Int. J. Electron. Commun. (AEÜ) 65 (2011) 794–798
Contents lists available at ScienceDirect
International Journal of Electronics and
Communications (AEÜ)
journal homepage: www.elsevier.de/aeue
Component reduced floating ±L, ±C and ±R simulators with grounded passive
components
Mehmet Sagbas ∗
Department of Electronics Engineering, Maltepe University, 34857 Maltepe, İstanbul, Turkey
a r t i c l e
i n f o
Article history:
Received 1 February 2010
Accepted 9 January 2011
Keywords:
Current backward transconductance
amplifier
Floating inductor simulator
Immittance simulator
Active networks
Analog signal processing circuits
a b s t r a c t
In this study, a novel immittance simulator circuit is proposed. The proposed circuit can simulate any one
of the floating positive or negative inductor simulator (±L), positive or negative capacitor simulator (±C)
and positive or negative resistor simulator (±R). It uses only one current backward transconductance
amplifier (CBTA) and two grounded passive components. The proposed simulator can be tuned electronically by changing the transconductance value of the CBTA. Moreover, the circuit does not require any
conditions of component matching. It has a good sensitivity performance with respect to the tracking
errors and the passive components. The performance of the proposed immittance simulator is demonstrated on the fourth-order voltage- and current-mode band-pass filters by using Pspice simulations
based on the 0.25 ␮m TSMC level-7 CMOS technology parameters.
© 2011 Elsevier GmbH. All rights reserved.
1. Introduction
The immittance function simulator can be applied in areas
like oscillator design, active filters, chaos circuits and cancellation of parasitic elements. Consequently, it has become a standard
research topic. The advent of integrated circuits has encouraged
the design of synthetic inductors, which can be used instead of the
physical inductors in passive filters. Furthermore, physical inductors are usually unwanted passive components in most of the
electronic configurations because their characteristics are far from
the ideal element behaviors. In addition, they occupy larger chip
area when compared to the other passive components such as
resistors and capacitors [1]. Although, it is difficult to implement
inductors and floating capacitors in the integrated circuits, several published circuits employing various active devices overcome
this difficulty [2–14]. However, they suffer from one or more of the
following drawbacks: (i) Use of an excessive number of active components, since, power consumptions are important for the circuit
designers, they look for simple structures employing no more than
a single active element. (ii) Use of high number of passive components. Moreover, a network using a minimum number of active
and passive components is important from the VLSI implementation point of view. (iii) Requiring any component matching. (iv) Use
of grounded passive component, since, a circuit using a grounded
capacitor and without requiring passive component matching con-
∗ Corresponding author. Tel.: +90 216 626 10 50.
E-mail addresses: sagbas@maltepe.edu.tr, sagbas@maltepe.edu.tr
1434-8411/$ – see front matter © 2011 Elsevier GmbH. All rights reserved.
doi:10.1016/j.aeue.2011.01.006
straints is very suitable for IC technology [15,16]. (v) Realizing only
grounded simulator circuits.
In this work, a novel floating inductor, capacitor and resistor
simulator circuit depending on the passive element choice is presented. The proposed circuit consists of only one CBTA as active
component, one grounded capacitor and one grounded resistor
for the floating inductor and capacitor simulators, one CBTA and
two grounded resistors for the floating resistor simulator. The proposed circuit can simulate any one of the floating ±L, ±C and ±R,
for which all values can be adjusted electronically by changing the
transconductance value of the CBTA. The negative passive component resistance, capacitance and inductance can be used for the
cancellation of the positive parasitic values, resistive, capacitive and
inductive, respectively [17]. The proposed circuit does not require
any component matching and it is tested in the fourth-order resistively terminated LC band-pass filter.
2. Current backward transconductance amplifier
A recent publication [18] introduced the concept and an implementation in the form of a circuit building block termed current
backward transconductance amplifier. The circuit symbol of the
CBTA with reference directions of the signals and its equivalent
circuit are given in Fig. 1. It can be characterized by the following
equations considering the non-ideal conditions:
Iz = gm (s)(Vp − Vn ),
In = −˛n (s)Iw
Vw = w (s)Vz ,
Ip = ap (s)Iw ,
(1)
M. Sagbas / Int. J. Electron. Commun. (AEÜ) 65 (2011) 794–798
795
Fig. 1. (a) Block diagram of the CBTA. (b) Equivalent circuit of the CBTA.
Table 1
The dimensions of the CMOS transistors.
W (␮m)/L (␮m)
PMOS transistors
M3 –M9
M15
M16 , M17 , M23 –M27 , M29
M28 and M30
NMOS Transistors
M1 , M2 , M13 , M14
M10 –M12
M18 , M19
M20
M21 and M22
M31 and M32
M33 and M34
20/1
1/0.25
2.5/0.25
10/0.25
Fig. 3. (a) Floating admittance. (b) Floating admittance simulator circuit.
10/1
2.5/1
0.5/0.25
2.5/0.25
2/0.25
2.25/0.25
10/0.25
In these equations ˛p (s), ˛n (s) and (s) are the current and
voltage gains, respectively and they can be expressed as
˛p (s) = ω˛p (1 − ε˛p )/(s + ω˛p ), ˛n (s) = ω˛n (1 − ␧˛n )/(s + ω˛n ), gm (s) =
go ωgm (1 − εgp )/(s + ωgm ) and w (s) = ωw (1 − εw )/(s + ωw ) with
|ε˛p | 1, |ε˛n | 1, |εgm | 1, and |ε | 1, where, go is the DC
transconductance gain. ε˛p and ε˛n denote the current tracking
errors, ε denotes the voltage tracking error, εgm denotes the
transconductance error and ω˛p , ω˛n , ωgm , ω denote the corner
frequencies. Note that, in the ideal case, the voltage and current
gains are w (s) = 1 and ˛p (s) = ˛n (s) = 1, respectively. The non-ideal
effects are discussed in Section 4.
The CMOS implementation of the CBTA is given in Fig. 2 [19,20].
The dimensions of the MOS transistors used in the CBTA implementation are given in Table 1.
In Fig. 2, the transconductance section is realized by using the
transistor M15 –M22 that is formed by MOS coupled pair and current
mirrors. Where, vin is the differential input voltage (vin = vp − vn ), io
is the output current of the transconductance section and IB is the
bias current. We will assume that all the MOS devices operate in
the saturation region. Let us assume that M19 and M20 are perfectly
matched and the current mirrors have unity current gain. io can be
given by
io = gm vin = (
2IB K)vin
(2)
where, the transconductance parameter K = Cox W/2L, is the
mobility of the carrier, Cox is the gate-oxide capacitance per unit
area, W is the effective channel width, L is the effective channel
length.
The studies mentioned above prove that the CBTA is a versatile
building block for the voltage- and current-mode signal-processing
applications. Considering these facts, in this study, the novel floating inductor, capacitor and resistor simulator circuits are proposed.
3. The proposed floating inductor, capacitor and resistor
simulator circuit
Consider the floating admittance in Fig. 3a and the simulator
circuit in Fig. 3b. The short-circuit admittance matrices of these
circuits can be respectively written as
[yij ] =
y11
y21
[yij ]=˛w
gm Y1
Y2
y12
y22
= Yf
+1 −1
−1 +1
Fig. 2. The CMOS implementation of the CBTA.
+1 −1
−1 +1
,
(3a)
,
where ˛p ≈ ˛n = ˛, and
Ip
In
= [yij ]
Vp
Vn
(3b)
796
M. Sagbas / Int. J. Electron. Commun. (AEÜ) 65 (2011) 794–798
Normalized active and passive sensitivities of the inductance Lf ,
the capacitance Cf and the resistance Rf are given by
yij
ij = 1
= Sgym
SYyij = −SYyij = S˛yij = S
w
1
(3c)
2
(i) If the admittances are chosen as Y1 = G1 and Y2 = sC2 , the input
admittance becomes
gm G1
[YL ] = ˛w
sC2
+1
−1
−1
+1
1
=
sLf
+1
−1
−1
+1
(4)
which represents a floating inductor whose inductance is
given by Lf = (1/˛w )(C2 /gm G1 ). In the ideal conditions
Lf = C2 /(gm G1 ). This means that the floating admittance, Yf , in
Fig. 3a can be simulated using the circuit in Fig. 3b and behaves
as a floating inductor between the p and n terminals. Setting
either Vn = 0 or Vp = 0, the proposed circuit can also be used as
a grounded inductor.
(ii) If Y1 = sC1 , Y2 = G2 are chosen for the circuit depicted in Fig. 3b,
the short circuit admittance matrix of the floating capacitor is
found to be
gm sC1
[YC ] = ˛w
G2
+1
−1
−1
+1
= sCf
+1
−1
−1
+1
(5)
where, Cf = ˛w gm C1 /G2 . In the ideal conditions, Cf = gm C1 /G2 .
(iii) If Y1 = G1 , Y2 = G2 are chosen for the circuit depicted in Fig. 3b,
the short circuit admittance matrix of the floating resistor is
found to be
[YR ] = ˛w
gm G1
G2
+1
−1
−1
+1
=
where, Rf = G2 /˛w gm G1 .
Rf = G2 /gm G1 .
1
Rf
In
+1
−1
−1
+1
the
(6)
ideal
conditions,
It is important to note that the proposed simulator circuit can
also simulate any one of the floating negative inductor (−L), the
floating negative capacitor (−C) and the floating negative resistor
(−R) by interchanging the p and n terminal inner connections of the
BJT implementation of the CBTA. It is also possible to implement the
grounded ±L, ±C and ±R simulator by grounding the p or n terminal
of the CBTA. Since, the Vn and Vp are zero as seen in Eq. (1).
Simulation of large positive and negative inductances without
using large capacitors is possible due to the difference term in the
denominator; this however needs attention to the passive sensitivities and tolerances of the passive components. Furthermore,
simulation of large negative capacitances can easily be performed
without needing for large capacitors since a capacitor ratio can be
used as multiplying factor. Similar discussions are also valid for the
resistor simulator.
4. Frequency limitations and simulation results
In order to prove workability of the proposed structures, Pspice
simulations are given. The first simulations include the performance analysis of the CMOS implementation of CBTA. All CBTAs
are simulated using the CMOS schematic implementation shown
in Fig. 2, with 0.25 ␮m TSMC level-7 CMOS technology parameters based on the dimensions of the CMOS transistor in Table 1
with DC power supply voltages equal to VDD = −VSS = 1.5 V for all
simulations.
Due to the non-idealities of the CBTA in Eq. (1), some discrepancies exhibit between the theoretical and the simulation results.
These non-idealities are found by using the Spice simulations as
below:
εgm = 0.0184,
εw = −0.035,
εp = −0.0142,
εn = 0.03
(7a)
Fig. 4. The equivalent circuit of the CBTA.
ωgm ∼
= 3700 Mrad/s,
ωw ∼
= 5150 Mrad/s,
ωp ∼
= 5020 Mrad/s,
ωn ∼
= 5150 Mrad/s
(7b)
As a result, the maximum operating frequency of the CBTA is
fmax = min{fp , fn , fgm , f } ∼
= 590 MHz.
The CBTA has the parasitic resistances and capacitances as
shown in Fig. 4. The parasitic resistance and capacitance values of
the CBTA are also found by using the Spice simulations and given
in Table 2.
Fig. 5 shows that the magnitudes of the impedances of an ideal
inductor and its simulator circuit can be made very close for a set of
selected values over many decades. The simulated data is approximately equal to the theoretical data between 800 Hz and 45 MHz.
The parasitic resistance of the inductor simulator is approximately
3 .
Fig. 6 shows that the magnitudes of the impedances of an ideal
capacitor and its simulator circuit can be made very close for a set of
selected values over many decades; the simulated data is approximately equal to the theoretical data between 2 kHz and 7 MHz. The
simulations also show that the proposed structure can simulate the
floating capacitor from 200 times smaller capacitors.
Fig. 7 shows that the magnitudes of the impedances of an ideal
resistor and its simulator circuit can be made very close for a set of
selected values over many decades. The simulated data is approximately equal to the theoretical data between 10 Hz and 100 MHz.
The functionality of the proposed circuit is also demonstrated on
the voltage- and current-mode band-pass filters design examples
shown in Fig. 8. In this figure, the presented circuits replace with the
inductor, capacitor and resistor simulator circuits shown in Fig. 3b.
The all CBTAs are modeled using 0.25 ␮m TSMC level-7 CMOS
implementation shown in Fig. 2 with the dimensions of the CMOS
transistor in Table 1. In the simulations, the voltage- and currentmode band-pass filters as explained above have cutoff frequencies
of ωc = 1 Mrad/s (fc = 159.16 kHz) and bandwidths of 3.18 kHz. The
inductance values L2 = L5 = C2 /gm G1 of the simulation example are
found by substituting the values of gm = 0.5 mS, R1 = 1/G1 = 500 and C2 = 140 pF. The inductance value L3 = L4 = C2 /gm G1 of the simTable 2
The parasitic impedances of the CBTA.
Parasitic impedances
Values
Rp
Rn
Rz
Rw
Cp
Cn
Cz
53 k
67 k
403 k
19.6 75 fF
990 fF
430 fF
Rp , Cp , Rn , Cn , Rz , Cz , Rw are the parasitic resistances and capacitances of the CBTA.
M. Sagbas / Int. J. Electron. Commun. (AEÜ) 65 (2011) 794–798
Fig. 5. The magnitude of the impedance of the proposed floating inductor (L = 1 mH).
Fig. 6. The magnitude of the impedance of the proposed floating capacitor (C = 100 nF).
Fig. 7. The magnitude of the impedance of the proposed resistor capacitor (R = 10 k).
Fig. 8. The voltage- and current-mode band-pass filters.
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798
M. Sagbas / Int. J. Electron. Commun. (AEÜ) 65 (2011) 794–798
Fig. 9. The magnitude and phase responses of the low-pass filter.
ulation example are obtain by taking gm = 0.5 mS, R1 = 1/G1 = 5 k
and C2 = 707 pF. The Pspice simulation results of the filter are given
in Fig. 9. The deviations in the cut-off frequency from theoretical
values are caused by the non-idealities of the CBTAs such as the
current and voltage tracking errors.
5. Conclusion
As a conclusion, a novel ideal floating inductor, capacitor and
resistor simulator circuit shown in of Fig. 3 is proposed using
CBTA. The proposed circuit has the following advantages: (i) It
uses only one CBTA and two passive components. (ii) It uses a
grounded capacitor, which is more suitable for IC fabrication [21].
(iii) Proposed simulator does not require any component-matching
to arrive at Eq. (3) and provides independent control of L. (iv) It has
low sensitivities. (v) The impedance value of the simulator can be
adjusted electronically. Therefore it is also suitable for fully integrated floating immittance realization. (vi) The proposed circuit
can simulate one of the floating ±L, ±C and ±R. (vii) The simulation
results demonstrate that the theoretical and simulation results are
in good agreement.
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Mehmet Sagbas received his BS degree in Electronics and
Communication Engineering from Istanbul Technical University in 2000. He received his MS degree in Electronics
Engineering from Fatih University in 2003. He received
his PhD in Electronics Engineering Department at Yıldız
Technical University in 2007. His research interests are
active circuits, analog integrated circuit design, digital signal processing, image processing and active filter design.
ID
446420
Title
Componentreducedfloating±L,±Cand±Rsimulatorswithgroundedpassivecomponents
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