J. of Active and Passive Electronic Devices, Vol. 7, pp. 345–356 Reprints available directly from the publisher Photocopying permitted by license only
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Generation of Two Output CCII and Two Output ICCII Based Current Mode Filters and Oscillators Ahmed M. Soliman Electronics and Communication Engineering Department Faculty of Engineering, Cairo University Giza Egypt
A well known current mode bandpass lowpass filter using two balanced output current conveyors is found to be a member of a family of eight current mode circuits. The discovery of the inverting current conveyor and its generalized forms of balanced output inverting current conveyors have resulted in the generation of the second member of the current mode bandpass lowpass filter family. The combination of both balanced output current conveyors and inverting current conveyors resulted in other six more current mode bandpass lowpass filters thus completing the family of eight circuits. The generation method introduced in this paper based on two output current conveyors and inverting current conveyors is also applied to two well known grounded passive element current mode oscillators to obtain four more new oscillator circuits. The proposed generation method can be applied to many other filter and oscillator circuits. Keywords: Two output current conveyor, Two-output inverting current conveyor, Generation method, Filters, Oscillators.
1 INTRODUCTION The single output second generation current conveyor family consists of two members. The two members are the CCII+ and CCII- introduced in [1]. The inverting second generation current conveyor family consists also of two members, namely ICCII+ and ICCII- introduced in [2].
*Corresponding author:
[email protected]
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The two output current conveyor family however has three members. They are the Balanced Output (BO) CCII shown in Fig. 1(a) [3-4], the Double Output (DO) CCII with two Z+ outputs shown in Fig. 1(b) and the DOCCII with two Z- outputs shown in Fig. 1(c).
FIGURE 1(a) Symbol of the balanced output CCII.
FIGURE 1(b) Symbol of the double output CCII++.
FIGURE 1(c) Symbol of the double output CCII- -.
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The two output inverting current conveyor family has also three members. They are the BOICCII shown in Fig. 2(a) [5], the DOICCII with two Z+ outputs shown in Fig. 2(b) and the DOICCII with two Z- outputs shown in Fig. 2(c).
FIGURE 2(a) Symbol of the balanced output ICCII.
FIGURE 2(b) Symbol of the double output ICCII++.
FIGURE 2(c) Symbol of the double output ICCII- -.
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2 DEFINITIONS OF TWO OUTPUT CCII AND ICCII FAMILY The BOCCII and the BOICCII are four-port active building blocks defined by:
Vx 0 ±1 IY 0 0 = I 1 0 Z+ I -1 0 Z-
0 0 0 0
0 0 0 0
Ix VY V Z + V Z-
(1)
The positive sign applies to the BOCCII and the negative sign applies to the BOICCII. The DOCCII and the DOICCII having two Z+ outputs are four-port active building blocks defined by:
Vx 0 ±1 I Y 0 0 = I 1 0 Z+ I 1 0 Z +
0 0 0 0
0 0 0 0
Ix VY V Z + V Z +
(2)
The positive sign applies to the DOCCII and the negative sign applies to the DOICCII. The DOCCII and the DOICCII having two Z- outputs are four-port active building blocks defined by:
Vx 0 ±1 IY 0 0 = I -1 0 Z- I -1 0 Z-
0 0 0 0
0 0 0 0
Ix VY V Z- V Z-
(3)
The positive sign applies to the DOCCII and the negative sign applies to the DOICCII.
3 Generation of current modE filter One of the most attractive current mode bandpass lowpass filters was introduced in [6]. It employs three-BOCCII, the first stage is a current follower to provide the very low input impedance. The current mode circuit shown in Fig. 3(a) was introduced in [7] and it represents a special case from the circuit in [6] after removing the first stage. The circuit of Fig. 3(a) has the
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FIGURE 3(a) Grounded passive component current mode filter using two BOCCII [7].
FIGURE 3(b) Grounded passive component current mode filter using two BOICCII [5].
attractive advantages that all of the five passive elements are grounded and the parasitic resistances RX and capacitances CZ can be easily compensated by subtracting their values from the corresponding resistance and capacitance in the circuit. It is worth noting the very low input impedance current mode filter reported in [6] is not directly compensated for RX of the first stage and one CZ of the third stage. The circuit of Fig. 3(b) using two BOICCII was introduced very recently in [5]. Figure 4 represents a generalized current mode version of the circuits of Fig. 3 by using two balanced output conveyors that can be either BOCCII or BOICCII. The parameter B represents the type of CCII, which is +1 for
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FIGURE 4 Generalized grounded passive component current mode filter.
CCII and -1 for ICCII. The parameter K represents the conveyor Z polarity which is +1 for Z+ and -1 for Z-. The circuit equations are given by:
IBP = Ii
-sB1K1C2R2 sC2R1R2 - B1K1B2K2 s C1C2R1R2 + R
ILP = Ii
-B1K1B2K2 sC2R1R2 - B1K1B2K2 s2 C1C2R1R2 + R
(4)
2
(5)
For the filter stability the quantity B1K1B2K2 must be negative. This can be achieved by eight different sign combinations resulting in eight alternative current mode filters as given in Table 1. The lowpass response polarity will be noninverting in each of the eight circuits. The bandpass response polarity is determined from the sign of -B1K1 and is given in Table 1. From the eight reported circuits only three of them were published before in [5]-[7], the other five circuits are new. The radian frequency ωO and Q are given by:
ωo =
1 C1C2R1R2
Q=R
C1 C2R1R2
(6)
4 GENERATION OF CURRENT MODE OSCILLATORS The current mode oscillator circuit in Fig. 5(a) employs two BOCCII, three grounded resistors and two grounded capacitors which is the minimum num-
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TABLE 1 Eight alternative current mode filters based on Fig. 4. Circuit
B1
K1
B2
K2
Conveyor 1
Conveyor 2
BP polarity
Ref.
1
+
+
+
-
BOCCII
BOCCII
Inverting
7
2
+
-
+
+
BOCCII
BOCCII
noninverting
7
3
-
+
-
-
BOICCII
BOICCII
noninverting
5
4
-
-
-
+
BOICCII
BOICCII
Inverting
New
5
-
+
+
+
BOICCII
BOCCII
noninverting
New
6
+
+
-
+
BOCCII
BOICCII
Inverting
New
7
+
-
-
-
BOCCII
BOICCII
noninverting
New
8
-
-
+
-
BOICCII
BOCCII
Inverting
New
FIGURE 5(a) Grounded passive component oscillator using two BOCCII [8].
ber of passive circuit elements to obtain independent control on condition of oscillation and frequency of oscillation. It has the attractive advantages that the parasitic resistances RX and capacitances CZ can be easily compensated by subtracting their values from the corresponding resistance and capacitance in the circuit. The circuit shown in Fig. 5(b) has the same topology but uses two BOICCII [9]. Two more new circuits will be generated by considering the generalized circuit shown in Fig. 6. The circuit characteristic equation is obtained as:
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FIGURE 5(b) Grounded passive component oscillator using two BOICCII [9].
FIGURE 6 Generalized grounded passive component oscillator.
s2 C1C2R1R2 + sC2R2 R1 - B1K1 + B1K1B2K2 = 0 R
(7)
The conditions of oscillation are given by:
R = R1
(8-a)
Generation of Two Output CCII and Two Output ICCII Based Current
B1K1 = +1 and B2K2 = +1
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(8-b)
It is seen that R controls the condition of oscillation without affecting the frequency of oscillation which is given by: ωo =
1 C1C2R1R2
(9)
The resistor R2 controls the frequency of oscillation without affecting the condition of oscillation. There are four possible sign combinations to satisfy equation (8-b) as given in Table 2 resulting in a family of four oscillator circuits, two of them are new. The current mode oscillator circuit in Fig. 7(a) employs a DOCCII and a BOCCII, three grounded resistors and two grounded capacitors which is the TABLE 2 Four alternative oscillator circuits based on Fig. 6. Circuit
B1
K1
B2
K2
Conveyor 1
Conveyor 2
1
+
+
+
+
BOCCII
BOCCII
8
2
+
+
-
-
BOCCII
BOICCII
New
3
-
-
-
-
BOICCII
BOICCII
9
4
-
-
+
+
BOICCII
BOCCII
New
FIGURE 7(a) Grounded passive component oscillator using DOCCII and BOCCII [8].
Ref.
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FIGURE 7(b) Grounded passive component oscillator using DOICCII and BOICCII [9].
minimum number of passive circuit elements to obtain independent control on condition of oscillation and frequency of oscillation. It has the same topology as the oscillator of Fig. 5(a) and all of its attractive advantages. The circuit shown in Fig. 7(b) has also the same topology but uses a DOICCII and a BOICCII [9]. Two more new circuits will be generated by considering the generalized circuit shown in Fig. 8. The circuit characteristic equation is obtained as:
FIGURE 8 Generalized grounded passive component oscillator using Double Output Conveyor and Balanced Output Conveyor.
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TABLE 3 Four alternative oscillator circuits based on Fig. 8. Circuit
B1
K1
B2
K2
Conveyor 1
Conveyor 2
1
+
+
+
-
DOCCII
BOCCII
8
2
+
+
-
+
DOCCII
BOICCII
New
3
-
-
+
-
DOICCII
BOCCII
9
4
-
-
-
+
DOICCII
BOICCII
New
s2 C1C2R1R2 + sC2R2 R1 - B1K1 - B1K1B2K2 = 0 R
Ref.
(10)
The conditions of oscillation are given by:
R = R1
(11-a)
B1K1 = +1 and B2K2 = -1
(11-b)
There are four possible sign combinations to satisfy equation (11-b) as given in Table 3 resulting in a family of four oscillator circuits, two of them are new. It should be noted that the second conveyor can also be a double output instead of a balanced output as the output terminal does not affect the condition of oscillation; it affects only output current polarity. 5 CONCLUSIONS A generation method based on the availability of BOCCII and BOICCII is introduced in this paper and applied to one of the most attractive current mode filters resulting in a family of eight filters five of them are new. The generation method introduced in this paper based on two output current conveyors and inverting current conveyors is also applied to two well known grounded passive element current mode oscillators to obtain four more new oscillator circuits. The proposed generation method can be applied to many other filter and oscillator circuits. REFERENCES [1] Sedra A. S. and Smith K. C., A second generation current conveyor and its applications, IEEE Trans. Circuit Theory, 17, 1970, 132–134. [2] Awad I. A. and Soliman A. M., Inverting second generation current conveyors: the missing building blocks, CMOS realizations and applications, Int. J. of Electronics, 86, 1999, 413–432.
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[3] Bruun, E, Constant bandwidth current mode operational amplifier, Electronics Letters, 27, 1991, 1673–1674. [4] Elwan H. O. and Soliman A. M, A novel CMOS current conveyor realization with an electronically tunable current mode filter suitable for VLSI, IEEE Trans. Circuits Systems II: Analog Digit Signal Processing, 43, 1996, 663–670. [5] Soliman A. M., New grounded capacitor current mode bandpass lowpass filters using two balanced output ICCII, Journal of Active and Passive Electronic Devices, 3, 2008, 175–184. [6] Soliman A. M., Current mode universal filter, Electronics Letters, 31, 1995, 1420–1421. [7] Soliman A. M., New current mode filters using current conveyors, International Journal of electronics and Communications (AEU) 51, 1997, 275–278. [8] Soliman A. M., Current mode CCII oscillators using grounded capacitors and resistors, International Journal of Circuit Theory and applications, 26, 1998, 431–438. [9] Soliman A. M., Current mode oscillators using inverting CCII, Journal of Active and Passive Electronic Devices, 6, 2011, 305–320. [10] H. O. Elwan and A. M. Soliman, Novel CMOS differential voltage current conveyor and its applications, IEE Proceedings-Circuits, Devices and Systems, 144, 1997, 195–200.
