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Journal of Circuits, Systems, and Computers
Article Title:
Tunable CMOS Active Inductor Using Widlar Current Source
Author(s):
Dhara P Patel, Shruti Oza-Rahurkar
DOI:
10.1142/S0218126619500270
Received:
28 December 2017
Accepted:
18 April 2018
To be cited as:
Dhara P Patel, Shruti Oza-Rahurkar, Tunable CMOS Active Inductor Using Widlar Current Source, Journal of Circuits, Systems, and Computers,
doi: 10.1142/S0218126619500270
Link to final version:
https://doi.org/10.1142/S0218126619500270
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Manuscript (pdf)
Tunable CMOS Active Inductor Using Widlar Current Source
Shruti Oza-Rahurkar§
Department of Electronics and Telecommunication,Bharti Vidyapeeth Deemed University
College of Engineering Laboratory,
Pune,Maharashtra 411043, India
§ shruti.oza11@gmail.com
Received (Day Month Year)
Revised (Day Month Year)
Accepted (Day Month Year)
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A novel tuning principle for simple gyrator based CMOS active inductor circuit is presented. The method makes use of widlar current source to enhance the quality factor.
The simulation of proposed active inductor provides maximum quality factor of 1819
at 2.88 GHz. The active inductor shows the inductive bandwidth of 1.66 GHz to 3.16
GHz and power consumption of 6.87 mW. The other characterization factors such as
linearity, supply voltage sensitivity and noise analysis are discussed. The performance of
tunable active inductor using widlar current source are compared with the same using
simple current mirror. An active inductor using conventional current mirror and widlar
current source have been implemented in 0.18 µm CMOS technology.
Keywords: Active inductor (AI); conventional current mirror (CCM); quality factor (Q);
widlar current source.
1. Introduction
EP
The increasing demand of RF integrated circuit is a significant reason that motivates to design power efficient and configurable architectures. The inductor has
been an essential component in RF system design blocks such as voltage controlled
oscillator, low noise amplifier, matching network, filter, power divider design, power
supply noise reduction etc 1 -7 . The drawbacks of spiral inductor are large chip area,
limited inductance value and weak quality factor, which are the main constraints
for RF design 8 . Moreover, advantages of active inductors are small chip area, high
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Dhara P Patel
Electronics and Communication Engineering Department, Charotar University of Science and
Technology, Changa,
Gujarat 388421, India∗
† dharapatel.ec@charusat.ac.in
∗ State
completely without abbreviations, the affiliation and mailing address, including country.
Typeset in 8 pt Times Italic.
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quality factor, wide inductance band and low voltage operation. The most vital advantage of active inductor over passive counterpart is its tunability. Nevertheless,
the main drawbacks are power consumption, higher noise, poor linearity - all these
are inherent in active inductor circuits 4 .
The several techniques have been employed successfully to implement active
inductor in literature 2 -12 . Each of them has attempted to achieve the optimal tradeoff between chip area, power consumption, quality factor, inductive bandwidth,
noise and tuning range. Tuning network is one of the key factors to improve the
performance of active inductor. Basically, current mirror is utilized for course tuning
and varactors are for fine tuning of active inductor 13 . Recently, Common gate (CG)Common source (CS) gyrator based active inductor has been discussed in 1 . Less
number of transistors proves the small chip area and low power consumption of
active inductor circuit but the higher value of parasitic series resistance and lower
value of parallel resistance value provide the lower value of quality factor.
The multi cascode stage has been used to reduce the series resistance in 1 ,
subsequently it increases the quality factor and self resonance frequency of active
inductor. It shows the wider inductive frequency range but the maximum quality
factor is 567. In proposed AI circuit, quality factor has been further improved by
adopting widlar current source and post layout results are compared with 1 .
In presented work, gyrator based an active inductor circuit is considered as
shown in Fig. 13 . It is composed of two transconductors realized by MOS transistors
in common source configuration connected in feedback configuration. The common
source facilitates low conductance at critical nodes (Zin and Zout ) and follows the
high quality factor of 1819 at 2.88 GHz. Two cases are discussed in paper. In first
case AI has been tuned by simple current mirror and in second case it has been tuned
by employing widlar current source. The results of both the cases are compared in
terms of quality factor, power consumption and supply voltage sensitivity, noise and
linearity. Based on intense literature review it is fair to assert that the adoption of
widlar current source in designing of active inductor has been demonstrated first
time.
The organization of paper is as follows. The core active inductor topology and
widlar current source are described in Section 2. The performance of active inductor
with widlar current source circuit is presented in Section 3. The simulation results
of AI are presented in Section 4. Finally, conclusions are summarized in Section 5.
2. The Core Active Inductor Topology
The CMOS based active inductor circuit and its simplified small signal model are
shown in Figs. 1 and 2, respectively. It is assumed that the gate-source capacitance
(Cgs ) is much greater than gate-drain capacitance (Cgd ). The input impedance Zin
at the input port is given by the following equation:
sCgs3 + gm4 + gds2 sCgs1 + gds3
1
1
+
+
(1)
Zin =
sCgs2
gds1
gm1 gm2 gm3
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Fig. 1. Conventional high quality factor active inductor.
Fig. 2. Small signal equivalent circuit of active inductor in Fig. 1.
0
Zin
sCgs3 + gm4 + gds2 sCgs1 + gds3
=
gm1 gm2 gm3
(2)
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By considering Cgs3 << Cgs1 + Cgs2 , the equivalent component values can be
derived as,
Cgs1 gm4 + gds2
Leq =
(3)
gm1 gm2 gm3
gds3 gm4 + gds2
Rs =
(4)
gm1 gm2 gm3
Cp = Cgs2
(5)
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Rp =
1
gds1
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Fig. 3. (a)Equivalent gyrator-C realization of the active inductor,(b) Simplified passive model.
For very high value of parallel resistance Rp of active inductor, the quality factor
can be determined as 14 ,
QL =
ωLeq
Rs
(7)
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For applications such as voltage controlled oscillator and band pass filters, the active inductors with a large quality factor are very important. There are various
techniques of enhancing the quality factor of active inductor such as basic cascode,
regulated cascode, negative resistor etc, though it is at the cost of power consumption 14 -15 . In the presented work, Q enhancement by reducing the effect of Rs has
been adequately discussed. The conductance at node 3 is responsible for the series
resistance of active inductor. Response of active inductor are observed by adopting
the simple current mirror and widlar current source at node 3.
2.1. Widlar Current Source
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The basic widlar current source is presented in Fig. 4 14 . The output impedance of
widlar current source is higher than simple current mirror by the factor of 1+gm8 Rs .
The modification of widlar current source as depicted in Fig. 4 are shown in Fig. 5.
In order to make it self biased R1 (in Fig. 4) is replaced with transistors M6 − M7
as shown in Fig. 5. The value of resistance Rs decreases the current of M8 while
the PMOS transistors (M6 and M7 ) require that Iout = Iref because they have
identical dimensions. Therefore, it can be written as,
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Where Leq , Rs , Rp and Cp are equivalent inductor, series resistance, parallel
resistance and parallel capacitance of active inductor circuit. According to eqs. (3)
and (4), it is noteworthy that Leq and Rs are independently tunable by Cgs1 and
gds3 , respectively. The gyrator circuit can be modelled as equivalent resonator as
shown in Fig. 3.
Vgs9 = Vgs8 + Iout Rs
(8)
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Fig. 4. Widlar current source.
Fig. 5. Self biased widlar current source.
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s
2Iout
+ VT H9 =
µn Cox (W/L)9
s
2Iout
+ VT H8 + Iout Rs
µn Cox K(W/L)8
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By ignoring the body effect,
s
2Iout
1 1− √
= Iout Rs
µn Cox (W/L)9
K
(9)
(10)
Simplified form,
Iout =
2
1 1 2
. 2 1− √
µn Cox (W/L)9 Rs
K
(11)
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As stated in eq. (11), current Iout will flow as long as K is not equal to 1. Constant
K is the (W/L) ratio of transistors M9 and M8 .
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Fig. 6. Active inductor using conventional current source.
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Fig. 7. Active inductor using widlar current source.
3. Performance of Active Inductor
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The primary effect of active inductor (as shown in Fig. 1) by adopting two different
tuning networks is analyzed. Figs. 6 and 7 represent the active indcutor circuit
using simple current mirror and widlar current source, respectively. In Fig. 6, the
current mirror is connected in shunt at node 3 and the conductance can be calculated as gds3 ||gds5 . In Fig. 7, the widlar current source is connected at the gate
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of transistor M5 . The degenerated source resistance Rs at the source of transistor
M8 will pull down the drain current of M5 and henceforth the value of gds5 will
be reduced. Consequently, the conductance at node 3 (gds3 ||gds5 ) will get diminished compared to former. The main property of widlar current source is its infinite
output impedance means very low conductance. The active inductor circuit using
widlar current source reduces the Rs and as per Eq. (7), it results into improvement
of quality factor.
In order to adopt a low power technique, transistor M1 of active inductor circuit
has been operated in sub-threshold region. To fulfill the sub-threshold condition,
gate-source voltage of transistor M1 is set slightly less than the threshold voltage.
The widlar current source generates low current compared to the current mirror
source 17 . Hence, it reduces static power and subsequently improves the total power
consumption.
The frequency range over which active inductor circuit behaves as an inductor is defined as inductive bandwidth and it is limited by series resistance Rs 14 .
The widlar current source reduces the series resistance and enhances the inductive
frequency range.
The supply voltage sensitivity of the inductance of active inductors is a figure-ofmerit quantifying the effect of the variation of the supply voltage on the inductance
of the active inductors. The supply independent widlar current source makes the
overall circuit less sensitive to the supply voltage variation.
4. Simulation Results
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In Fig. 6, the biasing current I2 is replaced with current mirror and in Fig. 7 same
with the widlar current source. To tune the circuits, MOSFET is biased in triode
region that functions as a resistor Rs .
The layout of active inductor using conventional current source and widlar current source are shown in Fig. 8 and 9, respectively.
The minimal output conductance of widlar current source reduces the series
resistance and improves the quality factor. The active inductor using widlar current
source results into maximum quality factor Qmax = 1819 at 2.88 GHz whereas using
current mirror provides Qmax = 269 at 3.6 GHz.
The micro current generation in widlar source reduces the static current of
active inductor and minimizes the power consumption. The power consumption
using simple current mirror is 10.2 mW whereas using widlar, it is 6.87 mW which
is comparable.
The inductive behavior of active inductor can be verified from the Bode plot.
The phase angle should be 90◦ in the the phase plot. The phase error is due to
parasitic series resistance RS and parallel resistance RP . Therefore, inductance
value can be calculated when the phase angle in phase plot becomes equal to 90◦ .
The corresponding frequency can be called as inductive frequency as illustrated in
Fig. 10. The inductive frequency as a function of control voltage (Vctrl ) is shown
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Fig. 9. Layout of active inductor using
widlar current source.
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Fig. 8. Layout of active inductor using conventional current source.
Fig. 10. Bode plot of active inductor as shown in Fig. 7 at Vctrl = 0.8V .
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Fig. 11. Variation in inductive frequency range with control voltage.
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Fig. 12. Supply sensitivity of active inductor using simple current mirror.
Fig. 13. Supply sensitivity of active inductor using widlar current mirror.
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in Fig. 11. The inductive bandwidth using simple current mirror is 0.9 GHz (3.1
GHz - 4 GHz), whereas using widlar current source it expands to 1.5 GHz (1.66
GHz - 3.16 GHz). It is clearly seen that widlar current source expands the inductive
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Fig. 14. Quality factor as a function of control voltage.
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Fig. 15. THD performance of active inductor.
Fig. 16. Noise performance of active inductor using conventional current mirror.
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bandwidth.
The widlar current source is supply independent that helps to reduce the overall
supply voltage sensitivity. The supply voltage sensitivity of active inductor has been
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Fig. 17. Noise performance of active inductor using widlar current source.
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measured over the tuning range. The active inductor with widlar current source
experiences the variation in range of 1.44 nH - 3.58 nH (as shown in Fig. 12)whereas
with current mirror it feels the changes in range of 5.14 nH - 34.2 nH (as shown in
Fig. 13). It is observable that the AI circuit using widlar current biasing is more
robust against voltage variation.
The nonlinear behavior of AI has been described by Total Harmonic Distortion
(THD). It describes the ratio of total harmonic current to fundamental current
when a fundamental ac input signal has been injected into the active inductor 9 .
As depicted in Fig.15, AI with current mirror shows slightly higher linearity than
same using widlar current source. Fig. 16 and 17, represent the noise analysis. AI
using widlar manifests better noise performance.
Active inductor using widlar current source uses additional two PMOS transistors (M6 and M7 ) as shown in Fig.7. The mobility of NMOS in submicron technologies is 4 to 5 times to that of PMOS. The lower value of mobility will restrict the
operation at high frequency. The addition of two PMOS transistors limit the higher
inductive frequency of active inductor. Therefore, AI using current mirror results
in high inductive frequency whereas by using widlar current source, it operates in
low inductive frequency range. Another tradeoff is that number of total transistors
are higher than conventional current mirror that increases the chip area.
Table 1 shows the comparison of active inductor by employing the two various
current sources - current mirror and widlar current source. AI with widlar current
source enhances the quality factor, noise performance, inductance variation against
supply voltage and power consumption. It follows the trade-offs with inductive
bandwidth, linearity and area consumption.
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Table 1. Comparison of active indcutor using two current sources.
AI using current mirror source
AI using widlar current source
269 at 3.6 GHz
0.9
5.14 - 34.2
16 - 22
< 44.68
616
10.2
1819 at 2.88 GHz
1.5
1.44 - 3.58
12.7 - 14.4
< 54
1230
6.87
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Table 2. Comparison of active indcutor.
Technology (µm)
Quality factor
Inductive frequency range (GHz)
THD (%)
Noise ( √nV )
Hz
Power dissipation (mW)
Area (µm2 )
5. Conclusion
[1 ]
This work (AI using widlar current source)
0.18
10-567
0.1 - 6.2
2
934.4
0.18
34-1819
1.9 -3.45
< 54
14.5
6.87
1230
Table 2 compares the performance of presented active inductor using widlar current
source with the architecture presented in 1 . The quality enhancement technique
offers the high quality factor that is comparable with 1 . The proposed circuit with
better quality factor can be used in RF applications for inductive bandwidth of 1.9
GHz to 3.45 GHz.
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