Keywords

1 Introduction

In this paper, a comparative study of biquad realizations using different realizations of the second generation current conveyor is presented. As compared to the conventional operational amplifiers, the current conveyor circuit provides high frequency range of operation [1,2,3]. Two circuit configurations have been chosen. One of the configurations belongs to the one input many output type filter category while the other configuration belongs to the many input and many output category. The first Universal filter circuit is having two CCII+ in current mode, and the second circuit is in voltage mode filter having three CCII+s. Both the filters have been simulated with all the realization of the current conveyors presented in below, and a comparison has been done in respect of input range, bias voltage, and cutoff frequency. PSPICE results of time response and frequency response of all the circuits have been presented. The simulation results of various active filters, low pass filter, band pass filter, and high pass filter, in current as well as voltage mode have given below.

2 Introduction to Current Conveyor (CCII)

Current conveyors are the most important building blocks in the field of analog signal processing in current mode as well as in voltage mode, but the current mode current conveyor circuits are widely used due to better performance and better results. In the most fundamental form, the CCII that is second generation of current conveyors are widely used. It is a four terminal device, these terminals are x, y, z, and ground. The x is an input terminal having low input impedance, y is also an input terminal having high input impedance, on the other hand z is an output terminal having high output impedance, and the fourth one grounded. It can perform many useful functions of analog signal processing when they are arranged in particular circuitry with other passive components [4,5,6]. In CCII, no current flows through terminal Y, in order to increase the flexibility of current conveyors. The ideal CCII appeared as an ideal transistor, with the perfect characteristics [1,2,3]. At the gate or base, no current flows through them, which is represented by terminal Y. The emitter or source voltage (appeared at terminal X) follows the voltage at terminal Y, as there was no base-emitter or gate-source voltage drop. There is infinite input impedance at gate or base (terminal Y); whereas, the emitter or source (X) has zero input impedance. The current that comes out of the emitter or source (terminal X) that reflects as a current in at the collector or drain (Z), but with an infinite output impedance (Fig. 1).

Fig. 1
A rectangle is labeled C C I I with the terminals Y and X on the left and terminal Y on the right. Arrows from terminals Y and X on the left lead to V y and V x via i y and i x, respectively. Another arrow from terminal Y on the right points towards V z via i z.

Circuit symbol of CCII

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The CCII can be expressed as a matrix as shown in Fig. 2 (Table 1):

$$\left[ {\begin{array}{*{20}c} {I_{Y} } \\ {V_{X} } \\ {I_{Z} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & { \pm 1} & 0 \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {V_{Y} } \\ {I_{X} } \\ {V_{Z} } \\ \end{array} } \right]$$
Fig. 2
A grid diagram with a point Z on the left and a point Y on the right. Both are marked as dots. Various lines, right facing arrows, and left facing arrows form a circuit. Several points are marked from M 1 through M 18.

CMOS realization of CCII

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Table 1 Aspect ratio for the CCII+ in transistor mode
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CCII+ that is shown in Fig. 2 uses 0.5 μm CMOS technology. When we apply the input at Y terminal, i.e., VY, and then we check the voltage at X terminal, i.e., VX, the relationship between X and Y is shown in Figs. 3, 4, 5, and 6.

Fig. 3
A line graph of V x versus V y. A linearly increasing line that passes through the origin is plotted.

Port relationship between VX and VY when we applied input DC sweep at Y terminal

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Fig. 4
A line graph of voltage in volts versus time in seconds. The waveform begins at (0, 0) and oscillates between negative 0.05 and positive 0.05.

Port relationship between VX and VY when we applied sinusoidal input voltage at Y terminal

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Fig. 5
A line graph of voltage in volts versus frequency in hertz. The line for V subscript 1 is drawn horizontally at 1 volt. The line for V subscript 2 starts parallel to the horizontal line, slightly below it, and drops down in a concave downward manner after (10 to the power 8, 0.995).

Port relationship between VX and VY when we applied AC input voltage at Y terminal

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Fig. 6
A line graph of V x versus V y. A linearly increasing line that passes through the origin is plotted.

Port relationship between IX and IZ when we applied input DC sweep at X terminal

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3 Filter Designing Using CCII

In this paper, a comparative study of biquad realizations using different realizations of the second generation current conveyor is presented. The current conveyor circuit provides high frequency range of operation as compared to conventional operational amplifiers. Two circuit configurations have been chosen. One of the configurations belongs to the single input multiple output type filter category while the other configuration belongs to the multiple input and multiple output category. The first circuit is a current mode universal filter using two CCII+ and the second circuit is a voltage mode filter using three CCII+s. Both the filters have been simulated with the realization of the current conveyor presented above, and a comparison has been done in respect of input range, bias voltage, and cutoff frequency. PSPICE results of time response and frequency response of all the circuits have been presented.

3.1 Current Mode Universal Filter

The Circuit shown in Fig. 7 represents the current mode Universal filter using two CCII+.

Fig. 7
Two rectangular boxes placed horizontally are labeled C C I I plus. The first box has the X, Y, and Z terminals on the left, bottom, and right, while the second box has the Y, X, and Z terminals on the left, bottom, and right, respectively. The circuit has 2 capacitors, C 1, C 2 and 2 resistors, R1, R2. The current has 1 input and 3 output points.

Current mode universal filter

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It may be noted that the three output currents are flowing through grounded elements and additional current followers will be required to drive the loads. The various transfer functions are as given below

$$T_{1} \left( s \right) = \frac{{I_{{{\text{out}}1}} \left( s \right)}}{{I_{{{\text{in}}}} \left( s \right)}} = - \frac{1}{{R_{1} R_{2} C_{1} C_{2} s^{2} + R_{2} C_{2} s + 1}}$$
(1)
$$T_{2} \left( s \right) = \frac{{I_{{{\text{out}}2}} \left( s \right)}}{{I_{{{\text{in}}}} \left( s \right)}} = - \frac{{R_{2} C_{2} s}}{{R_{1} R_{2} C_{1} C_{2} s^{2} + R_{2} C_{2} s + 1}}$$
(2)
$$T_{3} \left( s \right) = \frac{{I_{{{\text{out}}3}} \left( s \right)}}{{I_{{{\text{in}}}} \left( s \right)}} = \frac{{R_{1} R_{2} C_{1} C_{2} s^{2} }}{{R_{1} R_{2} C_{1} C_{2} s^{2} + R_{2} C_{2} s + 1}}$$
(3)

The three transfer functions are, respectively, of low pass filter (T1(s)), band pass filter (T2(s)), and high pass filter (T3(s)) with unity gain. The above universal filter is designed using translinear implementation of CCII+, CCII+ using flipped voltage follower, and CCII+ using AD844. Designed for fo = 50 kHz and Q = 0.707, with R1 = 10 kΩ, R2 = 20 kΩ, and C1 = C2 = 0.225 nF (Figs. 8, 9, 10, 11, 12, 13, 14, and 15).

Fig. 8
A line graph of the gain in hertz versus frequency in hertz. A horizontal line from (10 to the power 2, 0) decreases near the point (10 to the power 5, 0) to join a concave down curve near the point (10 to the power 8, negative 140), which ends at the point (10 to the power 10, negative 140).

Low pass filter response with a cutoff frequency of 46.43 kHz

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Fig. 9
A line graph of the gain in decibels versus frequency in hertz. A horizontal line from (0, 0) decreases near the point (10 to the power 5, 0), passes through the point (10 to the power 6, negative 50) to join a concave up curve, which joins a concave down curve, and finally decreases to end at (10 to the power 10, negative 150).

LPF response with a cutoff frequency of 49 kHz

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Fig. 10
A line graph of the gain in decibels versus frequency in hertz. A horizontal line from (10 to the power 0, 0) decreases near the point (10 to the power 5, 0), passes through the point (10 to the power 7, negative 100). It further decreases near the point (10 to the power 9, negative 170) to end at the point (10 to the power 11, negative 400).

LPF filter response using cutoff frequency 48.4 kHz

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Fig. 11
A line graph of the gain in decibels versus frequency in hertz. The line ascends linearly from (0, negative 70) to a peak at a point near (10 to the power 5, 0). It then falls linearly to join a horizontal line near the point (10 to the power 9, negative 100).

BPF response using cutoff frequency 46.32 kHz

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Fig. 12
A line graph of the gain in decibels versus frequency in hertz. The line ascends linearly from (0, negative 70) to a peak at a point near (10 to the power 5, 0). It then falls linearly to further join a concave up decreasing curve near the point (10 to the power 8, negative 50).

BPF response with a cutoff frequency of 48.8 kHz

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Fig. 13
A line graph of the gain in decibels versus frequency in hertz. The line ascends linearly from (10 to the power 2, negative 50) to a peak near the point (10 to the power 5, 0). It then decreases near the point (10 to the power 9, negative 75) to end near the point (10 to the power 11, negative 200).

BPF response with cutoff frequency 50.4 kHz

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Fig. 14
A line graph of the gain in decibels versus frequency in hertz. An increasing line from (0, negative 110) joins a horizontal line near the point (10 to the power 5, 0), which ends at the point (10 to the power 10, 0).

HPF response with a cutoff frequency of 46.8 kHz

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Fig. 15
A line graph of the gain in decibels versus frequency in hertz. An increasing line from (0, negative 130) joins a horizontal line near the point (10 to the power 5, 0) which ends at the point (10 to the power 10, 0).

HPF response with cutoff frequency 47.86 kHz

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From the responses, we have analyzed the highest frequency, lowest supply voltage, and lowest input current for low pass filter, band pass filter, and high pass filter. Table 2 summarizes these comparisons for the LP, BP, and HP filters.

Table 2 Evaluation of current mode universal filter for LPF, BPF & HPF
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3.2 Voltage Mode Universal Filter

Figure 16 shows a multiple input single output type voltage mode multifunction voltage mode filter and employs three second generation current conveyor [6, 7].

Fig. 16
Three rectangular boxes placed at the top, bottom, and bottom right are labeled C C I I plus. All three boxes have the X, Y, and Z terminals on the top, bottom, and right, respectively. The circuit has 2 capacitors, C1, C2, 2 resistors, R1, R2, and 4 voltage points, V 0, V 1, V 2, and V 3.

Voltage mode universal filter

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The output voltage Vo can be expressed as

$$V_{{\text{o}}} = \frac{{s^{2} C_{1} C_{2} V_{3} + sC_{1} G_{1} V_{2} + G_{1} G_{2} V_{1} }}{{s^{2} C_{1} C_{2} + sC_{1} G_{1} + G_{1} G_{2} }}$$
(4)

From Eq. (4), we can see

  • If V2 and V3 are equal (grounded), then second-order LPF can be obtained with the transfer function of Vo/V1.

  • If V1 and V3 are equal (grounded), then a second-order BPF can be obtained with the transfer function of Vo/V2.

  • If V1 and V2 are equal (grounded), then a second-order HPF can be obtained with the transfer function of Vo/V3.

Thus, the circuit is capable of realizing low pass, high pass, and band pass filter.

The transfer functions can realize low pass filter, band pass filter, and high pass filter with unity gain. The above multifunction filter is designed using translinear implementation of CCII+, designed for fo = 90 kHz and Q = 0.707, with R1 = 20 kΩ, R2 = 40 kΩ, and C1 = C2 = 0.0625 nF (Figs. 17, 18, 19, 20, 21, and 22).

Fig. 17
A line graph of the gain in decibels versus frequency in hertz. A horizontal line from (10 to the power 2, 0) first decreases from the point (10 to the power 5, 0), then increases from (10 to the power 6, negative 45) to become constant, then increases and finally decreases to end at the point (10 to the power 10, negative 35).

LPF response with a cutoff frequency of 83.8 kHz

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Fig. 18
A line graph of the gain in decibels versus frequency in hertz. A horizontal line from (10 to the power 2, 0) decreases near the point (10 to the power 5, 0), passes through the point (10 to the power 6, negative 40) to reach a minimum point. It then increases to end near the point (10 to the power 8, negative 25).

LPF response with cutoff frequency 82.8 kHz

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Fig. 19
A line graph of the gain in decibels versus frequency in hertz. A concave up curve increases from the point (10 to the power 2, negative 40) to reach its peak at (10 to the power 5, 0). It then decreases to form a concave up curve which connects to another concave up curve at the point (10 to the power 9, negative 25).

BPF response with cutoff frequency 85.114 kHz

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Fig. 20
A line graph of the gain in decibels versus frequency in hertz. An increasing line from (10 to the power 2, negative 55) reaches its peak at the point (10 to the power 5, 0), then decreases to reach the minimum point at (10 to the power 7, negative 60), and finally increases to end at the point (10 to the power 8, negative 18).

BPF response with cutoff frequency 85.3 kHz

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Fig. 21
A line graph of the gain in decibels versus frequency in hertz. The curve first increases in S shape till (10 to the power 5, 0). It then becomes constant to end at the point (10 to the power 8, 0).

HPF response with a cutoff frequency of 82.34 kHz

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Fig. 22
A line graph of the gain in decibels versus frequency in hertz. A concave up curve increases from slightly above the point (10 to the power 3, negative 60) to reach its peak near (10 to the power 5, 0). It then becomes constant to end at the point (10 to the power 8, 0).

HPF response with cutoff frequency of 89 kHz

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From the responses, we have analyzed the highest frequency, lowest supply voltage, and lowest input voltage for low pass filter, band pass filter, and high pass filter, and the results are summarized (Table 3).

Table 3 Evaluation of voltage mode universal filter for LPF, BPF & HPF
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4 Conclusion

In this paper, we have carried out a comparative study of different realizations of one current mode and one voltage mode universal filter circuit in respect of input current/voltage range, cutoff frequency, bias voltages. We have used the implementations of the translinear loops and the bipolar current conveyor available in the form of second generation current conveyor (CCII). The cutoff frequency of LPF in current mode realization is lower than that of voltage mode. In current mode, lowest input current is for HPF and highest input current is for LPF, on the other hand, lowest input voltage in voltage mode is for LPF and HPF and highest input voltage is for BPF.