A Design of a Symmetry-type Floating Impedance Scaling Circuit and Improvement of Operation Bandwidth Fujihiko Matsumoto, Syuzo Nishioka, Tatsuya Fujii, Takayuki Ohyama, Yuta Kobayashi, Takeshi Ohbuchi Department of Applied Physics, National Defense Academy 1-10-20, Hashirimizu, Yokosuka, 239-8686, Japan Telephone: +81-046-841-3810 ext 3629 Fax: +81-046-844-5912 Email: [email protected] (F. Matsumoto) I. v2 v1 Abstract—Low frequency and low power applications are required for biomedical devices. Thus, a large capacitance is needed for integration of low frequency active filters. To realize a smallsize low frequency active filter, impedance scaling techniques have been proposed. In this paper, a symmetry-type floating impedance scaling circuit is proposed. The proposed circuit is composed of a voltage follower and a current amplifier. The characteristics of the proposed circuit are confirmed by simulation. The proposed circuit works as a large capacitor, whose capacitance is multiplied by 50 times, in the frequency range from 10 Hz to 100 kHz. The frequency range becomes wider than the conventional circuit. Simulation results show validities and availability of the proposed symmetry-type floating scaling capacitor. i1 1 i2 Z Ni0 i0 Ni0 I NTRODUCTION Fig. 1. Filters are used to process various signals such as visuals, audios, and communications. Low frequency filter processing biomedical signals   from a few Hz to hundreds Hz requires a large time constant. In order to implement a large time constant, a large capacitance and a large resistance are needed. However, large capacitances and large resistances are impracticable in integrated circuits, which are required to be low-powered and downsized. The large resistance is implemented by a transconductor of low transconductance . The area occupied by a transconductor is much smaller than that of a resistor with the same resistance. In contrast, it is difficult to shrink the area occupied by large capacitances. As a method to realize a large capacitance, an impedance scaling circuit is proposed . The impedance scaling is a technique to reduce apparent impedance using current feedback. In this paper, a design of a symmetry-type floating impedance scaling circuit and the improvement method of operation bandwidth are proposed. The proposed circuit is applied to a fully differential 1st-order lowpass filter. The fully differential filter requires introducing of a common-mode rejection circuit. The interaction of the common-mode rejection circuit and the proposed floating impedance scaling circuit is confirmed by simulation. The common-mode impedance characteristics of the proposed impedance scaling circuit are verified by small-signal analysis. The effectiveness of the application to the lowpass filter of the proposed circuit is confirmed by simulation. II. Block Diagram of the Conventional Floating Scaling Circuit P RINCIPLE OF C ONVENTIONAL F LOATING I MPEDANCE S CALING C IRCUIT Fig.1 shows the block diagram of the conventional floating scaling circuit . This circuit is a composed of Differential Unity gain Amplifier (DUA) and a differential output current amplifier. The output voltage of the voltage follower is a voltage difference between v1 and v2 and is applied to the impedance element. The output current of the voltage follower is expressed as v1 − v2 i0 = . (1) Z Signal currents flowing through the impedance element is amplified by the current amplifier for current feedback. The differential output current amplifier multiplies a signal current i0 flowing through an impedance Z by N -times. The relationship of signal current i0 , i1 , and i2 are given by i1 = i2 = N i0 . (2) The apparent impedance of this circuit is expressed as Z v1 − v2 = . (3) Zsc = N i0 N The impedance is reduced by current feedback. If the impedance component Z is a capacitor which has capacitance C, Zsc is expressed as 1 Zsc = . (4) sCN M15 M5 M6 VDD Vb1 M16 M9 M24 M27 M23 M5 M4 M6 M28 Vb4 N :1 v1 v2 C M1 Vb3 M2 M19 M3 i1 v1 i2 v2 M30 M20 M4 i0 M29 M22 M26 M21 M8 1: N Vb4 M7 I1 VDD M3 Vb3 i1 i0 i2 M2 v2 M1 v1 C I1 M25 M1 M10 M11 M12 M13 M14 M31 Vb2 M18 Ni0 i0 1 i1 Z i0 v2 1 i0 M10 VSS Fig. 2. Circuit Diagram of the Conventional Floating Type Scaling Capacitor Circuit v1 M11 M9 gm5 i1 v1 Fig. 3. Block Diagram of the Proposed Symmetry-type Floating Scaling Capacitor Circuit This means that the circuit performs as floating capacitor having capacitance N C. Fig.2 shows the circuit diagram of the conventional circuit. The conventional circuit has current inverting amplifier for current feedback to i2 . Thus, the conventional circuit structure is asymmetry. P ROPOSED S YMMETRY- TYPE F LOATING I MPEDANCE S CALING C IRCUIT Fig.3 shows the block diagram of the proposed symmetrytype floating scaling capacitor circuit. This circuit is composed of two voltage followers and two current amplifiers. The output voltages of the voltage followers are applied to the impedance element Z. The signal current flowing through the impedance element is amplified with the current amplifier for current feedback. A. Basic Symmetry-type Floating Impedance Scaling Circuit The circuit diagram of the symmetry-type floating impedance scaling circuit based on the block diagram of Fig.3 is shown in Fig.4. Hereinafter, this circuit is called as “Proposed1”. The transistors M1 and M2 are source followers. The input voltage signal is applied to the capacitor C through the source followers. The current mirrors of M4 -M3 and M5 M6 perform as the current amplifier of N times. The signal current flowing through the capacitor is amplified by the current amplifier. Assuming that the resistance of the bias current sources M9 and M10 are enough large, the signal current flowing through the capacitor, i0 , is expressed as i0 = (v1 − v2 )sC. Rd 2C rd Fig. 5. Small Signal Equivalent Circuit of the Conventional Floating Type Scaling Capacitor Circuit (“Proposed1”) The impedance of this circuit is given by Zsc = v1 − v2 1 = . N (v1 − v2 )sC sCN (7) Therefore, the apparent capacitance is increased by N times. To confirm the frequency characteristics of “Proposed1” shown in Fig.4, the small-signal characteristics are analyzed. Assume that the fully differential voltages are applied to the both terminals, the input voltages are expressed as 1 vin 2 1 v2 = − vin . 2 v1 = (8) (9) The differential-mode half circuit of “Proposed1” is shown in Fig.5. The resistance rd indicates the drain resistance of the bias current source M10 . The resistance Rd indicates the resistance component observed from terminal v1 . The combined resistance Rd is the drain resistances connected in parallel and expressed as Rd = rd /(2N ). Assuming that gm rd ≫ 1, the impedance Z1 is given by Z1 = (6) v2 gm2 (5) The currents i1 and i2 are equal to N i, and expressed as i1 = i2 = N (v1 − v2 )sC. VSS Fig. 4. Circuit Diagram of the Symmetry-type Floating Type Scaling Capacitor Circuit (“Proposed1”) Ni0 III. M7 1: N N :1 gm6 i2 M8 v1 ≃ i1 2gm5 Rd (2Cs + gm2 ) ). ( gm5 gm2 gm6 2Cs + gm6 Rd (10) M19 M18 M17 VDD M15 M16 rd18 Rd gm4 Vb2 Vb2 M14 M4 M3 M13 i1 i2 M2 v2 M1 v1 Vb1 gm2 i1 v1 v2 2C gm8 Vb1 M10 M12 M8 M11 C M7 M6 M5 gm10 I1 gm6 M9 VSS N : 1 : 1 1 : 1 : N Fig. 6. Circuit Diagram of the Symmetry-type Floating Type Scaling Capacitor Circuit (“Proposed2”) The pole frequency ωp and the zero frequency ωz are given by 1 gm5 ≃ (11) gm6 Rd 2C Rd N 2C gm2 gm ωz ≃ ≃ , (12) 2C 2C where gm5 = gm2 = gm and gm6 = N gm . Because of rd > 1/gm , the pole frequency ωz is higher than the zero frequency ωp . The pole frequency depends on the resistance component Rd in the input terminal. The zero frequency depends on the conductance gm of the input source followers associated with capacitor employed in “Proposed1”. Fig. 7. Small Signal Equivalent Circuit of the Conventional Floating Type Scaling Capacitor Circuit (“Proposed2”) TABLE I. P OWER C ONSUMPTION AND A REA Power Consumption (µW) Area (µm2 ) 42.6 35.8 37.7 1230 1100 1134 Conventional Proposed1 Proposed2 ωp ≃ B. Improved Symmetry-type Floating Impedance Scaling Circuit The circuit diagram of the symmetry-type floating impedance circuit with improved operation bandwidth is shown in Fig.6. Hereinafter, this is called as “Proposed2”. The drain resistance of the bias current source M18 is indicated by the resistance rd18 . The resistance components Rd in the terminals v1 and v2 are larger, and the pole frequency is lower. The conductance components gm1 and gm2 associated with the capacitor are larger, the zero frequency is higher. In order to the resistance component at the terminals v1 and v2 is enlarge, the cascode stages configured with the common gate M11 -M14 is introduced. In order to the conductance component gm is enlarge, the negative feedback circuits are composed of M3 M8 . In order to confirm the frequency characteristics of “Proposed2”, the small-signal half circuit are analyzed. The smallsignal half circuit of “Proposed2” is shown in Fig.7. Assuming that gm rd ≫ 1, the impedance Z1 is given by v1 Z1 = i1 2Rd [(gm4 + gm8 )2Cs + gm2 gm4 gm6 rd18 ] (13) ≃ gm2 gm4 rd18 (gm10 Rd 2Cs + gm6 ) 2 2Rd (4Cs + gm rd ) ≃ 2 , (14) gm rd (N Rd 2Cs + 1) where gm2 = gm4 = gm6 = gm8 = gm , rd18 = rd , and gm10 = N gm . The pole frequency ωp and the zero frequency ωz are given by 1 (15) Rd N 2C g 2 rd ωz ≃ m . (16) 4C Comparing “Proposed2” with “Proposed1”, Rd becomes gm rd times with the cascode stages, the pole moves to lower frequency. Comparing (16) with (12), the zero frequency is multiplied by gm rd /2 times and moves to higher frequency. The impedance Z1 in the range between the pole and the zero frequencies, ωz ≫ ω ≫ ωp , is given by ωp ≃ g2 r d 2Rd · 4C(s + m 4C ) Z1 ≃ 2 gm rd · N Rd 2C(s + N R1d 2C ) (17) g2 r m d 4 · 4C (18) 2 gm rd N s 1 ≃ . (19) N Cs The “Proposed2” performs as an N -times capacitance in wider than “Proposed1”. ≃ TABLE I shows the comparison of the power consumption and the area. The power consumption and area are reduced by 11.5% and 7.8% in “Proposed2”, relatively. C. Simulation Results The validity of the proposed circuits is confirmed using simulation software SIMetrix(SIMetrix Technologies). The transistor model used in the simulation is BISIM3 0.18µm process model. The supply voltage is ± 0.9V. In order to realize the scaled capacitance of 500pF, N and the capacitance are set to 50 and 10pF, respectively. The tables of transistor size are shown in TABLE II and TABLE III. The impedance at the terminal v1 is confirmed simulation, where the terminal v2 is grounded. The simulation results of impedance and phase frequency characteristics are shown in TABLE II. T RANSISTOR S IZE OF P ROPOSED C IRCUIT (P ROPOSED 1) Transistors W (µm)/L(µm) M3 , M6 , M8 , M11 the others 90.0 /1.8 1.8 /1.8 Vin C1 Gm1 TABLE III. T RANSISTOR S IZE OF P ROPOSED C IRCUIT (P ROPOSED 2) Transistors W (µm)/L(µm) M9 -M14 , M16 , M19 the others 90.0 /1.8 1.8 /1.8 Vout CMR Gm2 Fig. 10. Lowpass Filter Employing Symmetry-type Floating Impedance Scaling Circuit (“Proposed LPF”) M7 M5 M6 I1 9 10 M2 Impedance[Ω] vCM 6 10 3 10 Ideal Proposed1 Proposed2 Conventional Fig. 11. 0 2 10 4 10 6 10 8 10 Frequency[Hz] Fig. 8. Impedance Characteristics Phase[degree] −180 −270 −2 10 αvinn M9 M4 I2 αvinp I5 Ideal Proposed1 Proposed2 Conventional 10 0 2 10 4 10 6 10 vinp vinn M15 αvinp M14 αvinn I6 M21 ioutp I4 M10 M11 M12 M13 vinp M6 M17 M16 vinn αvinn M18 M20 I7 I9 Vss Low-gm Linear OTA T HE B IAS C URRENT S OURCE Current Source Current (nA) (µm2 ) I1 = I8 I2 = I5 = I7 = I9 I3 = I4 I6 50 100 68.3 36.6 8 10 Frequency[Hz] Fig. 9. I3 vinn TABLE IV. −90 M19 M22 M2 M3 Fig. 12. M8 Vdd M1 90 M9 I8 M7 αvinp 0 M10 M5 M8 ioutn vinp M11 Common-mode Rejection Circuit I1 10 vCM M4 M12 0 10 −2 10 M3 M1 Phase Characteristics Fig.8 and Fig.9, respectively. The solid line indicates the proposed circuit of “Proposed2”, the dash-dotted line indicates the proposed circuit of “Proposed1”, the broken line indicates the conventional impedance scaling circuit , and the dotted line indicates the ideal capacitor of 500pF. From the impedance characteristic of “Proposed1”, it is seen that the pole and the zero are at the near frequencies. The phase characteristic dose not become –90◦ even in the frequency range, thus the operation bandwidth is very narrow. The impedance characteristic of “Proposed2” shows the capacitor characteristics in the range from 100Hz to 100kHz. It is notice that comparing “Proposed2” with “Proposed1”, the pole frequency is lower and the zero frequency is higher. Furthermore, comparing to the conventional circuit, the characteristics of “Proposed2” are improved in range higher frequency. IV. A PPLICATION TO F ULLY D IFFERENTIAL F ILTER A. Configuration of Fully differential Lowpass Filter Employing “Proposed2”, a fully differential 1st-order lowpass Filter(LPF) shown in Fig.10 designed in this research. The capacitor is implemented employing the floating impedance scaling circuit. The transfer function of the lowpass filter T (s) is expressed as T (s) = Gm1 , sC1 + Gm2 + 1/R (20) where Gm1 and Gm2 are the transconductances of OTAs, and R is the combined resistance composed of the symmetrytype impedance scaling circuit and the common-mode rejection circuit. The low-gm linear OTA shown in Fig.12 is used as Gm1 and Gm2 . TABLE IV shows the bias current in the OTA. The transconductance of the OTA is Gm1 = Gm2 = 606.7nS. In order to realize the LPF of fc =100Hz and the scaled capacitance 965.7pF, N and the capacitance is set to 50 and 19.31pF, respectively. 0 Rd rd18 −20 Gain gm4 iin vin −40 gm2 −60 Proposed LPF −80 Ideal Capacitor −100 Ideal −120 270 gm8 gm6 rd6 gm10 Fig. 14. Small Signal Equivalent Circuit of the Floating Type Scaling Capacitor Circuit for Common-mode Signal (“Proposed2”) 6 10 90 5 0 −90 −180 0 10 2 4 10 10 6 10 10 Impedance [Ω] Phase [degree] 180 8 10 4 10 CMR 3 10 Frequency [Hz] Fig. 13. CMR + ISC ISC 2 Frequency Characteristics of Lowpass Filter 10 90 Phase [degree] B. Frequency Characteristics The frequency characteristics of “Proposed LPF” shown in Fig.10 are shown in Fig.13. The solid line indicates the characteristics of “Proposed LPF”, the dashed line of “Ideal Capacitor” indicates the characteristics of the LPF in which the capacitor is an ideal element, and the dotted line of “Ideal” indicates the ideal LPF. 0 −90 −180 From Fig.13, the proposed circuit shows the characteristics as the floating capacitor. The pass band gain of “Proposed LPF” is reduced comparing “Ideal”. It can be considered that the pass band gain are reduced by the combined resistance component R of the common-mode rejection circuit and the impedance scaling circuits. 10 4 6 10 8 10 Frequency [Hz] Fig. 15. Common-mode Impedance of the half circuit is given by C. Common-mode Impedance Characteristics The current never flow when the same voltage are applied to the both terminals of passive elements, and the impedance is obviously infinite. However, because of the impedance scaling circuit is synthesized with transistors, the impedance to the same voltage at both terminal is finite, practically. Although it may not be correct expression, such an impedance is called “common-mode impedance” in this paper. Appling the common-mode voltage vCM to the both terminals of “Proposed2”, the output voltages of the source followers M1 and M2 are equal, currents do not flow in the capacitor C associated with the source followers. Thus, the capacitor C can be considered as an open element. The common-mode half circuit is shown in Fig.14. The rd6 , rd18 , and Rd indicates the drain resistances of the transistor M6 , the bias current source M18 , and the resistance component at the terminal v1 , respectively. Assuming that gm rd ≫ 1, the impedance ZCM Rd rd6 (gm4 + gm8 + gm4 gm6 rd18 ) rd6 (gm2 + gm4 + gm4 gm6 rd18 ) − gm10 Rd gm4 rd18 (21) Rd rd6 gm6 ≃ . (22) gm6 rd6 − gm10 Rd ZCM ≃ Moreover, assuming that we have Rd gm10 ≫ rd6 gm2 , rd6 , (23) N where gm6 = gm , gm10 = N gm . For the common-mode signal, the symmetry-type impedance scaling circuit performs as a negative resistance −rd6 /N due to positive current feedback. ZCM ≃ − The simulation results of the common-mode impedance and the phase characteristics are shown in Fig.15. The solid line of “CMR+ISC” indicates the result of the parallel of the common-mode rejection circuit and the symmetry-type Voltage [V] 0.1 0 −0.1 0 Fig. 16. employing the proposed circuit has been confirmed through the simulation results. By the small signal analysis, it had been shown that the proposed impedance scaling circuit becomes the negative conductance when the same voltages are applied to both terminals. This negative resistance can be ignored due to the small common-mode resistance of the common-mode rejection circuit. The future work is the improvement of the pass band gain and the application for the higher-order filters. Square Wave, 50Hz, ±200mVp-p Output Voltage ACKNOWLEDGMENT 0.2 This study was supported by JSPS Grant-in-Aid for Scientific Research (C 24560436). 0.1 Time [Sec] Transient Characteristic floating impedance scaling circuit, the dashed line of “CMR” indicates the common-mode rejection circuit, the dotted line of “ISC” indicates the symmetry-type impedance scaling circuit of“Proposed2”. From the phase characteristic of “ISC”, it is shown that the symmetry-type floating impedance scaling circuit performs as the negative resistance in lower frequency range. The phase characteristic of “ISC+CMR” performs as the positive resistance. Consequently, because of the combined impedance of “CMR” and “ISC” is positive from the characteristics of “CMR+ISC”, the operation of the LPF is stable. The transient Characteristic of the LPF employing the symmetrytype floating impedance scaling circuit, the common-mode rejection circuit, and low-gm linear OTA, is confirm. The simulation results of the transient Characteristic is shown in Fig.16. The input voltage signal is the square wave that is 50Hz, ±200mVp-p . The solid line of “Output Voltage” indicates the output waveform. There are no oscillation in the simulation results. It is seem that the operation proposed circuit is stable. V. C ONCLUSION In this paper, for the application of the biomedical signal processing, a design of a symmetry-type floating impedance scaling circuit and the improvement methods of those operation bandwidth had been proposed. The proposed circuit is simply composed of two source followers and two current controlled current source. The configuration of the proposed circuit is symmetry. From the small signal analysis, the improvement methods of the operating bandwidth are found. In order to lower the pole frequency, the resistance component in the parts of input terminals had been increased by introducing the common gate, and to enhance the zero frequency, the conductance component associated to the capacitor had been enhanced by negative feedback. To realize the scaled capacitance of 500pF, N and the capacitance are set to 50 and 10pF, respectively. The impedance characteristic of the synthesized impedance scaling circuit had shown the capacitor characteristics in the range from 10Hz to 100kHz. Comparing to the conventional impedance scaling circuit, the characteristics of the proposed circuit had been improved in side of high frequency. The power consumption and area are reduced comparing the conventional circuit. 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