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A novel Nth-order voltage-mode universal filter based on CMOS CFOA
Optik 127 (2016) 2226–2230
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
A novel Nth-order voltage-mode universal filter based on CMOS CFOA Chunyue Wang a,∗ , Junru Zhang a , Lixue Wang a , Wenxiao Shi a , Deng Jing b a b
College of Communication and Engineering, Jilin University, Changchun 130012, China Department of Computer Science, University of North Carolina at Greensboro 164 Petty Building, Greensboro, NC 27412, USA
a r t i c l e
i n f o
Article history: Received 10 May 2015 Accepted 16 November 2015 Keywords: Active circuit Nth-order universal filter Current feedback operational amplifier Voltage-mode
a b s t r a c t With the development of integrated circuits, the fully integrated continuous time filter has been focused widely. A Nth-order universal filter based on Current Feedback Operational Amplifier (CFOA) is proposed. Compared with available circuits, the proposed circuit using less components (2n CFOAs, n capacitors, and 3n resistors) can realize the universal filter functions without changing circuit configuration, and the operating frequency of proposed filter circuit is at least 10 MHz. All of capacitors in proposed circuit are grounded, this is another benefit from integration point of view. PSPICE simulations have been carried out using 0.18 m CMOS technology, and sensitivity analysis of proposed Nth-order low-pass filter circuit is completed. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction The current feedback operational amplifier (CFOA) is one of the most important active building blocks in fully integrated continuous time circuits [1–8]. Compared with traditional voltage-mode operational amplifiers, it has many essential advantages such as wider and nearly constant bandwidth independent of closed-loop gain, higher slew rate, lower sensitivity, larger dynamic range, lower power consumption, and ease of realizing various functions with lesser number of passive components. The fully integrated continuous time filter has been successfully applied in ICs for communication, significant efforts have been devoted to study of MOS transistor-only (MOS-only) active components [9–11] and filter circuits. The CMOS CFOAs are used to design Nth-order universal filter circuit in this article. Multifunction filter circuits have many possible applications such as three-way highfidelity loudspeakers in crossover networks, touchtone telephone systems, phase-locked loop FM stereo demodulators, analog sections of high-speed data communication systems, signal processing in cable modems, and so on [12]. Numerous analog circuits have been implemented based on CFOA [13,14,15,16,17,18,19,20,21]. The MOS-only circuits in [16] realize first- and second-order allpass filters without using any external passive components. But the function of the proposed circuit is simple. A third-order currentmode filter based on CMOS CFOA is presented in [17], and PSPICE simulations using 0.18 m TSMC CMOS technology are carried out.
∗ Corresponding author. Tel.: +86 18604304073. E-mail address: [email protected] (C. Wang). http://dx.doi.org/10.1016/j.ijleo.2015.11.127 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
A new multiple input multiple output (MIMO) circuit in [18] using 3 CFOAs can offer voltage-mode universal biquad, but the circuit employing 2 floating capacitors is unsuitable for integrated circuit implementation. A MIMO voltage-mode universal biquad is introduced in [19], the obtained circuit using only 2 CFOAs and grounded capacitors can be directly connected to the next stage. The mixed-mode universal biquad in [20] using specific current feedback operational amplifier (SCFOA) is presented. But currentmode and voltage-mode filter functions can be realized by changing the circuit topology, and the SCFOA is not commercially available. A fifth-order voltage-mode low-pass filter circuit is presented in [21]. The proposed circuit employs more active elements (5 CFOAs and 4 inverting amplifiers), and the function of the circuit is simple. There are also some Nth-order filter circuits used other active components in [22–25]. A novel Nth-order voltage-mode universal filter circuit is introduced in this article. The proposed circuit topology is introduced in Section 2. To verify the capability of the proposed circuit, PSPICE simulations using 0.18 m CMOS technology are provided in Section 3. And the sensitivity analysis of Nth-order filter circuit is given in Section 4. 2. Circuit design
⎡
The four ports relations of CFOA can be expressed as follows:
⎤ ⎡ vy ⎤ ⎢ ⎥ ⎣ ⎢ ⎥ ⎣ vx ⎦ = 1 0 0 ⎦ ⎣ ix ⎦ and vo = vz iy
iz
⎤
⎡
0
0
0
0
1 0
vz
(1)
C. Wang et al. / Optik 127 (2016) 2226–2230
2227
Fig. 1. Circuit symbol of the CFOA.
Fig. 3. Layout of CMOS CFOA (39.40 m × 37.85 m).
Fig. 4. The circuit of Nth-order voltage-mode filter using CFOAs.
Fig. 2. CMOS implementation of CFOA.
The circuit symbol of a CFOA is shown in Fig. 1. The CMOS implementation circuit of CFOA is shown in Fig. 2, which is used in PSPICE simulations. Layout of CMOS CFOA is shown in Fig. 3, the area of CFOA layout is 39.40 m × 37.85 m. A voltage buffer is formed by M1–M2 which makes the voltage of X-terminal follow the voltage of Y-terminal. Two current followers are formed by M7–M10 and M21–M24 which transfer the current from X-terminal to Z-terminal. Another voltage buffer is formed by M11–M12 whose function is identical to the one between Y and X. The circuit configuration of Nth-order voltage-mode filter circuit is designed as Fig. 4. It should be mentioned that all capacitors in Fig. 4 is grounded, this is an attractive benefit in integration. In Fig. 4, Ri1 = R2 (i = 1, 2, . . ., n + 1), R1 = R2 = ·· · = Rn , C1 = C2 = ·· · = Cn . The output voltage Vo of the circuit in Fig. 4 is calculated as follows:
Vo =
−1 Vn+1 + n−1 Vn s−1 + n−1 n−1 Vn−1 s−2 + · · · + n−1 · · · 2−1 V2 s−n+1 + n−1 · · · 1−1 V1 s−n
1+
n−1 s−1
+
−1 −2 n−1 n−1 s
= Rm Cm (m = 1, 2, . . ., n)
+···+
−1 n−1 n−1
···
2−1 s−n+1
+
−1 n−1 n−1 · · ·1−1 s−n
(i) if n is an even V2 = V4 = ·· · = Vn = − Vi , (ii) if n is an odd V1 = V3 = ·· · = Vn = − Vi .
(2)
The realization of the 5 Nth-order filter functions can be achieved by changing the status of input voltage (Vi ): (a) Low-pass filter function: V2 = V3 = ·· · = Vn = Vn+1 = 0, V1 = Vi (b) High-pass filter function: V1 = V2 = ·· · = Vn−1 = Vn = 0, Vn+1 = Vi (c) Band-pass filter function: V1 = V2 = ·· · = Vm−1 = Vm+1 = ·· · = Vn = Vn+1 = 0, Vm = Vi (m = / 1 and m = / n + 1) (d) Band-stop filter function: V2 = V3 = ·· · = Vn−1 = Vn = 0, V1 = Vn+1 = Vi (e) All-pass filter function:
V1 = V3 = ·· · = Vn−1 = Vn+1 = Vi ,
number:
V2 = V4 = ·· · = Vn−1 = Vn+1 = Vi ,
The parameters comparison of Nth-order active filter circuits between published articles and this paper is shown in Table 1. From the above comparison, we can see that the proposed circuit uses less components and realizes the universal filter functions.
3. Example and simulations To verify the performance of proposed circuit, PSPICE simulations take third-order and fourth-order Butterworth filters for examples. Design a third-order Butterworth filter circuit, the normalized transfer function (TF) of the third-order Butterworth filter is: H(s) =
m
number:
s3 − 2s2 + 2s − 1 s3 + 2s2 + 2s + 1
(3)
The time constants of third-order Butterworth filter are: 1 = 2, 2 = 1, 3 = 0.5. The values of resistors are given as: R21 = R22 = R31 = R32 = R41 = R42 = 0.25 k˝, R1 = R2 = R3 = 10 k˝, and the parameters of capacitors are calculated as: C1 = 200 F, C2 = 100 F, C3 = 50 F. The anti-normalization values of capacitors are: C1 = 3.18 pF, C2 = 1.59 pF, C3 = 0.796 pF. The natural frequency of the third-order Butterworth filter is 10 MHz. When V1 = Vi , V2 = V3 = V4 = 0, the amplitude-frequency response curve of lowpass filter is shown in Fig. 5. When V4 = Vi , V1 = V2 = V3 = 0, the amplitude-frequency response curve of high-pass filter is depicted in Fig. 6. When V3 = Vi , V1 = V2 = V4 = 0, the amplitude-frequency response curve of band-pass filter is depicted in Fig. 7. When V2 = V4 = − Vi , V1 = V3 = Vi , the amplitude-frequency response curve of all-pass filter is depicted in Fig. 8.
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C. Wang et al. / Optik 127 (2016) 2226–2230
Table 1 The comparison of Nth-order active filter circuits. Article
Active components
Passive components
CMOS technology
Function
Change circuit topology
[22]
2n + 1 CCIIs voltage-mode 2n + 2 CCIIs current-mode 2n OTAs n + 1 AD844s 2n + 2 OTAs n + 2 OTAs 2n CFOAs
n Grounded capacitors2n + 2 resistors n Grounded capacitors2n + 2 resistors n Floating capacitors n Grounded capacitors5n + 3 resistors n Grounded capacitors n Grounded capacitors n Grounded capacitors 3n resistors
0.18 m TSMC
Universal Universal Universal
Yes
[23] [24] [25] Proposed circuit
– – UMC05 0.18 m TSMC
Fig. 5. Simulation curve of third-order low-pass filter.
Universal Low-passHigh-pass Band-pass Universal
Yes Yes No No
Fig. 9. Simulation curve of fourth-order low-pass filter.
Fig. 6. Simulation curve of third-order high-pass filter.
Fig. 10. Simulation curve of fourth-order band-pass filter.
Another example is fourth-order Butterworth filter, whose natural frequency is 10 MHz. The normalized transfer function of the fourth-order Butterworth filter is:
H (s) = Fig. 7. Simulation curve of third-order band-pass filter.
Fig. 8. Simulation curve of third-order all-pass filter.
s4 − 2.613s3 + 3.414s2 − 2.613s + 1 s4 + 2.613s3 + 3.414s2 + 2.613s + 1
(4)
The time constants of fourth-order Butterworth filter are: 1 = 2.613, 2 = 1.307, 3 = 0.765, 4 = 0.383. The values of resistors are given as: R21 = R22 = R31 = R32 = R41 = R42 = R51 = R52 = 110 ˝, R1 = R2 = R3 = R4 = 5 K˝. And the parameters of capacitors are calculated as: C1 = 522.6 F, C2 = 261.4 F, C3 = 153 F, C4 = 76.6 F. The values of anti-normalization capacitors are: C1 = 8.3174 pF, C2 = 4.1603 pF, C3 = 2.4351 pF, C4 = 1.2191 pF. When V1 = Vi , V2 = V3 = V4 = V5 = 0, the amplitudefrequency response curve of low-pass filter is depicted in Fig. 9. When V3 = Vi , V1 = V2 = V4 = V5 = 0, the amplitudefrequency response curve of band-pass filter is depicted in Fig. 10.
C. Wang et al. / Optik 127 (2016) 2226–2230 Table 2 Sensitivities of third-order Butterworth low-pass filter.
4. Sensitivity analysis of proposed filter circuit The TF of Nth-order low-pass filter can be described as (3): H0 H0 = Tn (s) an sn + an−1 sn−1 + an−2 sn−2 + · · · + a1 s1 + 1
H(s) =
=
⎧ m ωi 2 ⎪ ⎪
H0 ˘ ⎪ ω ⎪ i i=1 s2 + ⎪ s + ωi2 ⎨ Q
m
0
SlQ1
−1/2
0
1
0
Sl j
–1
1
–1
0
R2 (C2 )
R3 (C3 )
R4 (C4 )
Rij (i = 2, 3, 4, 5 ; j = 1, 2)
–0.85
0.35
0.35
–0.85
0
SlQ1
–0.35
0.85
–0.85
0.35
0
–0.85
–0.85
0.35
0
0.85
0
Slω2 j
0.35
SlQ2
–0.85
j
⎡ (4)
⎢ ⎣
A3 = ⎢
1 y1 xz1 + y1 0
ωi Qi
And the TF of Nth-order low-pass filter can be changed to (5):
⎧ m 1 ⎪ ⎨ H0 ˘ (y + z s + 1) i i=1 i H (s) = 1 ⎪ H0 m ⎩
˘ xs + 1 i=1 (yi + zi s + 1)
(5) n = 2m + 1
Let
an−1 = fn−1 (y1 , z1 , y2 , z2 , . . ., x)
(6)
···
f
f
Syn2
⎢ fn−1 fn−1 fn−1 ⎢ Sy Sy2 ⎢ 1 Sz1 ⎢ f ⎢ Syn−2 Szfn−2 Syfn−2 ⎢ 1 2 1 ⎢ ⎣ f
f
f
Sz11
Sy11
Sy12
⎤ ⎡ y1 ⎤ ⎡ an ⎤ Sl Sl j j ⎥ ⎢ an−1 ⎥ fn−1 ⎥ ⎢ z1 ⎥ ⎥ Sl · · · Sx ⎥ ⎢ Sl ⎥ ⎢ ⎥ j ⎢ yj ⎥ ⎢ ⎥ ⎢ ⎥ a n−2 ⎢ ⎥ 2 fn−2 ⎥ · = ⎢ ⎥ S S · · · Sx ⎥ ⎢ lj ⎥ ⎢ lj ⎥ ⎢ ⎥ ⎥ ⎣ ⎦ ⎢ ⎥ ⎦ ⎣ ⎦ ··· ···
···
f
Sxn
f
Sxn−3
Slx j
(7)
j
⎥ ⎥. ⎦
0
0
0.5
A3 = ⎣ 0.5 0.5
1
⎤
0.5 ⎦ . 0.5
The Tn (s) of third-order filter in Fig. 9 is: 2 + R C s + 1, = R1 R2 R3 C1 C2 C3 s3 + R1 R2 C1 C2 s so we have Tn (s) 1 1 1 0 a xyz S = 1 lj = R1 , and S = 1 . The sensitivity matrix 1 1 SRω1
⎤
⎡
⎤
0 ⎢ 1⎥ of R1 is: ⎣ S ⎦ = ⎣ − ⎦. 2 SR −1 1 Using above method, we can calculate all sensitivities of thirdorder and fourth-order low-pass filter as Table 2 and Table 3. From Table 2 and Table 3, we can see that the sensitivities of the proposed third-order filter circuit are low, and the sensitivities of a few components will increase for fourth-order filter.
5. Simulation analysis
j
⎧ ω 1 y ⎪ Sl i = − Sl i ⎪ ⎪ 2 j ⎨ j 1
⎤
a
Sl 1
and
Q y z Sl i = Sl i − Sl i ⎪ j j 2 j ⎪ ⎪ ⎩ S = −Sx l l
1 xz1 xz1 + y1 x z1 + x
H (s) = H0 /Tn (s) =
1 Q1 R1
Using (4) and (6), we can get Szn1
1
⎡
a1 = f1 (y1 , z1 , y2 , z2 , . . ., x)
0 xz1 xz1 + y1 z1 z1 + x
is:
The Tn (s) of third-order Butterworth filter is: Tn (s) = (s + 1)(s2 + s + 1), so the A3 is calculated as:
⎡
n = 2m
⎧ an = fn (y1 , z1 , y2 , z2 , . . ., x) ⎪ ⎪ ⎪ ⎨
f
2.062
The TF of third-order system H0 / (xs + 1) y1 s2 + z1 s + 1 , we can get
1
Syn1
–2.061
Qi ωi
i ω2 ⎪ ⎪ ⎪ ⎪ ⎩ zi = 1
⎡
Rij (i = 2, 3, 4 ; j = 1, 2)
R1 (C1 )
j
⎧ 1 ⎪ x= ⎪ ⎪ ⎪ ⎨
⎪ ⎪ ⎪ ⎩
R3 (C3 )
Slω1 j
n = 2m
We introduce three parameters: x, yi , zi
y =
0
(3)
1
ωi
–1
Table 3 Sensitivities of fourth-order Butterworth low-pass filter.
⎪ ⎪ n = 2m + 1 ˘ 2 ⎪ s ⎪ ⎪ i=1 1 s ⎪ ⎩ +1 + s + 1 2 H0
R2 (C2 )
0
j
i
⎪ H0 m ωi 2 ⎪ ⎪
n = 2m + 1 ˘ ⎪ ⎪ ⎩ s + i=1 s2 + ωi s + ωi2 Qi
=
R1 (C1 ) Slω1 j
n = 2m
⎧ m 1 ⎪ H0 ˘ ⎪ 2 ⎪ i=1 1 s ⎪ ⎪ + s + 1 ⎪ ⎨ Qi ωi ωi2
2229
(8)
j
where li (j = 1, 2, . . ., n) represent Rj and Cj in proposed filter circuit, and we use A · Sxyz = Sa to replace (9). So we can calculate sensitivities of Nth-order low-pass filter circuit by A and Sa .
PSPICE simulation used the CMOS CFOA circuit given by Fig. 2. The supply voltages are given as: VDD = − VSS = 1.65 V, Vb1 = −0.35 V, and Vb2 = −1 V. The power consumption of proposed third-order filter is 48 mW, DC component is −4.116 mV. The total harmonic distortion of third-order low-pass filter at 100 KHz is 2.39%, which is an evidence to see that there is no significant distortion. The power consumption of proposed fourth-order filter is 64 mW which is higher than third-order filter as using more components. The Monte Carlo analysis of fourth-order Butterworth low-pass filter is shown in Fig. 11 where the error coefficient of resistors is 5% and the error coefficient of capacitors is 10%.
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C. Wang et al. / Optik 127 (2016) 2226–2230
[7]
[8]
[9] [10]
[11]
Fig. 11. The Monte Carlo analysis of fourth-order Butterworth low-pass filter.
[12]
6. Conclusions
[13]
A CFOA Nth-order voltage-mode versatile filter circuit based is proposed. Third-order and fourth-order Butterworth filters as applications for presented circuit are given in this article. The Monte Carlo analysis of fourth-order Butterworth low-pass filter is given to see that the sensitivities of proposed circuit are low. The PSPICE simulations verify the theoretical design. The design technique in this article has some characteristics: (1) using only one kind of active components and all the capacitors are grounded. (2) compared with available literature, using less components to realize Nth-order universal filter circuit. (3)completing sensitivity analysis of Nth-order filter circuit.
[14]
References [1] S. Topaloglu, M. Sagbas, F. Anday, Three-input single-output second-order filters using current-feedback amplifiers, AEU Int. J. Electron. Commun. 66 (8) (2012) 683–686. [2] A. Lahiri, M. Gupta, Realizations of grounded negative capacitance using CFOAs, Circuits Syst. Signal Process. 30 (1) (2011) 143–155. [3] G. Raikos, C. Psychalinos, Low-voltage current feedback operational amplifiers, Circuits Syst. Signal Process. 28 (3) (2009) 377–388. [4] R. Nandi, T.K. Bandyopadhyay, S.K. Sanyal, Selective filters and sinusoidal oscillators using CFA transimpedance pole, Circuits Syst. Signal Process. 28 (3) (2009) 349–359. [5] A.A. Tammam, K. Hayatleh, M. Ben-Esmael, Critical review of the circuit architecture of CFOA, Int. J. Electron. 101 (4) (2014) 441–451. [6] M. ElGuindy, A.H. Madian, Low-Voltage Fully Differential CMOS Neural Amplifier based on CFOA, in: Proc. 2013 IEEE Int. Conf.
[15]
[16] [17]
[18] [19]
[20] [21]
[22] [23]
[24]
[25]
Electronics, Circuits, and Systems, Abu Dhabi, United Arab Emirates, 2013, pp. 526–529. M.T. Abuelma’atti, New grounded immittance function simulators using single current feedback operational amplifier, Analog. Integr. Circuits Signal Process. 71 (1) (2012) 95–100. R. Senani, D.R. Bhaskar, New lossy/loss-less synthetic floating inductance configuration realized with only two CFOAs, Analog. Integr. Circuits Signal Process. 73 (3) (2012) 981–987. H. Jassim, A new design technique of CMOS current feed back operational amplifier (CFOA), Circuits Syst. 4 (1) (2013) 11–15. Zhang Yaowen, Yang Li, Design of CMOS current-feedback op-amps based on 0.25 m technology, in: Proc. Int. Conf. on Computer Science and Service System, Nanjing, China, 2011, pp. 3156–3159. A. Pena-Perez, E. Tlelo-Cuautle, A. Diaz-Mendez, Design of a CMOS Compatible CFOA and its Application in Analog Filtering, IEEE Lat. Am. Trans. 5 (2) (2007) 71–75. N. Herencsar, J. Koton, K. Vrba, Voltage-mode universal filters employing single modified current feedback operational amplifier (MCFOA), in: Proc. Int. Conf. on Electrical and Electron. Engineering, Bursa, Turkey, 2009, pp. II-83–(pp.II–L870. S. Topaloglu, M. Sagbas, F. Anday, Three-input single-output second-order filters using current-feedback amplifiers, AEU Int. J. Electron. Commun. 66 (2012) 683–686. I.M. Pandiev, Analysis and design of CFOA-based high speed amplifier circuits, in: Proc. 20th Telecommunications Forum, Belgrade, Serbia, 2012, pp. 979–982. K. Garg, R. Bhagat, B. Jainti, A novel multifunction modified CFOA based inverse filter, in: Proc 2012 IEEE Fifth India Int. Conf. on Power Electron, Delhi, 2012, pp. 1–5. H.A. Yildiz, S. Ozoguz, O. Cicekoglu, On the realization of MOS-only allpass filter, Circuits Syst. Signal Process. 32 (3) (2013) 1455–1465. L.A. Said, A.H. Madian, M.H. Ismail, Active realization of doubly terminated LC ladder filters using current feedback operational amplifier (CFOA) via linear transformation, AEU Int. J. Electron. Commun. 65 (9) (2011) 753. N.A. Shah, S.Z. Iqbal, M.F. Rather, Versatile voltage-mode CFA-based universal filter, AEU Int. J. Electron. Commun. 59 (3) (2005) 192–194. J.W. Horng, Voltage-mode universal biquad with five inputs and two outputs using two current feedback amplifiers, Indian J. Eng. Mater. Sci. 20 (2) (2013) 87–91. E. Yuce, Fully integrable mixed-mode universal biquad with specific application of the CFOA, AEU Int. J. Electron. Commun. 64 (4) (2010) 304–309. Liang Yu Peng, Yi Gang He, Jie Wu, Realization of the voltage-mode fifth-order low-pass filter based on current-feedback amplifier, J. Circuits Syst. 8 (6) (2003) 129–131. J.W. Horng, Analytical synthesis of general high-order voltage/current transfer functions using CCIIs, Microelectron. J. 43 (8) (2012) 546–554. Y. Sun, J.K. Fidler, Synthesis and performance analysis of universal minimum component integrator-based IFLF OTA-grounded capacitor filter, IEE Proc. Circuits Devices Syst. 143 (2) (1996) 107–114. C. Acar, Nth-order voltage transfer function synthesis using a commercially available active component: signal-flow graph approac, Electron. Lett. 32 (21) (1996) 1933–1934. C.M. Chang, B.M. Al-Hashimi, Y. Sun, New high-order filter structures using only single-ended-input OTAs and grounded capacitors, IEEE Trans. Circuits Syst. Express Briefs 51 (9) (2004) 458–463.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
A novel Nth-order voltage-mode universal filter based on CMOS CFOA Chunyue Wang a,∗ , Junru Zhang a , Lixue Wang a , Wenxiao Shi a , Deng Jing b a b
College of Communication and Engineering, Jilin University, Changchun 130012, China Department of Computer Science, University of North Carolina at Greensboro 164 Petty Building, Greensboro, NC 27412, USA
a r t i c l e
i n f o
Article history: Received 10 May 2015 Accepted 16 November 2015 Keywords: Active circuit Nth-order universal filter Current feedback operational amplifier Voltage-mode
a b s t r a c t With the development of integrated circuits, the fully integrated continuous time filter has been focused widely. A Nth-order universal filter based on Current Feedback Operational Amplifier (CFOA) is proposed. Compared with available circuits, the proposed circuit using less components (2n CFOAs, n capacitors, and 3n resistors) can realize the universal filter functions without changing circuit configuration, and the operating frequency of proposed filter circuit is at least 10 MHz. All of capacitors in proposed circuit are grounded, this is another benefit from integration point of view. PSPICE simulations have been carried out using 0.18 m CMOS technology, and sensitivity analysis of proposed Nth-order low-pass filter circuit is completed. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction The current feedback operational amplifier (CFOA) is one of the most important active building blocks in fully integrated continuous time circuits [1–8]. Compared with traditional voltage-mode operational amplifiers, it has many essential advantages such as wider and nearly constant bandwidth independent of closed-loop gain, higher slew rate, lower sensitivity, larger dynamic range, lower power consumption, and ease of realizing various functions with lesser number of passive components. The fully integrated continuous time filter has been successfully applied in ICs for communication, significant efforts have been devoted to study of MOS transistor-only (MOS-only) active components [9–11] and filter circuits. The CMOS CFOAs are used to design Nth-order universal filter circuit in this article. Multifunction filter circuits have many possible applications such as three-way highfidelity loudspeakers in crossover networks, touchtone telephone systems, phase-locked loop FM stereo demodulators, analog sections of high-speed data communication systems, signal processing in cable modems, and so on [12]. Numerous analog circuits have been implemented based on CFOA [13,14,15,16,17,18,19,20,21]. The MOS-only circuits in [16] realize first- and second-order allpass filters without using any external passive components. But the function of the proposed circuit is simple. A third-order currentmode filter based on CMOS CFOA is presented in [17], and PSPICE simulations using 0.18 m TSMC CMOS technology are carried out.
∗ Corresponding author. Tel.: +86 18604304073. E-mail address: [email protected] (C. Wang). http://dx.doi.org/10.1016/j.ijleo.2015.11.127 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
A new multiple input multiple output (MIMO) circuit in [18] using 3 CFOAs can offer voltage-mode universal biquad, but the circuit employing 2 floating capacitors is unsuitable for integrated circuit implementation. A MIMO voltage-mode universal biquad is introduced in [19], the obtained circuit using only 2 CFOAs and grounded capacitors can be directly connected to the next stage. The mixed-mode universal biquad in [20] using specific current feedback operational amplifier (SCFOA) is presented. But currentmode and voltage-mode filter functions can be realized by changing the circuit topology, and the SCFOA is not commercially available. A fifth-order voltage-mode low-pass filter circuit is presented in [21]. The proposed circuit employs more active elements (5 CFOAs and 4 inverting amplifiers), and the function of the circuit is simple. There are also some Nth-order filter circuits used other active components in [22–25]. A novel Nth-order voltage-mode universal filter circuit is introduced in this article. The proposed circuit topology is introduced in Section 2. To verify the capability of the proposed circuit, PSPICE simulations using 0.18 m CMOS technology are provided in Section 3. And the sensitivity analysis of Nth-order filter circuit is given in Section 4. 2. Circuit design
⎡
The four ports relations of CFOA can be expressed as follows:
⎤ ⎡ vy ⎤ ⎢ ⎥ ⎣ ⎢ ⎥ ⎣ vx ⎦ = 1 0 0 ⎦ ⎣ ix ⎦ and vo = vz iy
iz
⎤
⎡
0
0
0
0
1 0
vz
(1)
C. Wang et al. / Optik 127 (2016) 2226–2230
2227
Fig. 1. Circuit symbol of the CFOA.
Fig. 3. Layout of CMOS CFOA (39.40 m × 37.85 m).
Fig. 4. The circuit of Nth-order voltage-mode filter using CFOAs.
Fig. 2. CMOS implementation of CFOA.
The circuit symbol of a CFOA is shown in Fig. 1. The CMOS implementation circuit of CFOA is shown in Fig. 2, which is used in PSPICE simulations. Layout of CMOS CFOA is shown in Fig. 3, the area of CFOA layout is 39.40 m × 37.85 m. A voltage buffer is formed by M1–M2 which makes the voltage of X-terminal follow the voltage of Y-terminal. Two current followers are formed by M7–M10 and M21–M24 which transfer the current from X-terminal to Z-terminal. Another voltage buffer is formed by M11–M12 whose function is identical to the one between Y and X. The circuit configuration of Nth-order voltage-mode filter circuit is designed as Fig. 4. It should be mentioned that all capacitors in Fig. 4 is grounded, this is an attractive benefit in integration. In Fig. 4, Ri1 = R2 (i = 1, 2, . . ., n + 1), R1 = R2 = ·· · = Rn , C1 = C2 = ·· · = Cn . The output voltage Vo of the circuit in Fig. 4 is calculated as follows:
Vo =
−1 Vn+1 + n−1 Vn s−1 + n−1 n−1 Vn−1 s−2 + · · · + n−1 · · · 2−1 V2 s−n+1 + n−1 · · · 1−1 V1 s−n
1+
n−1 s−1
+
−1 −2 n−1 n−1 s
= Rm Cm (m = 1, 2, . . ., n)
+···+
−1 n−1 n−1
···
2−1 s−n+1
+
−1 n−1 n−1 · · ·1−1 s−n
(i) if n is an even V2 = V4 = ·· · = Vn = − Vi , (ii) if n is an odd V1 = V3 = ·· · = Vn = − Vi .
(2)
The realization of the 5 Nth-order filter functions can be achieved by changing the status of input voltage (Vi ): (a) Low-pass filter function: V2 = V3 = ·· · = Vn = Vn+1 = 0, V1 = Vi (b) High-pass filter function: V1 = V2 = ·· · = Vn−1 = Vn = 0, Vn+1 = Vi (c) Band-pass filter function: V1 = V2 = ·· · = Vm−1 = Vm+1 = ·· · = Vn = Vn+1 = 0, Vm = Vi (m = / 1 and m = / n + 1) (d) Band-stop filter function: V2 = V3 = ·· · = Vn−1 = Vn = 0, V1 = Vn+1 = Vi (e) All-pass filter function:
V1 = V3 = ·· · = Vn−1 = Vn+1 = Vi ,
number:
V2 = V4 = ·· · = Vn−1 = Vn+1 = Vi ,
The parameters comparison of Nth-order active filter circuits between published articles and this paper is shown in Table 1. From the above comparison, we can see that the proposed circuit uses less components and realizes the universal filter functions.
3. Example and simulations To verify the performance of proposed circuit, PSPICE simulations take third-order and fourth-order Butterworth filters for examples. Design a third-order Butterworth filter circuit, the normalized transfer function (TF) of the third-order Butterworth filter is: H(s) =
m
number:
s3 − 2s2 + 2s − 1 s3 + 2s2 + 2s + 1
(3)
The time constants of third-order Butterworth filter are: 1 = 2, 2 = 1, 3 = 0.5. The values of resistors are given as: R21 = R22 = R31 = R32 = R41 = R42 = 0.25 k˝, R1 = R2 = R3 = 10 k˝, and the parameters of capacitors are calculated as: C1 = 200 F, C2 = 100 F, C3 = 50 F. The anti-normalization values of capacitors are: C1 = 3.18 pF, C2 = 1.59 pF, C3 = 0.796 pF. The natural frequency of the third-order Butterworth filter is 10 MHz. When V1 = Vi , V2 = V3 = V4 = 0, the amplitude-frequency response curve of lowpass filter is shown in Fig. 5. When V4 = Vi , V1 = V2 = V3 = 0, the amplitude-frequency response curve of high-pass filter is depicted in Fig. 6. When V3 = Vi , V1 = V2 = V4 = 0, the amplitude-frequency response curve of band-pass filter is depicted in Fig. 7. When V2 = V4 = − Vi , V1 = V3 = Vi , the amplitude-frequency response curve of all-pass filter is depicted in Fig. 8.
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Table 1 The comparison of Nth-order active filter circuits. Article
Active components
Passive components
CMOS technology
Function
Change circuit topology
[22]
2n + 1 CCIIs voltage-mode 2n + 2 CCIIs current-mode 2n OTAs n + 1 AD844s 2n + 2 OTAs n + 2 OTAs 2n CFOAs
n Grounded capacitors2n + 2 resistors n Grounded capacitors2n + 2 resistors n Floating capacitors n Grounded capacitors5n + 3 resistors n Grounded capacitors n Grounded capacitors n Grounded capacitors 3n resistors
0.18 m TSMC
Universal Universal Universal
Yes
[23] [24] [25] Proposed circuit
– – UMC05 0.18 m TSMC
Fig. 5. Simulation curve of third-order low-pass filter.
Universal Low-passHigh-pass Band-pass Universal
Yes Yes No No
Fig. 9. Simulation curve of fourth-order low-pass filter.
Fig. 6. Simulation curve of third-order high-pass filter.
Fig. 10. Simulation curve of fourth-order band-pass filter.
Another example is fourth-order Butterworth filter, whose natural frequency is 10 MHz. The normalized transfer function of the fourth-order Butterworth filter is:
H (s) = Fig. 7. Simulation curve of third-order band-pass filter.
Fig. 8. Simulation curve of third-order all-pass filter.
s4 − 2.613s3 + 3.414s2 − 2.613s + 1 s4 + 2.613s3 + 3.414s2 + 2.613s + 1
(4)
The time constants of fourth-order Butterworth filter are: 1 = 2.613, 2 = 1.307, 3 = 0.765, 4 = 0.383. The values of resistors are given as: R21 = R22 = R31 = R32 = R41 = R42 = R51 = R52 = 110 ˝, R1 = R2 = R3 = R4 = 5 K˝. And the parameters of capacitors are calculated as: C1 = 522.6 F, C2 = 261.4 F, C3 = 153 F, C4 = 76.6 F. The values of anti-normalization capacitors are: C1 = 8.3174 pF, C2 = 4.1603 pF, C3 = 2.4351 pF, C4 = 1.2191 pF. When V1 = Vi , V2 = V3 = V4 = V5 = 0, the amplitudefrequency response curve of low-pass filter is depicted in Fig. 9. When V3 = Vi , V1 = V2 = V4 = V5 = 0, the amplitudefrequency response curve of band-pass filter is depicted in Fig. 10.
C. Wang et al. / Optik 127 (2016) 2226–2230 Table 2 Sensitivities of third-order Butterworth low-pass filter.
4. Sensitivity analysis of proposed filter circuit The TF of Nth-order low-pass filter can be described as (3): H0 H0 = Tn (s) an sn + an−1 sn−1 + an−2 sn−2 + · · · + a1 s1 + 1
H(s) =
=
⎧ m ωi 2 ⎪ ⎪
H0 ˘ ⎪ ω ⎪ i i=1 s2 + ⎪ s + ωi2 ⎨ Q
m
0
SlQ1
−1/2
0
1
0
Sl j
–1
1
–1
0
R2 (C2 )
R3 (C3 )
R4 (C4 )
Rij (i = 2, 3, 4, 5 ; j = 1, 2)
–0.85
0.35
0.35
–0.85
0
SlQ1
–0.35
0.85
–0.85
0.35
0
–0.85
–0.85
0.35
0
0.85
0
Slω2 j
0.35
SlQ2
–0.85
j
⎡ (4)
⎢ ⎣
A3 = ⎢
1 y1 xz1 + y1 0
ωi Qi
And the TF of Nth-order low-pass filter can be changed to (5):
⎧ m 1 ⎪ ⎨ H0 ˘ (y + z s + 1) i i=1 i H (s) = 1 ⎪ H0 m ⎩
˘ xs + 1 i=1 (yi + zi s + 1)
(5) n = 2m + 1
Let
an−1 = fn−1 (y1 , z1 , y2 , z2 , . . ., x)
(6)
···
f
f
Syn2
⎢ fn−1 fn−1 fn−1 ⎢ Sy Sy2 ⎢ 1 Sz1 ⎢ f ⎢ Syn−2 Szfn−2 Syfn−2 ⎢ 1 2 1 ⎢ ⎣ f
f
f
Sz11
Sy11
Sy12
⎤ ⎡ y1 ⎤ ⎡ an ⎤ Sl Sl j j ⎥ ⎢ an−1 ⎥ fn−1 ⎥ ⎢ z1 ⎥ ⎥ Sl · · · Sx ⎥ ⎢ Sl ⎥ ⎢ ⎥ j ⎢ yj ⎥ ⎢ ⎥ ⎢ ⎥ a n−2 ⎢ ⎥ 2 fn−2 ⎥ · = ⎢ ⎥ S S · · · Sx ⎥ ⎢ lj ⎥ ⎢ lj ⎥ ⎢ ⎥ ⎥ ⎣ ⎦ ⎢ ⎥ ⎦ ⎣ ⎦ ··· ···
···
f
Sxn
f
Sxn−3
Slx j
(7)
j
⎥ ⎥. ⎦
0
0
0.5
A3 = ⎣ 0.5 0.5
1
⎤
0.5 ⎦ . 0.5
The Tn (s) of third-order filter in Fig. 9 is: 2 + R C s + 1, = R1 R2 R3 C1 C2 C3 s3 + R1 R2 C1 C2 s so we have Tn (s) 1 1 1 0 a xyz S = 1 lj = R1 , and S = 1 . The sensitivity matrix 1 1 SRω1
⎤
⎡
⎤
0 ⎢ 1⎥ of R1 is: ⎣ S ⎦ = ⎣ − ⎦. 2 SR −1 1 Using above method, we can calculate all sensitivities of thirdorder and fourth-order low-pass filter as Table 2 and Table 3. From Table 2 and Table 3, we can see that the sensitivities of the proposed third-order filter circuit are low, and the sensitivities of a few components will increase for fourth-order filter.
5. Simulation analysis
j
⎧ ω 1 y ⎪ Sl i = − Sl i ⎪ ⎪ 2 j ⎨ j 1
⎤
a
Sl 1
and
Q y z Sl i = Sl i − Sl i ⎪ j j 2 j ⎪ ⎪ ⎩ S = −Sx l l
1 xz1 xz1 + y1 x z1 + x
H (s) = H0 /Tn (s) =
1 Q1 R1
Using (4) and (6), we can get Szn1
1
⎡
a1 = f1 (y1 , z1 , y2 , z2 , . . ., x)
0 xz1 xz1 + y1 z1 z1 + x
is:
The Tn (s) of third-order Butterworth filter is: Tn (s) = (s + 1)(s2 + s + 1), so the A3 is calculated as:
⎡
n = 2m
⎧ an = fn (y1 , z1 , y2 , z2 , . . ., x) ⎪ ⎪ ⎪ ⎨
f
2.062
The TF of third-order system H0 / (xs + 1) y1 s2 + z1 s + 1 , we can get
1
Syn1
–2.061
Qi ωi
i ω2 ⎪ ⎪ ⎪ ⎪ ⎩ zi = 1
⎡
Rij (i = 2, 3, 4 ; j = 1, 2)
R1 (C1 )
j
⎧ 1 ⎪ x= ⎪ ⎪ ⎪ ⎨
⎪ ⎪ ⎪ ⎩
R3 (C3 )
Slω1 j
n = 2m
We introduce three parameters: x, yi , zi
y =
0
(3)
1
ωi
–1
Table 3 Sensitivities of fourth-order Butterworth low-pass filter.
⎪ ⎪ n = 2m + 1 ˘ 2 ⎪ s ⎪ ⎪ i=1 1 s ⎪ ⎩ +1 + s + 1 2 H0
R2 (C2 )
0
j
i
⎪ H0 m ωi 2 ⎪ ⎪
n = 2m + 1 ˘ ⎪ ⎪ ⎩ s + i=1 s2 + ωi s + ωi2 Qi
=
R1 (C1 ) Slω1 j
n = 2m
⎧ m 1 ⎪ H0 ˘ ⎪ 2 ⎪ i=1 1 s ⎪ ⎪ + s + 1 ⎪ ⎨ Qi ωi ωi2
2229
(8)
j
where li (j = 1, 2, . . ., n) represent Rj and Cj in proposed filter circuit, and we use A · Sxyz = Sa to replace (9). So we can calculate sensitivities of Nth-order low-pass filter circuit by A and Sa .
PSPICE simulation used the CMOS CFOA circuit given by Fig. 2. The supply voltages are given as: VDD = − VSS = 1.65 V, Vb1 = −0.35 V, and Vb2 = −1 V. The power consumption of proposed third-order filter is 48 mW, DC component is −4.116 mV. The total harmonic distortion of third-order low-pass filter at 100 KHz is 2.39%, which is an evidence to see that there is no significant distortion. The power consumption of proposed fourth-order filter is 64 mW which is higher than third-order filter as using more components. The Monte Carlo analysis of fourth-order Butterworth low-pass filter is shown in Fig. 11 where the error coefficient of resistors is 5% and the error coefficient of capacitors is 10%.
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C. Wang et al. / Optik 127 (2016) 2226–2230
[7]
[8]
[9] [10]
[11]
Fig. 11. The Monte Carlo analysis of fourth-order Butterworth low-pass filter.
[12]
6. Conclusions
[13]
A CFOA Nth-order voltage-mode versatile filter circuit based is proposed. Third-order and fourth-order Butterworth filters as applications for presented circuit are given in this article. The Monte Carlo analysis of fourth-order Butterworth low-pass filter is given to see that the sensitivities of proposed circuit are low. The PSPICE simulations verify the theoretical design. The design technique in this article has some characteristics: (1) using only one kind of active components and all the capacitors are grounded. (2) compared with available literature, using less components to realize Nth-order universal filter circuit. (3)completing sensitivity analysis of Nth-order filter circuit.
[14]
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