A Digitally Programmable Voltage-Mode Multifunction Filter Using CCDVCCs Chaiyan Chanapromma*, Winai Jaikla** and Montree Siripruchyanun† *
Computer Engineering Program, Faculty of Industrial Technology, Uttaradit Rajabhat University, Muang, Uttaradit, 53000, THAILAND Tel: +66-5-541-1096 Ext. 1635, Fax: +66-5-541-1296 Email:
[email protected] ** Electric and Electronic Program, Faculty of Industrial Technology, Suan Sunandha Rajabhat University, Dusit, Bangkok, 10300, THAILAND Tel: +66-2-243-2240 Ext. 317, Fax: +66-2-241-5935, E-mail:
[email protected] † Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, THAILAND Tel: +66-2- 913-2500 Ext. 3328 Fax. +66-2-587-8255, E-mail:
[email protected]
Abstract— This article presents a voltage-mode multi-function filter performing completely standard functions: low-pass, highpass, band-pass, band-reject and all-pass functions, current controlled differential voltage current conveyors (CCDVCCs). The features of the circuit are that: the quality factor and pole frequency can be tuned independently via the input bias currents: the circuit description is very simple, consisting of merely 2 CCDVCCs, 1 resistor and 2 capacitors. Only one external resistor and without any component matching conditions, the proposed circuit is very appropriate to further develop into an integrated circuit. Additionally, each function response can be selected by suitably selecting input signals with digital method. The PSPICE simulation results are depicted. The given results agree well with the theoretical anticipation.
I.
speed, wide bandwidth and simple implementation [13-14]. However, from our investigations, there are seen that the DVCC can not be controlled the parasitic resistances at current input ports so when it is used in a circuit, it must unavoidably require some external passive components, especially the resistors. This makes it not appropriate for IC implementation due to occupying more chip area, consuming high power and without electronic controllability. On the other hand, the introduced current controlled differential voltage current conveyor (CCDVCC) [15] has the advantage of electronic adjustability over the DVCC. The aim of this paper is to propose a voltage-mode multifunction filter, emphasizing on use of the CCDVCCs. The features of proposed circuit are that: the proposed multifunction filter can provide completely standard functions (low-pass, high-pass, band-pass, band-reject and all-pass) without changing circuit topology: the circuit description is very simple, it uses only 1 resistor and 2 capacitors as passive elements, which is suitable for fabricating in monolithic chip or off-the-shelf implementation: quality factor and pole frequency can be independently adjusted. The performances of proposed circuit are illustrated by PSPICE simulations, they show good agreement as mentioned.
INTRODUCTION
In analog signal processing applications it may be desirable to employ active filters. They can be found in many applications: e.g., communication, measurement and instrumentation and control systems [1-2]. One of most popular analog filters is a multi-function filter since it can provide several functions, depending on desired selections. The literature surveys show that the voltage-mode multifunction filter circuits [3-12] have been reported. Unfortunately, these reported circuits suffer from one or more of following weaknesses: • Excessive use of the active and/or passive elements [3, 5-6, 7, 9, 11]. • Requirement for changing circuit topologies to achieve several functions [4, 9, 12]. • Lack of electronic adjustability 3-9, 11-12]. • The pole frequency and quality factor can not be tuned independently [8-9]. The differential voltage current conveyor (DVCC) is a reported active component, especially suitable for a class of analog signal processing [13]. The fact is that the device can operate in both current and voltage-modes, provides flexibility and enables a variety of circuit designs. In addition, it can offer advantageous features such as high slew-rate, high
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II.
PRINCIPLE OF OPERATION
A.
Basic Concept of CCDVCC CCDVCC properties are similar to the conventional DVCC, except that the CCDVCC has finite input resistance Rx at the x input terminal [15]. This parasitic resistance can be controlled by the bias current IB as shown in RX =
VT , 2I B
(1)
where VT is the thermal voltage, equal to 26mV at room temperature. The relationship between the voltage and current variables among X, Y1, Y2 and Z ports of an ideal CCDVCC can be described by
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ISCIT 2009
⎡VX ⎤ ⎡ RX ⎢ ⎥ ⎢ ⎢ IY 1 ⎥ = ⎢0 ⎢ IY 2 ⎥ ⎢ 0 ⎢ ⎥ ⎢ ⎣⎢ I Z ⎦⎥ ⎣1
Vin1
1 − 1 0⎤ ⎡ I X ⎤ ⎢ ⎥ 0 0 0 ⎥⎥ ⎢VY 1 ⎥ . 0 0 0 ⎥ ⎢VY 2 ⎥ ⎥⎢ ⎥ 0 0 0 ⎦ ⎣⎢VZ ⎦⎥
Vin 2
(2)
Fig. 2.
IB
VY 1 VY 2
IY 1 IY 2
Y1 CCDVCC Z Y2 X IX VX
Y1
IZ
Y2
VZ
Z
X
Proposed Voltage-mode Multi-function Filter
Vin1
Vin2
Vin3 0
BP
0
1
HP
1
0
0
BR
1
0
1
AP
1
-1
1
LP
0
0
1
ω0 =
IX
Q0 =
CCDVCC (a) Symbol (b) Equivalent circuit
Proposed Voltage-mode Multi-function Filter The proposed voltage-mode multi-function filter is shown in Fig. 2, where IB1 and IB2 are input bias currents of CCDVCC1, and CCDVCC2, respectively. By routine analysis of the circuit in Fig. 2, the output voltage can be obtained to be
1 , C1C2 Rx1 Rx 2
Q0 = RQ
C1 , C2 Rx1 Rx 2
VT
I B1 I B 2 , C1C2
(6)
C1 I B1 I B 2 . C2
(7)
ω0
Q0
=
1 . C1 RQ
(8)
In the same view, the bandwidth can be linearly tuned by RQ. Another advantage of the proposed circuit is that the high Q0 circuit can be obtained by setting RQ.
(3)
From Eq. (3), Vin1, Vin2 and Vin3 can be chosen as in Table I to obtain a standard function of the 2nd–order network. Moreover, it is found in Table I that each function response can be selected by digital method. The pole frequency (ω0) and quality factor (Q0) of each filter response can be expressed as
ω0 =
2 RQ
BW =
Vin1 s 2 + s VO =
2 VT
From Eqs. (6) and (7), we found that the quality factor can be adjusted independently from the pole frequency by varying RQ. Furthermore, the pole frequency can be adjusted by IB1 and IB2. Thus bandwidth (BW) is given by
B.
1 1 Vin 2 + Vin 3 C1 RQ C1C2 Rx1 Rx 2 . 1 1 s2 + s + C1 RQ C1C2 Rx1 Rx 2
Input selections
VO
(b) Fig. 1.
VO
where Rx = VT / 2 I B , Eqs. (4) and (5) are subsequently modified to
Rx
Vd = VY 1 − VY 2
C2
Filter Responses
IZ = I X
1
IY 2 = 0 Vd
Y2 Z CCDVCC Y1 X
TABLE I The Vin1, Vin2 and Vin3 values selection for each filter function response
(a)
IY 1 = 0
Y1 Z CCDVCC Y2 X
RQ
Vin3
The symbol and the equivalent circuit of the CCDVCC are illustrated in Fig. 1.
IB2
I B1
C1
C.
(4)
(5)
Circuit Sensitivities The sensitivities of the proposed circuit can be found as 1 1 S IωB01 = S IωB02 = ; SCω10 = SCω20 = − ; SVωT0 = −1 , 2 2
(9)
1 1 S IQB01 = S IQB02 = SCQ10 = ; SCQ20 = − ; S RQQ0 = 1 , 2 2
(10)
S RBW = SCBW = −1 . Q 1
(11)
Therefore, all the active and passive sensitivities are equal or less than unity in magnitude.
898
VCC Q10
Q24
Q23
Q11
Q25 Q26
Q12 Q22
Q21 Q6
Q7
Y1
Q8
Q9
X
Q3
Q2
Q4
Fig. 3.
III.
Non-Ideal case For non-ideal case, the CCDVCC can be respectively characterized with the following equations VX = β VY 1 + γ VY 2 + RX I X ,
(12a)
IZ = α I X ,
(12b)
Vin1 s 2 + s
(13)
In this case, the ω0 and Q0 are changed to
Q0 = RQ
α1α 2 β1γ 2
C1C2 Rx 2 Rx 3
,
α1α 2 β1γ 2 C1 C2 Rx1 Rx 2
100d
(14)
.
Phase
ω0 =
Q16
VEE
SIMULATION RESULTS
To prove the performances of the proposed circuit, the PSPICE simulation program was used. The PNP and NPN transistors employed in the proposed circuit were simulated by respectively using the parameters of the PR200N and NR200N bipolar transistors of ALA400 transistor array from AT&T [16]. Fig. 3 depicts schematic description of the CCDVCC used in the simulations. All CCDVCCs were biased with ±1.5V power supplies, C1=C2=1nF, RQ=1kΩ, IA=IB1=IB2=50µA are chosen to obtain intrinsic resistances values of 260Ω. It yields the pole frequency of 558kHz, while calculated value of this parameter from Eq. (6) is 612kHz (deviated by 8.82%). The results shown in Fig. 4 are the gain and phase responses of the multi-function filter obtained from Fig. 2. There are clearly seen that the proposed filter can provide low-pass, high-pass, band-pass, band-reject and allpass functions, dependent on digital selection as shown in Table I, without modifying circuit topology. Fig. 5 display gain responses of band-pass function for different RQ values. It is shown that the quality factor can be adjusted by RQ as depicted in Eq. (7) without affecting the pole frequency. Maximum power consumption is about 1.72mW.
where α is the frequency dependent current gain, besides β and γ are the frequency dependent voltage gains. These gains are ideally equal to unity. In practical, they depend on the frequency of operation, temperature and transistor parameters of the CCDVCC. In the case of non-idea and reanalyzing the proposed filter in Fig. 2, it yields the output voltage to be
αα γ γ 1 Vin 2 + 1 2 1 2 Vin 3 C1 RQ C1C2 Rx1 Rx 2 , α1α 2 β1γ 2 1 2 s +s + C1 RQ C1C2 Rx 2 Rx 3
Q17 Q15
Internal Construction of CCDVCC
D.
VO =
Q14
Q13
Gain (dB)
Q1
Z
Q20
Q19
IB
IA
0
0d -40
Gain Phase
-100d -80 1.0k
(15)
10k
100k 1.0M Frequency (Hz)
(a) Phase
Practically, the α, γ and β originate from intrinsic resistances and stray capacitances in the CCDVCC. These errors affect the sensitivity to temperature and high frequency response of the proposed circuit, then the CCDVCC should be carefully designed to achieve these errors as low as possible. Consequently, these deviations are very small and can be ignored.
Gain (dB)
Y2
(b)
899
10M
100M
100d
[3]
0 -5
0d
[4]
-10
Gain Phase
-15 -100d -20 1.0k
10k
[5] 100k 1.0M Frequency (Hz)
10M
100M
[6] [7]
Gain (dB)
Phase
(c)
[8] [9]
Phase
Gain (dB)
(d)
[10]
[11] [12]
(e) Fig. 4.
Gain (dB)
20 0
-40
Gain and phase responses of the biquad for (a) BP (b) HP (c) BR (d) AP (e) LP.
[13]
RQ=0.25kΩ RQ=0.5kΩ RQ=1kΩ RQ=2kΩ RQ=3kΩ RQ=4kΩ
-80 1.0k
Fig. 5.
[14] [15] 10k
100k 1.0M Frequency (Hz)
10M
100M
[16]
Proposed Band-pass Responses at Different Values of RQ
IV. CONCLUSIONS The digitally controllable voltage-mode multi-function filter based on CCDVCCs has been presented. The advantages of the proposed circuit are that: it performs lowpass, high-pass, and band-pass functions from the same circuit configuration without component matching conditions: the quality factor and the pole frequency can be independently controlled. The circuit description comprises only 2 CCDVCCs, 1 resistor and 2 capacitors, which is attractive for either IC or off-the-shelf implementation. With ±1.5V supplies, the total power consumption is about 1.72mW for all bias currents of 50µA. REFERENCES [1] [2]
A. S. Sedra, and K. C. Smith, Microelectronic circuits, 3rd ed., Florida: Holt, Rinehart and Winston, 1991. M. A. Ibrahim, S. Minaei, and H. A. Kuntman, “A 22.5 MHz currentmode KHN-biquad using differential voltage current conveyor and grounded passive elements,” Int. J. Electron. Commun. (AEU), vol. 59, pp. 311-318, 2005.
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