Cascadable Current-Mode Biquad Filter and Quadrature Oscillator ...
Circuits Syst Signal Process (2009) 28: 99–110 DOI 10.1007/s00034-008-9072-5
Cascadable Current-Mode Biquad Filter and Quadrature Oscillator Using DO-CCCIIs and OTA Montree Siripruchyanun · Winai Jaikla
Received: 30 June 2007 / Revised: 23 November 2007 / Published online: 15 October 2008 © Birkhäuser Boston 2008
Abstract This article introduces a circuit which can function both as a quadrature oscillator and as a universal biquad filter (lowpass, highpass, bandpass). When the circuit functions as a universal biquad filter, the quality factor and pole frequency can be tuned orthogonally via the input bias currents. When it functions as a quadrature oscillator, the oscillation condition and oscillation frequency can be adjusted independently by the input bias currents. The proposed circuit can work as either a quadrature oscillator or a biquad filter without changing the circuit topology. The amplitude of the proposed oscillator can be independently controlled via the input bias currents. The proposed oscillator can be applied to provide amplitude modulated/amplitude shift keyed signals with the above-mentioned major advantages. The circuit is very simple, consisting of four dual-output second generation current controlled current conveyors (DO-CCCIIs), one operational transconductance amplifier (OTA), and two grounded capacitors. Without any external resistors and using only grounded elements, this circuit is therefore suitable for IC architecture. PSPICE simulation results are depicted here, and the given results agree well with the theoretical analysis. The power consumption is approximately 7.32 mW at ±2.5 V supply voltages. Keywords DO-CCCII · OTA · Quadrature oscillator · Biquad filter
M. Siripruchyanun () Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, Bangsue, Bangkok, 10800, Thailand e-mail: [email protected] W. Jaikla Electric and Electronic Program, Faculty of Industrial Technology, Suan Sunandha Rajabhat University, Dusit, Bangkok, 10300, Thailand e-mail: [email protected]
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1 Introduction In electrical engineering, an oscillator and a filter are two basic important building blocks which are frequently employed. Among several types of oscillators, the quadrature oscillator is widely used because the circuit provides two sinusoids with a 90◦ phase difference, such as in quadrature mixers and single-sideband devices for telecommunications [9]. Similarly, there is considerable attention today on the applications and advantages of realizing various active transfer functions, called universal biquad filters. A universal filter may be used in phase-locked loop FM stereo demodulators, and in crossover networks used in three-way high fidelity loudspeakers [5]. However, the current-mode universal filter has been more popular than the voltage-mode variety, due to requirements in low-voltage environments such as portable and battery-powered equipments. Since a low-voltage operating circuit becomes necessary, the current-mode technique is more ideally suited to this purpose than the voltage-mode type. There is a growing interest in synthesizing current-mode circuits because of their potential advantages, such as larger dynamic range, higher signal bandwidth, greater linearity, simpler circuitry, and lower power consumption [12]. However, our investigations show that previous works have proposed versatile quadrature oscillator and biquad filter devices using different high-performance active building blocks [6–8, 10], such as current-controlled current conveyors [10], current-controlled current differencing buffered amplifiers (CCCDBAs) [6], and current-controlled current differencing transconductance amplifiers (CCCDTAs) [7, 8]. Reportedly, the outputs of these circuits do not have high output impedances, making the cascadability challenging. The operational transconductance amplifier (OTA) and second generation currentcontrolled current conveyor (CCCII) have received considerable attention as active components, because the transconductance and parasitic resistance can be adjusted electronically, which is especially suitable for analog circuits [3, 14]. The flexibility of the devices to operate in both current and voltage modes allows for a variety of circuit designs. Also, the application of dual-output current conveyors and the OTA has been useful for constructing current-mode circuits from a reduced number of active components [13–15]. The purpose of this paper is to introduce a current-mode universal biquad filter, using dual-output (DO)-CCCIIs and an OTA, providing three standard transfer functions (lowpass, highpass, and bandpass) and an independently adjustable pole frequency and quality factor. When there is no input current and under appropriate conditions, the proposed circuit can provide current-mode quadrature sinusoidal and amplitude modulated (AM)/amplitude shift keyed (ASK) signals. Moreover, the output currents have high impedance, which facilitates cascading in current mode. The circuit construction consists of four DO-CCCIIs, one OTA, and two grounded capacitors (beneficial to an IC implementation). The PSPICE simulation results are also shown, and they are in correspondence with the theoretical analysis.
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Fig. 1 OTA (a) symbol and (b) equivalent circuit
2 Circuit Principle 2.1 The Operational Transconductance Amplifier (OTA) An ideal OTA has infinite input and output impedances. The output current of an OTA is given by Io = gm (V+ − V− ),
(1)
where gm is the transconductance of the OTA. For a bipolar OTA, the transconductance can be expressed by gm =
IB , 2VT
(2)
where IB and VT are the bias current and thermal voltage, respectively. The symbol and the equivalent circuit of the OTA are illustrated in Fig. 1(a) and (b), respectively. 2.2 The Dual-Output Second Generation Current-Controlled Current Conveyor (DO-CCCII) The characteristics of the ideal DO-CCCII are matrix: ⎡ ⎤ ⎡ IY 0 0 ⎣ VX ⎦ = ⎣ 1 RX IZ1,Z2 0 ±1
represented by the following hybrid ⎤⎡ ⎤ 0 VY 0 ⎦ ⎣ IX ⎦ , VZ 0
(3)
where RX =
VT . 2IB
(4)
The symbol and the equivalent circuit of the DO-CCCII are illustrated in Fig. 2(a) and (b), respectively.
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Fig. 2 DO-CCCII (a) symbol and (b) equivalent circuit
Fig. 3 Proposed circuit working as a universal filter
2.3 The Proposed Circuit Operating as a Universal Filter Figure 3 demonstrates the circuit scheme of the proposed circuit working as a universal filter. From routine analysis of the circuit in Fig. 3, the following current transfer functions are obtained: s2
IHP = Iin s2 +
s 1 C1 Rx4
ILP = Iin s2 +
1/C1 C2 Rx5 Rx2 1 gm3 s C1 Rx4 − gm3 + C1 C2 Rx2
− gm3 +
gm3 C1 C2 Rx2
,
(5) (6)
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and IBP = Iin s2 +
s/C1 Rx2 − gm3 +
s 1 C1 Rx4
gm3 C1 C2 Rx2
.
From (5)–(7), the parameters ω0 and Q0 can be expressed as gm3 ω0 = C1 C2 Rx2 and
(7)
(8)
C1 gm3 . C2 Rx2
Rx4 Q0 = 1 − gm3 Rx4
(9)
Substituting the transconductance and intrinsic resistance as depicted in (2) and (4), we obtain 1 IB2 IB3 (10) ω0 = VT C1 C2 and
2 Q0 = 4IB4 − IB3
C1 IB2 IB3 . C2
(11)
From (10) and (11), we see that the quality factor can be adjusted independently from the pole frequency by varying IB4 . Another advantage of the proposed circuit is that a high Q0 circuit can be obtained by setting 4IB4 close to IB3 , which differs from conventional universal filters in which the maximum Q0 is limited by their component values. Thus, the bandwidth (BW) is given by BW =
ω0 4IB4 − IB3 = . Q0 2VT C1
(12)
From (10) and (11), if IB2 = IB3 = IB and IB4 = kIB , which can be easily realized by using a programmable current mirror [1, 11], then the pole frequency and quality factor are subsequently modified to be 1 IB ω0 = (13) VT C1 C2 and
2 Q0 = 4k − 1
C1 . C2
(14)
From (13) and (14), note that the pole frequency can be linearly adjusted by IB without disturbing the quality factor, while the quality factor can be adjusted independently from the pole frequency by k.
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Fig. 4 Proposed circuit working as a quadrature oscillator
2.4 Circuit Sensitivities The sensitivities of the proposed circuit can be found as 1 1 ω ω ω ω SIB20 = SIB30 = ; SC10 = SC20 = − ; 2 2 IB3 1 1 Q Q SIB30 = + SIB20 = ; 2 2 4IB4 − IB3
ω
SVT0 = −1,
(15) (16)
and Q
SIB40 = −
4IB4 ; 4IB4 − IB3
1 Q SC10 = ; 2
1 Q SC20 = − . 2
(17)
Therefore, all the active and passive sensitivities are equal to or less than unity in magnitude. 2.5 The Proposed Circuit Operating as a Quadrature Oscillator If no input current is applied to the circuit, as depicted in Fig. 4, the characteristic equation of the system can be expressed as s2 +
1 gm3 s − gm3 + = 0. C1 Rx4 C1 C2 Rx2
(18)
From (18), it is clear that the proposed circuit can be set as an oscillator if 1 = gm3 . Rx4
(19)
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Equation (19) is considered as the condition of oscillation, and this is achieved by setting 4IB4 = IB3 . Then the characteristic equation of the system becomes s2 +
gm3 = 0. C1 C2 Rx2
(20)
From (20), the oscillation frequency (ω0 ) of this system can be obtained as ω0 =
gm3 . C1 C2 Rx2
(21)
Substituting the transconductance and intrinsic resistance as depicted in (2) and (4), the oscillation frequency is equal to (10). We see that the oscillation condition can be controlled independently from the oscillation frequency by IB4 and IB3 , while the oscillation frequency can be controlled by IB2 . The current-mode quadrature sinusoidal signals can be obtained at IO1 and IO2 . In addition, note that the amplitude of the sinusoidal signal in current-mode IO5 can be proportionally controlled by IB5 , so if IB5 is used as a modulating signal, the AM and ASK signals can be obtained at IO5 . Moreover, the proposed circuit enables easy cascading in current mode, due to the high output impedances. In fact, we can realize the proposed circuit by using only OTAs, in which case the pole and oscillation frequencies will be changed to be ω0 = 2V1T ICB21 ICB32 , but if we use an OTA and CCCIIs the pole and oscillation frequencies will be equal to ω0 = 1 VT
IB2 IB3 C1 C2 .
A comparison of these two equations for the same pole frequency (ω0 ) shows that the first equation needs to employ greater bias currents. This is important because when bias currents are greater, the power consumption will be subsequently greater. Moreover, the circuit needs a differencing voltage to the current converter, so an OTA will be used for this structure. Although we could realize this by using only CCCIIs, we would have to use two CCCIIs instead of an OTA, so the circuit would have an increased number of active elements. 2.6 Non-Ideal Case For the non-ideal case, the OTA can be characterized with the following equation: IO = gm (a+ V+ − a− V− ).
(22)
The parameters a+ and a− are the transferred values. Similarly, the non-ideal operation of the DO-CCCII can be represented with the following equations: VX = βVY + IX RX ,
(23)
IZ1 = αIX ,
(24)
and IZ2 = γ IX .
(25)
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The parameters α, γ , and β are the voltage/current transfer values, deviating from one, based on the internal circuit construction. In the non-ideal case, a new analysis of the proposed filter circuit in Fig. 3 yields the following transfer functions: IHP = Iin s2 + ILP = Iin s2 +
s C1
α1 α4 β4 Rx4
s α1 α4 β4 C1 Rx4
γ1 s 2
− gm3 α1 a− + α1 α2 α5 β1 β2 C1 C2 Rx5 Rx2
− gm3 α1 a− +
,
gm3 α1 α2 β2 a+ C1 C2 Rx2
gm3 α1 αβ2 a+ C1 C2 Rx2
(26)
,
(27)
.
(28)
and IBP = Iin s2 +
s α1 α4 β4 C1 Rx4
α1 γ2 β2 s C1 Rx2
− gm3 α1 a− +
gm3 α1 α2 β2 a+ C1 C2 Rx2
In this case, the ω0 , Q0, and BW are changed to ω0 =
gm3 α1 α2 β2 a+ , C1 C2 Rx2
Rx4 Q0 = α1 α4 β4 − gm3 Rx4 α1 a−
(29) C1 gm3 α1 α2 β2 a+ , C2 Rx2
(30)
and BW =
α1 α4 β4 − gm3 Rx4 α1 a− . C1 Rx4
(31)
Practically, the α, γ , and β originate from the intrinsic resistances and stray capacitances in the OTA and DO-CCCII. These errors affect the sensitivity to temperature and the high frequency response of the proposed circuit; thus, the OTA and the DO-CCCII should be carefully designed to minimize these errors. Consequently, these deviations are very small and can be ignored in theory.
3 Simulation Results To prove the performances of the proposed circuit, a PSPICE simulation was performed for examination and experimentation. The PNP and NPN transistors employed in the proposed circuit were simulated, respectively, by using the parameters of the PR200N and NR200N bipolar transistors of the ALA400 transistor array from AT&T [4]. Figure 5 and Fig. 6 depict the respective schematic description of the OTA and DO-CCCII used in the simulations. The circuit was biased with ±2.5 V supply voltages, C1 = C2 = 1 nF, IB1 = IB2 = IB4 = 100 µA, IB3 = 200 µA, and IB5 = 55 µA. This yields a pole frequency of 831 kHz. The calculated value of this parameter from (10) yields 866 kHz (deviating by 4.04%). This deviation stems from
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Fig. 5 Internal construction of OTA
Fig. 6 Internal construction of DO-CCCII [2]
Fig. 7 Gain responses of the proposed circuit working as universal biquad filter
the non-ideal properties of the OTA and DO-CCCIIs employed in the circuit, as depicted in Sect. 2.6; thus, the OTA and the DO-CCCIIs should be carefully designed to minimize these errors. The results shown in Fig. 7 are the gain responses of the proposed biquad filter obtained from Fig. 3. It shows that the proposed filter allows simultaneous lowpass (LP), highpass (HP), and bandpass (BP) responses. By varying
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Circuits Syst Signal Process (2009) 28: 99–110
Fig. 8 BP responses for different values of IB4
Fig. 9 BP responses for different values of IB
Fig. 10 The current-mode sinusoidal signal in transition region
Fig. 11 Simulation result of the quadrature outputs
IB4 to be 55 µA, 80 µA, and 100 µA, only the quality factor is changed, as shown in Fig. 8. This confirms that the quality factor can be adjusted by IB4 , which is independent of the pole frequency, as analyzed in (10) and (11). Figure 9 shows the gain responses of the bandpass functions where IB is set to 40 µA, 80 µA, and 160 µA, respectively, and k = 0.3. This shows that the pole frequency can be adjusted without affecting the quality factor, as analyzed in (13) and (14). Figures 10 and 11 show simulated quadrature output waveforms where IB1 = IB2 = IB4 = IB5 = 100 µA and IB3 = 404 µA. This yields an oscillation frequency of 1.06 MHz. The calculated value of this parameter from (10) is 1.23 MHz (deviating by 13.82%). Figure 12 shows the simulated output spectrum, where the total harmonic distortion (THD) is about 0.68%. The simulated results of the proposed circuit, serving as an AM and an ASK signal generator, are also illustrated in Figs. 13 and 14, respectively. Figure 15 depicts the plots of the simulated and theoretical
Circuits Syst Signal Process (2009) 28: 99–110 Fig. 12 Simulation result of the output spectrum
Fig. 13 Result of operation as AM
Fig. 14 Result of operation as ASK
Fig. 15 Oscillation frequencies versus IB2 in the proposed circuit at various capacitances
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Circuits Syst Signal Process (2009) 28: 99–110
oscillation frequency versus the bias currents IB2 at C1 and C2 with identical values, at 0.1 nF, 1 nF, and 10 nF. It is seen that the simulation results are in accordance with the theoretical analysis shown in (21). 4 Conclusions The presented circuit can function, both as a current-mode quadrature oscillator, and as a current-mode universal biquad filter (lowpass, highpass, and bandpass), without changing of the circuit topology. When the circuit functions as a current-mode universal biquad filter, the quality factor and pole frequency can be tuned orthogonally via the input bias currents. With no input current and under suitable conditions, the proposed circuit can function as a quadrature oscillator. The oscillation condition and oscillation frequency can be independently adjusted by the input bias currents. Moreover, the oscillator can provide the AM/ASK signals that are widely used in communication systems. The PSPICE simulation results correspond with the theoretical ones. With its simple construction, requiring four DO-CCCIIs, one OTA, and two grounded capacitors, this circuit is well suited for an IC architecture. References 1. D. Chandrika, R.A. Jaime, L.M. Antonio, C. Ramon, Architectures of class AB CMOS mirrors with programmable gain. Analog Integr. Circuit Signal Process. 42, 197–202 (2005) 2. W. Chunhua, Z. Qiujing, Y. Wei, A second current controlled current conveyor realization using Wilson current mirrors. Int. J. Electron. 94, 699–706 (2007) 3. A. Fabre, O. Saaid, F. Wiest, C. Boucheron, Current controllable bandpass filter based on translinear conveyors. Electron. Lett. 31, 1727–1728 (1995) 4. D.R. Frey, Log-domain filtering: an approach to current-mode filtering. IEE Proc. Circuit Devices Syst. 140, 406–416 (1993) 5. M.A. Ibrahim, S. Minaei, H.A. Kuntman, A 22.5 MHz current-mode KHN-biquad using differential voltage current conveyor and grounded passive elements. Int. J. Electron. Commun. (AEU) 59, 311– 318 (2005) 6. W. Jaikla, M. Siripruchyanun, A versatile quadrature oscillator and universal biquad filter using CCCDBAs, in Proceedings of ECTI Conference 2006, Ubon Ratchathani, Thailand, May 2006, pp. 501– 504 7. W. Jaikla, M. Siripruchyanun, A versatile quadrature oscillator and universal biquad filter using dualoutput current controlled current differencing transconductance amplifier, in Proceedings of ISCIT 2006, Bangkok, Thailand, 2006, pp. 1072–1075 8. W. Jaikla, M. Siripruchyanun, CCCDTAs-based versatile quadrature oscillator and universal biquad filter, in Proceedings of ECTI Conference 2007, Chiang Rai, Thailand, 2007, pp. 1065–1068 9. I.A. Khan, S. Khawaja, An integrable gm-C quadrature oscillator. Int. J. Electron. 87, 1353–1357 (2000) 10. W. Kiranon, J. Kesorn, W. Sangpisit, N. Kamprasert, Electronically tunable multifunctional translinear-C filter and oscillator. Electron. Lett. 33, 573–574 (1997) 11. B. Sedighi, M.S. Bakhtiar, Variable gain current mirror for high-speed applications. IEICE Electron. Express 4, 277–281 (2007) 12. C. Toumazou, F.J. Lidgey, D.G. Haigh, Analogue IC Design: The Current-Mode Approach (Peter Peregrinus, London, 1990) 13. T. Tsukutani, S. Edasaki, Y. Sumi, Y. Fukui, Current-mode universal biquad filter using OTAs and DO-CCII. Frequenz 60, 237–240 (2006) 14. T. Tsukutani, M. Higashimura, M. Ishida, S. Tsuiki, Y. Fukui, A general class of current-mode highorder OTA-C filters. Int. J. Electron. 81, 663–669 (1996) 15. T. Tsukutani, Y. Sumi, Y. Fukui, Novel current-mode biquad filter using OTAs and DO-CCII. Int. J. Electron. 94, 99–105 (2007)
Cascadable Current-Mode Biquad Filter and Quadrature Oscillator Using DO-CCCIIs and OTA Montree Siripruchyanun · Winai Jaikla
Received: 30 June 2007 / Revised: 23 November 2007 / Published online: 15 October 2008 © Birkhäuser Boston 2008
Abstract This article introduces a circuit which can function both as a quadrature oscillator and as a universal biquad filter (lowpass, highpass, bandpass). When the circuit functions as a universal biquad filter, the quality factor and pole frequency can be tuned orthogonally via the input bias currents. When it functions as a quadrature oscillator, the oscillation condition and oscillation frequency can be adjusted independently by the input bias currents. The proposed circuit can work as either a quadrature oscillator or a biquad filter without changing the circuit topology. The amplitude of the proposed oscillator can be independently controlled via the input bias currents. The proposed oscillator can be applied to provide amplitude modulated/amplitude shift keyed signals with the above-mentioned major advantages. The circuit is very simple, consisting of four dual-output second generation current controlled current conveyors (DO-CCCIIs), one operational transconductance amplifier (OTA), and two grounded capacitors. Without any external resistors and using only grounded elements, this circuit is therefore suitable for IC architecture. PSPICE simulation results are depicted here, and the given results agree well with the theoretical analysis. The power consumption is approximately 7.32 mW at ±2.5 V supply voltages. Keywords DO-CCCII · OTA · Quadrature oscillator · Biquad filter
M. Siripruchyanun () Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, Bangsue, Bangkok, 10800, Thailand e-mail: [email protected] W. Jaikla Electric and Electronic Program, Faculty of Industrial Technology, Suan Sunandha Rajabhat University, Dusit, Bangkok, 10300, Thailand e-mail: [email protected]
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Circuits Syst Signal Process (2009) 28: 99–110
1 Introduction In electrical engineering, an oscillator and a filter are two basic important building blocks which are frequently employed. Among several types of oscillators, the quadrature oscillator is widely used because the circuit provides two sinusoids with a 90◦ phase difference, such as in quadrature mixers and single-sideband devices for telecommunications [9]. Similarly, there is considerable attention today on the applications and advantages of realizing various active transfer functions, called universal biquad filters. A universal filter may be used in phase-locked loop FM stereo demodulators, and in crossover networks used in three-way high fidelity loudspeakers [5]. However, the current-mode universal filter has been more popular than the voltage-mode variety, due to requirements in low-voltage environments such as portable and battery-powered equipments. Since a low-voltage operating circuit becomes necessary, the current-mode technique is more ideally suited to this purpose than the voltage-mode type. There is a growing interest in synthesizing current-mode circuits because of their potential advantages, such as larger dynamic range, higher signal bandwidth, greater linearity, simpler circuitry, and lower power consumption [12]. However, our investigations show that previous works have proposed versatile quadrature oscillator and biquad filter devices using different high-performance active building blocks [6–8, 10], such as current-controlled current conveyors [10], current-controlled current differencing buffered amplifiers (CCCDBAs) [6], and current-controlled current differencing transconductance amplifiers (CCCDTAs) [7, 8]. Reportedly, the outputs of these circuits do not have high output impedances, making the cascadability challenging. The operational transconductance amplifier (OTA) and second generation currentcontrolled current conveyor (CCCII) have received considerable attention as active components, because the transconductance and parasitic resistance can be adjusted electronically, which is especially suitable for analog circuits [3, 14]. The flexibility of the devices to operate in both current and voltage modes allows for a variety of circuit designs. Also, the application of dual-output current conveyors and the OTA has been useful for constructing current-mode circuits from a reduced number of active components [13–15]. The purpose of this paper is to introduce a current-mode universal biquad filter, using dual-output (DO)-CCCIIs and an OTA, providing three standard transfer functions (lowpass, highpass, and bandpass) and an independently adjustable pole frequency and quality factor. When there is no input current and under appropriate conditions, the proposed circuit can provide current-mode quadrature sinusoidal and amplitude modulated (AM)/amplitude shift keyed (ASK) signals. Moreover, the output currents have high impedance, which facilitates cascading in current mode. The circuit construction consists of four DO-CCCIIs, one OTA, and two grounded capacitors (beneficial to an IC implementation). The PSPICE simulation results are also shown, and they are in correspondence with the theoretical analysis.
Circuits Syst Signal Process (2009) 28: 99–110
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Fig. 1 OTA (a) symbol and (b) equivalent circuit
2 Circuit Principle 2.1 The Operational Transconductance Amplifier (OTA) An ideal OTA has infinite input and output impedances. The output current of an OTA is given by Io = gm (V+ − V− ),
(1)
where gm is the transconductance of the OTA. For a bipolar OTA, the transconductance can be expressed by gm =
IB , 2VT
(2)
where IB and VT are the bias current and thermal voltage, respectively. The symbol and the equivalent circuit of the OTA are illustrated in Fig. 1(a) and (b), respectively. 2.2 The Dual-Output Second Generation Current-Controlled Current Conveyor (DO-CCCII) The characteristics of the ideal DO-CCCII are matrix: ⎡ ⎤ ⎡ IY 0 0 ⎣ VX ⎦ = ⎣ 1 RX IZ1,Z2 0 ±1
represented by the following hybrid ⎤⎡ ⎤ 0 VY 0 ⎦ ⎣ IX ⎦ , VZ 0
(3)
where RX =
VT . 2IB
(4)
The symbol and the equivalent circuit of the DO-CCCII are illustrated in Fig. 2(a) and (b), respectively.
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Fig. 2 DO-CCCII (a) symbol and (b) equivalent circuit
Fig. 3 Proposed circuit working as a universal filter
2.3 The Proposed Circuit Operating as a Universal Filter Figure 3 demonstrates the circuit scheme of the proposed circuit working as a universal filter. From routine analysis of the circuit in Fig. 3, the following current transfer functions are obtained: s2
IHP = Iin s2 +
s 1 C1 Rx4
ILP = Iin s2 +
1/C1 C2 Rx5 Rx2 1 gm3 s C1 Rx4 − gm3 + C1 C2 Rx2
− gm3 +
gm3 C1 C2 Rx2
,
(5) (6)
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and IBP = Iin s2 +
s/C1 Rx2 − gm3 +
s 1 C1 Rx4
gm3 C1 C2 Rx2
.
From (5)–(7), the parameters ω0 and Q0 can be expressed as gm3 ω0 = C1 C2 Rx2 and
(7)
(8)
C1 gm3 . C2 Rx2
Rx4 Q0 = 1 − gm3 Rx4
(9)
Substituting the transconductance and intrinsic resistance as depicted in (2) and (4), we obtain 1 IB2 IB3 (10) ω0 = VT C1 C2 and
2 Q0 = 4IB4 − IB3
C1 IB2 IB3 . C2
(11)
From (10) and (11), we see that the quality factor can be adjusted independently from the pole frequency by varying IB4 . Another advantage of the proposed circuit is that a high Q0 circuit can be obtained by setting 4IB4 close to IB3 , which differs from conventional universal filters in which the maximum Q0 is limited by their component values. Thus, the bandwidth (BW) is given by BW =
ω0 4IB4 − IB3 = . Q0 2VT C1
(12)
From (10) and (11), if IB2 = IB3 = IB and IB4 = kIB , which can be easily realized by using a programmable current mirror [1, 11], then the pole frequency and quality factor are subsequently modified to be 1 IB ω0 = (13) VT C1 C2 and
2 Q0 = 4k − 1
C1 . C2
(14)
From (13) and (14), note that the pole frequency can be linearly adjusted by IB without disturbing the quality factor, while the quality factor can be adjusted independently from the pole frequency by k.
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Fig. 4 Proposed circuit working as a quadrature oscillator
2.4 Circuit Sensitivities The sensitivities of the proposed circuit can be found as 1 1 ω ω ω ω SIB20 = SIB30 = ; SC10 = SC20 = − ; 2 2 IB3 1 1 Q Q SIB30 = + SIB20 = ; 2 2 4IB4 − IB3
ω
SVT0 = −1,
(15) (16)
and Q
SIB40 = −
4IB4 ; 4IB4 − IB3
1 Q SC10 = ; 2
1 Q SC20 = − . 2
(17)
Therefore, all the active and passive sensitivities are equal to or less than unity in magnitude. 2.5 The Proposed Circuit Operating as a Quadrature Oscillator If no input current is applied to the circuit, as depicted in Fig. 4, the characteristic equation of the system can be expressed as s2 +
1 gm3 s − gm3 + = 0. C1 Rx4 C1 C2 Rx2
(18)
From (18), it is clear that the proposed circuit can be set as an oscillator if 1 = gm3 . Rx4
(19)
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Equation (19) is considered as the condition of oscillation, and this is achieved by setting 4IB4 = IB3 . Then the characteristic equation of the system becomes s2 +
gm3 = 0. C1 C2 Rx2
(20)
From (20), the oscillation frequency (ω0 ) of this system can be obtained as ω0 =
gm3 . C1 C2 Rx2
(21)
Substituting the transconductance and intrinsic resistance as depicted in (2) and (4), the oscillation frequency is equal to (10). We see that the oscillation condition can be controlled independently from the oscillation frequency by IB4 and IB3 , while the oscillation frequency can be controlled by IB2 . The current-mode quadrature sinusoidal signals can be obtained at IO1 and IO2 . In addition, note that the amplitude of the sinusoidal signal in current-mode IO5 can be proportionally controlled by IB5 , so if IB5 is used as a modulating signal, the AM and ASK signals can be obtained at IO5 . Moreover, the proposed circuit enables easy cascading in current mode, due to the high output impedances. In fact, we can realize the proposed circuit by using only OTAs, in which case the pole and oscillation frequencies will be changed to be ω0 = 2V1T ICB21 ICB32 , but if we use an OTA and CCCIIs the pole and oscillation frequencies will be equal to ω0 = 1 VT
IB2 IB3 C1 C2 .
A comparison of these two equations for the same pole frequency (ω0 ) shows that the first equation needs to employ greater bias currents. This is important because when bias currents are greater, the power consumption will be subsequently greater. Moreover, the circuit needs a differencing voltage to the current converter, so an OTA will be used for this structure. Although we could realize this by using only CCCIIs, we would have to use two CCCIIs instead of an OTA, so the circuit would have an increased number of active elements. 2.6 Non-Ideal Case For the non-ideal case, the OTA can be characterized with the following equation: IO = gm (a+ V+ − a− V− ).
(22)
The parameters a+ and a− are the transferred values. Similarly, the non-ideal operation of the DO-CCCII can be represented with the following equations: VX = βVY + IX RX ,
(23)
IZ1 = αIX ,
(24)
and IZ2 = γ IX .
(25)
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The parameters α, γ , and β are the voltage/current transfer values, deviating from one, based on the internal circuit construction. In the non-ideal case, a new analysis of the proposed filter circuit in Fig. 3 yields the following transfer functions: IHP = Iin s2 + ILP = Iin s2 +
s C1
α1 α4 β4 Rx4
s α1 α4 β4 C1 Rx4
γ1 s 2
− gm3 α1 a− + α1 α2 α5 β1 β2 C1 C2 Rx5 Rx2
− gm3 α1 a− +
,
gm3 α1 α2 β2 a+ C1 C2 Rx2
gm3 α1 αβ2 a+ C1 C2 Rx2
(26)
,
(27)
.
(28)
and IBP = Iin s2 +
s α1 α4 β4 C1 Rx4
α1 γ2 β2 s C1 Rx2
− gm3 α1 a− +
gm3 α1 α2 β2 a+ C1 C2 Rx2
In this case, the ω0 , Q0, and BW are changed to ω0 =
gm3 α1 α2 β2 a+ , C1 C2 Rx2
Rx4 Q0 = α1 α4 β4 − gm3 Rx4 α1 a−
(29) C1 gm3 α1 α2 β2 a+ , C2 Rx2
(30)
and BW =
α1 α4 β4 − gm3 Rx4 α1 a− . C1 Rx4
(31)
Practically, the α, γ , and β originate from the intrinsic resistances and stray capacitances in the OTA and DO-CCCII. These errors affect the sensitivity to temperature and the high frequency response of the proposed circuit; thus, the OTA and the DO-CCCII should be carefully designed to minimize these errors. Consequently, these deviations are very small and can be ignored in theory.
3 Simulation Results To prove the performances of the proposed circuit, a PSPICE simulation was performed for examination and experimentation. The PNP and NPN transistors employed in the proposed circuit were simulated, respectively, by using the parameters of the PR200N and NR200N bipolar transistors of the ALA400 transistor array from AT&T [4]. Figure 5 and Fig. 6 depict the respective schematic description of the OTA and DO-CCCII used in the simulations. The circuit was biased with ±2.5 V supply voltages, C1 = C2 = 1 nF, IB1 = IB2 = IB4 = 100 µA, IB3 = 200 µA, and IB5 = 55 µA. This yields a pole frequency of 831 kHz. The calculated value of this parameter from (10) yields 866 kHz (deviating by 4.04%). This deviation stems from
Circuits Syst Signal Process (2009) 28: 99–110
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Fig. 5 Internal construction of OTA
Fig. 6 Internal construction of DO-CCCII [2]
Fig. 7 Gain responses of the proposed circuit working as universal biquad filter
the non-ideal properties of the OTA and DO-CCCIIs employed in the circuit, as depicted in Sect. 2.6; thus, the OTA and the DO-CCCIIs should be carefully designed to minimize these errors. The results shown in Fig. 7 are the gain responses of the proposed biquad filter obtained from Fig. 3. It shows that the proposed filter allows simultaneous lowpass (LP), highpass (HP), and bandpass (BP) responses. By varying
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Fig. 8 BP responses for different values of IB4
Fig. 9 BP responses for different values of IB
Fig. 10 The current-mode sinusoidal signal in transition region
Fig. 11 Simulation result of the quadrature outputs
IB4 to be 55 µA, 80 µA, and 100 µA, only the quality factor is changed, as shown in Fig. 8. This confirms that the quality factor can be adjusted by IB4 , which is independent of the pole frequency, as analyzed in (10) and (11). Figure 9 shows the gain responses of the bandpass functions where IB is set to 40 µA, 80 µA, and 160 µA, respectively, and k = 0.3. This shows that the pole frequency can be adjusted without affecting the quality factor, as analyzed in (13) and (14). Figures 10 and 11 show simulated quadrature output waveforms where IB1 = IB2 = IB4 = IB5 = 100 µA and IB3 = 404 µA. This yields an oscillation frequency of 1.06 MHz. The calculated value of this parameter from (10) is 1.23 MHz (deviating by 13.82%). Figure 12 shows the simulated output spectrum, where the total harmonic distortion (THD) is about 0.68%. The simulated results of the proposed circuit, serving as an AM and an ASK signal generator, are also illustrated in Figs. 13 and 14, respectively. Figure 15 depicts the plots of the simulated and theoretical
Circuits Syst Signal Process (2009) 28: 99–110 Fig. 12 Simulation result of the output spectrum
Fig. 13 Result of operation as AM
Fig. 14 Result of operation as ASK
Fig. 15 Oscillation frequencies versus IB2 in the proposed circuit at various capacitances
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Circuits Syst Signal Process (2009) 28: 99–110
oscillation frequency versus the bias currents IB2 at C1 and C2 with identical values, at 0.1 nF, 1 nF, and 10 nF. It is seen that the simulation results are in accordance with the theoretical analysis shown in (21). 4 Conclusions The presented circuit can function, both as a current-mode quadrature oscillator, and as a current-mode universal biquad filter (lowpass, highpass, and bandpass), without changing of the circuit topology. When the circuit functions as a current-mode universal biquad filter, the quality factor and pole frequency can be tuned orthogonally via the input bias currents. With no input current and under suitable conditions, the proposed circuit can function as a quadrature oscillator. The oscillation condition and oscillation frequency can be independently adjusted by the input bias currents. Moreover, the oscillator can provide the AM/ASK signals that are widely used in communication systems. The PSPICE simulation results correspond with the theoretical ones. With its simple construction, requiring four DO-CCCIIs, one OTA, and two grounded capacitors, this circuit is well suited for an IC architecture. References 1. D. Chandrika, R.A. Jaime, L.M. Antonio, C. Ramon, Architectures of class AB CMOS mirrors with programmable gain. Analog Integr. Circuit Signal Process. 42, 197–202 (2005) 2. W. Chunhua, Z. Qiujing, Y. Wei, A second current controlled current conveyor realization using Wilson current mirrors. Int. J. Electron. 94, 699–706 (2007) 3. A. Fabre, O. Saaid, F. Wiest, C. Boucheron, Current controllable bandpass filter based on translinear conveyors. Electron. Lett. 31, 1727–1728 (1995) 4. D.R. Frey, Log-domain filtering: an approach to current-mode filtering. IEE Proc. Circuit Devices Syst. 140, 406–416 (1993) 5. M.A. Ibrahim, S. Minaei, H.A. Kuntman, A 22.5 MHz current-mode KHN-biquad using differential voltage current conveyor and grounded passive elements. Int. J. Electron. Commun. (AEU) 59, 311– 318 (2005) 6. W. Jaikla, M. Siripruchyanun, A versatile quadrature oscillator and universal biquad filter using CCCDBAs, in Proceedings of ECTI Conference 2006, Ubon Ratchathani, Thailand, May 2006, pp. 501– 504 7. W. Jaikla, M. Siripruchyanun, A versatile quadrature oscillator and universal biquad filter using dualoutput current controlled current differencing transconductance amplifier, in Proceedings of ISCIT 2006, Bangkok, Thailand, 2006, pp. 1072–1075 8. W. Jaikla, M. Siripruchyanun, CCCDTAs-based versatile quadrature oscillator and universal biquad filter, in Proceedings of ECTI Conference 2007, Chiang Rai, Thailand, 2007, pp. 1065–1068 9. I.A. Khan, S. Khawaja, An integrable gm-C quadrature oscillator. Int. J. Electron. 87, 1353–1357 (2000) 10. W. Kiranon, J. Kesorn, W. Sangpisit, N. Kamprasert, Electronically tunable multifunctional translinear-C filter and oscillator. Electron. Lett. 33, 573–574 (1997) 11. B. Sedighi, M.S. Bakhtiar, Variable gain current mirror for high-speed applications. IEICE Electron. Express 4, 277–281 (2007) 12. C. Toumazou, F.J. Lidgey, D.G. Haigh, Analogue IC Design: The Current-Mode Approach (Peter Peregrinus, London, 1990) 13. T. Tsukutani, S. Edasaki, Y. Sumi, Y. Fukui, Current-mode universal biquad filter using OTAs and DO-CCII. Frequenz 60, 237–240 (2006) 14. T. Tsukutani, M. Higashimura, M. Ishida, S. Tsuiki, Y. Fukui, A general class of current-mode highorder OTA-C filters. Int. J. Electron. 81, 663–669 (1996) 15. T. Tsukutani, Y. Sumi, Y. Fukui, Novel current-mode biquad filter using OTAs and DO-CCII. Int. J. Electron. 94, 99–105 (2007)
