics. The authors would like to thank Erman Timurdogan
and Zhan Su of Analog Photonics for providing the p-i-n
phase shifter building block and GlobalFoundries for access
to the 8XP process technology. They would also like to thank
Prof. Schow for helpful discussions and Prof. Bowers and
Prof. Rodwell for access to measurement equipment. They
acknowledge Integrand for access to EMX software.
R EFERENCES
capability with reported LiNbO3 modulators. In addition, this
is the first reported work based on an integrated electronicphotonic solution for RoF with small size and weight.
VIII. C ONCLUSION
This work reports a co-designed SiGe LNA and SiP-based
MZM for SFDR of up to 120 dB · Hz2/3 and operating
up to 20 GHz. A broadband analog predistortion scheme is
introduced that forwards IM2 distortion products into the SiGe
driver to eliminate IM3 distortion generated by the SiP MZM.
The results demonstrate that SiP MZMs are capable of meeting
high-performance criteria for RoF links and meet or surpass commercial LiNbO3 and III–V modulator performance.
Prospects for future co-integration of SiP and RF electronics
on a single platform could support the linearization of photonic
devices.
A PPENDIX
The Volterra kernels are defined by
1
(17a)
1 + j ωa C Ri
−1 j C1 Ri (ωa + ωb )A1 ( j ωa )A1 ( j ωb )
A2 ( j ωa , j ωb ) =
2
1 + j (ωa + ωb )C0 Ri
(17b)
A1 ( j ωa ) =
and, (17c), as shown at the bottom of the previous page, where
A12 =
1
(A1 ( j ωa )A2 ( j ωb , j ωc )
3
+ A1 ( j ωb )A2 ( j ωa , j ωc )
+ A1 ( j ωc )A2 ( j ωa , j ωb )).
(17d)
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Navid Hosseinzadeh (Member, IEEE) received
the M.Sc. degree in electrical engineering from
the Sharif University of Technology, Tehran, Iran,
in 2014, and the Ph.D. degree in electrical and computer engineering from the Department of Electrical
and Computer Engineering, University of California
at Santa Barbara, Santa Barbara, CA, USA, in 2020.
He is currently a Post-Doctoral Researcher with
the University of California at Santa Barbara. His
research interests include RF/millimeter-wave integrated circuit (IC) design in silicon and compound
semiconductor technologies, silicon photonics integrated circuits, and quantum computers. In 2019, he was a Research and Development Intern with
PsiQuantum Corporation, Palo Alto, CA, USA.
Dr. Hosseinzadeh serves as a Reviewer for IEEE M ICROWAVE AND
W IRELESS C OMPONENTS L ETTERS , IEEE T RANSACTION ON C IRCUITS
AND S YSTEMS —I: R EGULAR PAPERS , IEEE T RANSACTION ON C IR CUITS AND S YSTEMS —II: E XPRESS B RIEFS , and IEEE T RANSACTION ON
M ICROWAVE T HEORY AND T ECHNIQUES .
Aditya Jain received the B.Eng. degree from the
University of Birla Institute of Technology and Science, Pilani, India, in 2010, and the Ph.D. degree
from the Department of Electrical Engineering, Iowa
State University, Ames, IA, USA, in 2016.
From 2016 to 2018, he was a Post-Doctoral
Fellow with the University of California at Santa
Barbara (UCSB), Santa Barbara, CA, USA. His
research interests include silicon photonics and
metamaterials.
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HOSSEINZADEH et al.: DISTRIBUTED LNA FOR BROADBAND LINEARIZATION
Roger Helkey (Senior Member, IEEE) received the
B.S. degree in engineering from Caltech, Pasadena,
CA, USA, and the Ph.D. degree in optoelectronics
from the University of California, Santa Barbara,
CA, USA.
Previously, he was Associate Director with the
UCSB Institute for Energy Efficiency, Santa Barbara.
He is currently a Senior Data Engineer at Evidation
Health, Santa Barbara. At Calient Networks, Goleta,
CA, USA, he developed optical switches as a lowpower alternative to electrical switches for data center and telecommunications applications. He has authored four book chapters
and received 42 patents.
He is a Fellow of the OSA.
13
James F. Buckwalter (Senior Member, IEEE)
received the Ph.D. degree in electrical engineering from the California Institute of Technology,
Pasadena, CA, USA, in 2006.
From 1999 to 2000, he was a Research Scientist
with Telcordia Technologies, Morristown, NJ, USA.
In 2004, he joined the IBM T. J. Watson Research
Center, Yorktown Heights, NY, USA. In 2006,
he joined the Faculty of the University of California at San Diego, La Jolla, CA, as an Assistant
Professor, where he became an Associate Professor
in 2012. He is currently a Professor of electrical and computer engineering
with the University of California at Santa Barbara, Santa Barbara, CA.
Dr. Buckwalter was a recipient of the 2004 IBM Ph.D. Fellowship,
the 2007 Defense Advanced Research Projects Agency Young Faculty Award,
the 2011 NSF CAREER Award, and the 2015 IEEE MTT-S Young Engineer
Award.
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