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A novel configuration for voltage-mode biquads using a single current conveyor
m
Microelectronics Journal, 23 (1992) 359-362
A Novel Configuration for Voltage-Mode Biquads Using a Single Current Conveyor Masami Higashimura Department of ElectricalEngineering, Matsue Collegeof Technology, 14-4, Nishi-ikuma, Matsue, 690 Japan
A novel general circuit configuration for the realisation of voltage-modebiquad falterswith a high input impedance,which enables the circuits to be cascaded without requiring any impedancematchingdevice,is presented.The circuitcan realise lowpass, highpass, bandpass, notch, and allpass transfer functionswith a singlecurrent conveyor(CCII) and four or six passive elements.
This paper presents a novel general circuit configuration which realises voltage-mode lowpass, highpass, bandpass, notch and allpass falters using a single CCII with high input impedance. The voltage tracking error of a CCII has no effects on o90 and Q of the transfer functions.
1. Introduction
2. Circuit Configuration
any active-RC circuits for the realisation of voltage-mode and current-mode transfer functions using a single current conveyor (CCII) [1] have been published in the literature [2-17]. However, no circuits which use a single CCII to realise any type of voltage-mode transfer functions with high input impedance have been reported. A high input impedance enables the circuits to be used in cascade without requiring any impedance matching device, and minimizing the number of CCIIs has the obvious advantage of low cost and low power consumption.
Figure 1 shows a proposed circuit configuration which realises voltage-mode transfer functions. Assuming a CCII to be ideal (i, =' 0, Vx = vy and iz = - ix), analysis yields the following transfer function:
M
V2= y3(ylys--y2y4) (1) VI Y~(Y2Y3+Y2Y4+y2y5 +y3Y5 +Y4Y5) + y2yay5 The circuit offers very high input impedance as i r = 0. By suitably choosing admittances, we can realise any type of transfer function. As an example,
0 0 2 6 - 2 6 9 2 / 9 2 / $ 5 . 0 0 © 1992, Elsevier Science Publishers Ltd.
359
m
0
1E
<
M. Higashimura/Voltage-Mode Biquads
Y3
Y5
I
Y'i
CCIIVI
y
0
m
z
V2 0
Y2
Fig. 1. Proposed circuit configuration for realising biquad transfer functions.
if
y,=l/R~,
)'3=1/R3, y 4 = 5 C 4 and fonowi~glowpass filter
~12~-5C2,
Ys = oo (short circuit), the can be realised:
(2)
(
1
~,/2
coO = \ C2C4R1R3, ]
(3)
and
,
(q
Q-C2+C~4
\
R3
J
(4)
Sensitivity analysis of the lowpass filter yields S~,° ~- S~;,= SR3 o,. . . . -
S Q`=-SQ
-
C a -- C 4 2 - 2 ( C 2 + C4 )
S~, = SQ~=-1/2 .
(5)
/
(6)
( ! ~,,2 C1C3R2R4]
(8)
SR2Rio-- Sa4~l)0---SOI0Cl= Sc~ ~° = ScQ, = -- Scq, = -- 1/2
(9) (10)
As the third example, if yl = 1/R1, y2 = oo (short circuit), y3 = 1/R3, y4 = sC4 andys = sC5, a bandpass filter can be realised. Then, coo and Q are given by 1 ~ 1/2 co,, = \ C4CsR1R3]
1 (C4C5R,]1/2 Q-C4+Cs \ R3 /
(11)
(12)
Sensitivity analysis of the bandpass filter yields
If y, =sC1, y2 = 1/R2, y3 =sC3, ]I4 = 1//G and Y5 = oo (short circuit), a highpass filter can be realised. Then coo and Q are given by
360
<
R2- R4 s ~ = - s~2 - 20% + e , )
where
coo =
(C3R2R4'~ '/2
Sensitivity analysis o f the highpass filter yields
V2 1 V~I=s2C2C4R1R3 + se3(c 2 + C4) -.1- 1
S~;
1
Q -- R2 + R4 \
,,,o_ s ~ , = s ~ , = s~;,= s.~ - - S~,=S~=-1/2
(13)
C4 -- C5 ScQs= -- ScQ'-- 2(C4 + Cs)
(14)
As the fourth example, if),3 = oo, eqn (1) becomes V2 _ yly5 - - Y2y4
(7)
V1
Yff2 + Yff5
(15)
Microelectronics Journal, VoL 23, No. 5
If }/1 = l/R1, z2 = 1/}/2 = R2 + 1/sC2, }/3 = o0, }/4 = 1/R4 and ys = sCs + 1/Rs, an allpass filter can be realised with
2(R2 C5) R1 \Rs+~2 +1=£
~21= kv
}/3 [.}tl}/5 --
~ti}/2}/4 q-
(1 --
k,)}/2ys]
yl (y2y3 + yff4 + yff5 + }/3y5 + y4ys) + }/2}/5[Y4 + (1 -- k/)}/3]
(19)
(16)
From eqn. (19) it is obvious that voltage tracking error has no effect on COoand Q.
and a notch fiher can be realised with R2 Rs
+
Cs C2
__
R1 R4
(17)
Let the hybrid matrix ofa nonideal CCII be given by
[i] [o o o][v] Vx iz
=
K, 0+
0 I~.
0 0
(18)
ix vz
where kv = 1 - e,, k, = 1 - e, and ev (1G I << 1), e, (I ei I << 1) denote the voltage and current tracking errors, respectively. Then, eqn. (1) becomes as the following equation:
3. Experimental Result Figure 2 shows the calculated frequency responses of a Butterworth lowpass falter with R1 = 2R3 = 20 k f l , C2 = C4 = 10 nF, co0/(2rr) = 1125-4 Hz, ev = 0 and ei = 0, 0.02 and 0"05. The experiment was carried out using a CCII which was constructed using an operational amplifier (LF356N) together with current mirrors composed of transistors (pnp: 2SA721 and npn: 2SC1327) [14, 18]. The experimental result agrees well with the characteristic calculated using e i = 0.02. Similarly, highpass, bandpass, allpass and notch filters worked successfully.
0
-20
-40 t9
-60 -
Theoretical
0.02 ~
Experimental
X~ ~i =0
-80 0
a
l
l
100
Ik Frequency(Hz)
10k
100k
Fig. 2. Frequency responses of a lowpass filter.
361
d2 0 1E
<
M. Higashimura/Voltage-Mode Biquads
"0 !.__
CD a2 4. Conclusion
A novel general circuit configuration for realising any type of voltage-mode second-order transfer function with high input impedance is presented. The voltage tracking error has no effect on o90and Q. The suitability of CCIIs as the active elements to realise basic building blocks for the design ofbiquad fdters has been established.
[8] [9] [10] [11] [12]
References [1] A.S. Sedra and K. C. Smith, A second generation current conveyor and its applications, IEEE Trans. Circuit Theory, CT-17 (1970) 132-133. [2] A. M. Sohman, Inductorless realization of an all-pass transfer function using the current conveyor, IEEE Trans. Circuit Theory, CT-20 (1973) 80-81. [3] A. M. Sohman, Another realization of an all-pass or a notch filter using a current conveyor, Int. J. Electron., 35 (1973) 135-136. [4] P. Aronhime, Transfer-function synthesis using a current conveyor, IEEE Trans. Circuits Syst., CAS-21 (1974) 312-313. [5] K. Gopal, Comment on "Inductorless realization of an all-pass transfer function using the current conveyor", IEEE Trans. Circuits Syst., CAS-21 (1974) 704-705. [6] T. S. Rathore and S. M. Dasgupta, Current-conveyor realisation of transfer function, Proc. IEE, 122 (1975) 1119-1120. [7] T.S. Rathore, A few more analog computer simulations of
362
[13]
[14] [15] [16]
[17] [18]
RC voltage transfer functions, Proc. IEEE, 64 (1976) 560-561. T.S. Rathore and S. M. Dasgupta, Synthesis of RC voltage functions with arbitrary gain constant, Proc. IEE, 123 (1976) 986-987. A. M. Soliman, Two novel active RC canonic bandpass networks using the current conveyor, Int. J. Electron., 42 (1977) 49-54. R. I. Salawu, Realization of an all-pass transfer function using the second generation current conveyor, Proc. IEEE, 68 (1980) 183-184. T. S. Rathore, Active complementary networks, IEEE Trans. Circuits Syst., CAS-27 (1980) 1278-1279. C.P. Chong and K. C. Smith, Biquadratic fiker sections employing a single current conveyor, Electron. Lett., 22 (1986) 1162-1164. M. Higashimura, M. Ishida, M. Hara and Y. Fukui, Realisation of biquadratic transfer function using single current conveyor, Trans. IEICE Japan, J71-A (1988) 228-234. M. Higashimura and Y. Fukui, Reahsation of all-pass and notch filters using a single current conveyor, Int. J. Electron., 65 (1988) 823-828. K. Pal, A high input impedance all-pass realisation using a single current conveyor, Microelectronics J., 21 (1990) 45-47. M. Higashimura and Y. Fukui, Realisation of current transfer function using a single current conveyor, IEICE Technical Report, IEICE, Japan, CAS89-56 (1989) 15-21. S.I. Liu, H. W. Tsao andJ. Wu, Cascadable current-mode single CCII biquads, Electron. Lett., 26 (1990) 2005-2006. B. Wilson, High performance current conveyor implementation, Electron. Lett., 20 (1984) 990-991.
Microelectronics Journal, 23 (1992) 359-362
A Novel Configuration for Voltage-Mode Biquads Using a Single Current Conveyor Masami Higashimura Department of ElectricalEngineering, Matsue Collegeof Technology, 14-4, Nishi-ikuma, Matsue, 690 Japan
A novel general circuit configuration for the realisation of voltage-modebiquad falterswith a high input impedance,which enables the circuits to be cascaded without requiring any impedancematchingdevice,is presented.The circuitcan realise lowpass, highpass, bandpass, notch, and allpass transfer functionswith a singlecurrent conveyor(CCII) and four or six passive elements.
This paper presents a novel general circuit configuration which realises voltage-mode lowpass, highpass, bandpass, notch and allpass falters using a single CCII with high input impedance. The voltage tracking error of a CCII has no effects on o90 and Q of the transfer functions.
1. Introduction
2. Circuit Configuration
any active-RC circuits for the realisation of voltage-mode and current-mode transfer functions using a single current conveyor (CCII) [1] have been published in the literature [2-17]. However, no circuits which use a single CCII to realise any type of voltage-mode transfer functions with high input impedance have been reported. A high input impedance enables the circuits to be used in cascade without requiring any impedance matching device, and minimizing the number of CCIIs has the obvious advantage of low cost and low power consumption.
Figure 1 shows a proposed circuit configuration which realises voltage-mode transfer functions. Assuming a CCII to be ideal (i, =' 0, Vx = vy and iz = - ix), analysis yields the following transfer function:
M
V2= y3(ylys--y2y4) (1) VI Y~(Y2Y3+Y2Y4+y2y5 +y3Y5 +Y4Y5) + y2yay5 The circuit offers very high input impedance as i r = 0. By suitably choosing admittances, we can realise any type of transfer function. As an example,
0 0 2 6 - 2 6 9 2 / 9 2 / $ 5 . 0 0 © 1992, Elsevier Science Publishers Ltd.
359
m
0
1E
<
M. Higashimura/Voltage-Mode Biquads
Y3
Y5
I
Y'i
CCIIVI
y
0
m
z
V2 0
Y2
Fig. 1. Proposed circuit configuration for realising biquad transfer functions.
if
y,=l/R~,
)'3=1/R3, y 4 = 5 C 4 and fonowi~glowpass filter
~12~-5C2,
Ys = oo (short circuit), the can be realised:
(2)
(
1
~,/2
coO = \ C2C4R1R3, ]
(3)
and
,
(q
Q-C2+C~4
\
R3
J
(4)
Sensitivity analysis of the lowpass filter yields S~,° ~- S~;,= SR3 o,. . . . -
S Q`=-SQ
-
C a -- C 4 2 - 2 ( C 2 + C4 )
S~, = SQ~=-1/2 .
(5)
/
(6)
( ! ~,,2 C1C3R2R4]
(8)
SR2Rio-- Sa4~l)0---SOI0Cl= Sc~ ~° = ScQ, = -- Scq, = -- 1/2
(9) (10)
As the third example, if yl = 1/R1, y2 = oo (short circuit), y3 = 1/R3, y4 = sC4 andys = sC5, a bandpass filter can be realised. Then, coo and Q are given by 1 ~ 1/2 co,, = \ C4CsR1R3]
1 (C4C5R,]1/2 Q-C4+Cs \ R3 /
(11)
(12)
Sensitivity analysis of the bandpass filter yields
If y, =sC1, y2 = 1/R2, y3 =sC3, ]I4 = 1//G and Y5 = oo (short circuit), a highpass filter can be realised. Then coo and Q are given by
360
<
R2- R4 s ~ = - s~2 - 20% + e , )
where
coo =
(C3R2R4'~ '/2
Sensitivity analysis o f the highpass filter yields
V2 1 V~I=s2C2C4R1R3 + se3(c 2 + C4) -.1- 1
S~;
1
Q -- R2 + R4 \
,,,o_ s ~ , = s ~ , = s~;,= s.~ - - S~,=S~=-1/2
(13)
C4 -- C5 ScQs= -- ScQ'-- 2(C4 + Cs)
(14)
As the fourth example, if),3 = oo, eqn (1) becomes V2 _ yly5 - - Y2y4
(7)
V1
Yff2 + Yff5
(15)
Microelectronics Journal, VoL 23, No. 5
If }/1 = l/R1, z2 = 1/}/2 = R2 + 1/sC2, }/3 = o0, }/4 = 1/R4 and ys = sCs + 1/Rs, an allpass filter can be realised with
2(R2 C5) R1 \Rs+~2 +1=£
~21= kv
}/3 [.}tl}/5 --
~ti}/2}/4 q-
(1 --
k,)}/2ys]
yl (y2y3 + yff4 + yff5 + }/3y5 + y4ys) + }/2}/5[Y4 + (1 -- k/)}/3]
(19)
(16)
From eqn. (19) it is obvious that voltage tracking error has no effect on COoand Q.
and a notch fiher can be realised with R2 Rs
+
Cs C2
__
R1 R4
(17)
Let the hybrid matrix ofa nonideal CCII be given by
[i] [o o o][v] Vx iz
=
K, 0+
0 I~.
0 0
(18)
ix vz
where kv = 1 - e,, k, = 1 - e, and ev (1G I << 1), e, (I ei I << 1) denote the voltage and current tracking errors, respectively. Then, eqn. (1) becomes as the following equation:
3. Experimental Result Figure 2 shows the calculated frequency responses of a Butterworth lowpass falter with R1 = 2R3 = 20 k f l , C2 = C4 = 10 nF, co0/(2rr) = 1125-4 Hz, ev = 0 and ei = 0, 0.02 and 0"05. The experiment was carried out using a CCII which was constructed using an operational amplifier (LF356N) together with current mirrors composed of transistors (pnp: 2SA721 and npn: 2SC1327) [14, 18]. The experimental result agrees well with the characteristic calculated using e i = 0.02. Similarly, highpass, bandpass, allpass and notch filters worked successfully.
0
-20
-40 t9
-60 -
Theoretical
0.02 ~
Experimental
X~ ~i =0
-80 0
a
l
l
100
Ik Frequency(Hz)
10k
100k
Fig. 2. Frequency responses of a lowpass filter.
361
d2 0 1E
<
M. Higashimura/Voltage-Mode Biquads
"0 !.__
CD a2 4. Conclusion
A novel general circuit configuration for realising any type of voltage-mode second-order transfer function with high input impedance is presented. The voltage tracking error has no effect on o90and Q. The suitability of CCIIs as the active elements to realise basic building blocks for the design ofbiquad fdters has been established.
[8] [9] [10] [11] [12]
References [1] A.S. Sedra and K. C. Smith, A second generation current conveyor and its applications, IEEE Trans. Circuit Theory, CT-17 (1970) 132-133. [2] A. M. Sohman, Inductorless realization of an all-pass transfer function using the current conveyor, IEEE Trans. Circuit Theory, CT-20 (1973) 80-81. [3] A. M. Sohman, Another realization of an all-pass or a notch filter using a current conveyor, Int. J. Electron., 35 (1973) 135-136. [4] P. Aronhime, Transfer-function synthesis using a current conveyor, IEEE Trans. Circuits Syst., CAS-21 (1974) 312-313. [5] K. Gopal, Comment on "Inductorless realization of an all-pass transfer function using the current conveyor", IEEE Trans. Circuits Syst., CAS-21 (1974) 704-705. [6] T. S. Rathore and S. M. Dasgupta, Current-conveyor realisation of transfer function, Proc. IEE, 122 (1975) 1119-1120. [7] T.S. Rathore, A few more analog computer simulations of
362
[13]
[14] [15] [16]
[17] [18]
RC voltage transfer functions, Proc. IEEE, 64 (1976) 560-561. T.S. Rathore and S. M. Dasgupta, Synthesis of RC voltage functions with arbitrary gain constant, Proc. IEE, 123 (1976) 986-987. A. M. Soliman, Two novel active RC canonic bandpass networks using the current conveyor, Int. J. Electron., 42 (1977) 49-54. R. I. Salawu, Realization of an all-pass transfer function using the second generation current conveyor, Proc. IEEE, 68 (1980) 183-184. T. S. Rathore, Active complementary networks, IEEE Trans. Circuits Syst., CAS-27 (1980) 1278-1279. C.P. Chong and K. C. Smith, Biquadratic fiker sections employing a single current conveyor, Electron. Lett., 22 (1986) 1162-1164. M. Higashimura, M. Ishida, M. Hara and Y. Fukui, Realisation of biquadratic transfer function using single current conveyor, Trans. IEICE Japan, J71-A (1988) 228-234. M. Higashimura and Y. Fukui, Reahsation of all-pass and notch filters using a single current conveyor, Int. J. Electron., 65 (1988) 823-828. K. Pal, A high input impedance all-pass realisation using a single current conveyor, Microelectronics J., 21 (1990) 45-47. M. Higashimura and Y. Fukui, Realisation of current transfer function using a single current conveyor, IEICE Technical Report, IEICE, Japan, CAS89-56 (1989) 15-21. S.I. Liu, H. W. Tsao andJ. Wu, Cascadable current-mode single CCII biquads, Electron. Lett., 26 (1990) 2005-2006. B. Wilson, High performance current conveyor implementation, Electron. Lett., 20 (1984) 990-991.