Current-Mode First-Order Versatile Filter Using Translinear Current Conveyors with Controlled Current Gain

Abstract

This paper offers a new current-mode first-order versatile filter employing two translinear current conveyors with controlled current gain and one grounded capacitor. The proposed filter offers the following features: realization of first-order transfer functions of low-pass, high-pass, and all-pass current responses from single topology, availability of non-inverting and inverting transfer functions for all current responses, electronic control of current gain for all current responses, no requirement of component-matching conditions for realizing all current responses, low-input impedance and high-output impedance which are required for current-mode circuits, and electronic control of the pole frequency for all current responses. The proposed first-order versatile filter is used to realize a quadrature sinusoidal oscillator to confirm the advantage of the new topology. To confirm the functionality and workability of new circuits, the proposed circuit and its application are simulated by the SPICE program using transistor model process parameters NR100N (NPN) and PR100N (PNP) of bipolar arrays ALA400-CBIC-R from AT&T.

1. Introduction

Second-generation current conveyor (CCII) has been widely accepted to realize current-mode filters because the CCII offers better signal bandwidth, linearity, and dynamic range performances compared with operational amplifier (op-amp) based [1,2]. First-order filters are important sub-circuits for applications such as quadrature oscillators [3], multiphase oscillators [4], and high-order filters [5]. Usually, universal first-order filters are the circuits that can realize three filtering functions such as low-pass (LP), high-pass (HP), and all-pass (AP), into a single topology. Several universal first-order filters are available in the open literature [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]. It should be noted that the universal first-order filter is an interesting topic for publications because many papers on this topic were published in a few years ago [28,29,30,31,32,33,34]. Considering the mode of operations, these first-order filters can be classified as voltage-mode (VM) filters [6,7,8,9,10,11,12,13,14], current-mode (CM) filters [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], and mixed-mode (MM) filters [31,32,33,34]. This work is focused on CM filters that should provide low-input and high-output impedances, which is ideal for CM circuits because they can be connected to applications without buffer circuit requirements. Single-input three-output current filters are required because, when a single input signal is used, variant filtering functions can be obtained at the outputs without additional circuitry requirements, such as a current splitter circuit used to split a single currency into multiple currents for multi-input current filters.

Considering CM and MM filters in [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34], only the circuits in [15,24] can realize six transfer functions into a single topology, namely, both non-inverting and inverting transfer functions of LP, HP, and AP are obtained. However, the current gain of these transfer functions cannot be controlled. The first-order filter that can adjust the current gain of transfer functions has been proposed in [16], but only three transfer functions of LP, HP, and AP filters are obtained. The circuits that offer low-input and high-output impedances have been reported in [15,21,25,26,29], and several filters offer electronic control of the pole frequency [17,25,26,27,30,31,32,34]. However, these first-order filters cannot control the gain of transfer functions, and some of these filters offer only three transfer functions LP, HP, and AP filters. The circuits in [16,19,24] use a floating capacitor, which is not ideal for integrated circuits. The circuits in [29,34] require two identical input signals, so an additional current splitter circuit is needed.

Filters that can provide current gains of transfer functions are required because they can be used as a parameter for applications such as the condition of oscillation for oscillator circuits, which will be demonstrated in this paper. In addition, filters that offer the ability to electronically tune the pole frequency can provide advantages in case of easy compensation when the pole frequency deviates due to temperature, power supply, and process variations. Moreover, filters that can tune the pole frequency using a single parameter, such as a single bias current without matching conditions for any parameter during the tuning process, are of interest because they can be easily controlled in practice.

In this paper, a new current-mode current-controlled versatile first-order filter employing two translinear current conveyors with controlled current gain and one grounded capacitor is proposed. The circuit can simultaneously realize non-inverting and inverting transfer functions of LP, HP, and AP current answers with low-input and high-output impedances; hence six transfer functions can be obtained. The current gain and pole frequency of all transfer functions can be electronically controlled. To the best of the authors’ knowledge, there is no first-order current filter published in the literature that works similarly to this work. The non-ideal analysis of the proposed filter is further investigated. The HP filter is chosen for application to the quadrature oscillator by incorporating a lossy integrator. The proposed first-order filter and quadrature oscillator are simulated using the SPICE program to validate the theoretical formulations. The paper is organized as follows: Section 2 describes the structure of the second-generation current-controlled current conveyor (CCCII) and the proposed current-mode versatile first-order filter. Section 3 provides the non-ideality analysis for the proposed circuit. Section 4 presents an application of a current-mode quadrature oscillator. The simulation results of the CCCII, the filter, and the oscillator are shown in Section 5. Section 6 concludes the paper.

2. Circuit Description

The second-generation current-controlled current conveyor (CCCII) was first introduced in [35]. Compared with the conventional second-generation current conveyors (CCII) that have three terminals (y-, x-, and z-terminals), CCCII has parasitic resistance R_x at the x-terminal that usually can be controlled by bias current, and its ideal characteristic can be given by

$$\left(\begin{array}{c}{I}_y\\ V_x\\ I_z\end{array}\right)=\left(\begin{array}{ccc}0& 0& 0\\ 1& R_x& 0\\ 0& 1& 0\end{array}\right)=\left(\begin{array}{c}{V}_y\\ I_x\\ V_z\end{array}\right)$$

(1)

The y- and z-terminals possess high impedances (infinite for ideal), and the x-terminal has the parasitic resistance R_x.

It should be noted that the CCCII has a unity voltage gain between the y- and x-terminals and a unity current gain between the x- and z-terminals. To increase the performance of CCCII or CCII by controlling the current gain between x- and z-terminals, the CCCII/CCII with controlled current gain has been proposed [36,37,38,39,40,41]. Thus, a CCCII with controlled current gain has a limited resistance R_x at x-terminal and the current gain between the x- and z-terminals. Therefore, there are two parameters (R_x and current gain) available for user applications in the single CCCII with controlled current gain.

Figure 1 shows the proposed translinear current conveyors with controlled current gain, which was realized using bipolar junction transistors (BJTs). It was modified from [35] by adding current mirrors with adjustable gain (Q₂₂–Q₂₅ and Q₂₆–Q₂₉) [2,36].

To obtain the required plus and minus current outputs of the translinear current conveyor, adding additional current mirrors and cross-coupled current mirrors [42] are used. Consider a translinear-mixed loop (Q₁ to Q₄) and assume Q₅–Q₈ and Q₁₀–Q₁₂ around the loop are identical; the limited resistance R_x at x-terminal can be given by [35]

$$R_x=\frac{V_T}{2I_{set}}$$

(2)

where I_set is the bias current, and V_T is the thermal voltage (V_T = 25.8 mV at room temperature). It should be noted that the resistance R_x can be controlled by the dc bias current I_set.

Consider positive and negative current mirrors with adjustable gain by assuming that Q₂₂–Q₂₅ and Q₂₆–Q₂₉ are identical; the current gain k of the current conveyor in Figure 1 can be given by [2,36]

$$k=\frac{I_a}{I_b}$$

(3)

Thus, the signal current from x- to kz-terminals is amplified by the factor k, which can be given by I_a/I_b (k = I_a/I_b). It should be noted that the factor k can be linearly controlled, which can only be obtained using BJT-based CCCII in Figure 1. Therefore, the port characteristics of the translinear current conveyor with controlled current gain in Figure 1 can be expressed by

$$\left(\begin{array}{c}\begin{array}{c}{I}_y\\ V_x\\ I_z\end{array}\\ I_{kz}\end{array}\right)=\left(\begin{array}{c}\begin{array}{ccc}0& 0& 0\\ 1& R_x& 0\\ 0& \pm 1& 0\end{array}\begin{array}{c}0\\ 0\\ 0\end{array}\\ \begin{array}{ccc}0& \pm k& 0\end{array}0\end{array}\right)=\left(\begin{array}{c}\begin{array}{c}{V}_y\\ I_x\\ V_z\end{array}\\ V_{kz}\end{array}\right)$$

(4)

The proposed current-mode versatile first-order filter is shown in Figure 2. It consists of two translinear current conveyors with controlled current gains and one grounded capacitor. The use of grounded capacitors is advantageous for integrated circuits because their behavior is less affected by noise and stray capacitance effects compared to circuits using floating capacitors. It should be noted that the input signal is applied to the low-impedance (x-terminal) of CCCII, while the output signals are obtained from the high-impedance (z-terminal) of CCCII. Thus, the proposed filter provides low-input and high-output impedances.

Using (4) and nodal analysis, the current outputs I_o1, I_o2, I_o3, and I_o4 of the proposed filter in Figure 2 can be given by

$$I_{o1}=-I_{o2}=k_1\left(\frac{{sC}_1{R}_{x2}}{{sC}_1{R}_{x2}+1}\right)I_{in}$$

(5)

$$I_{o3}=-I_{o4}=k_2\left(\frac{1}{{sC}_1{R}_{x2}+1}\right)I_{in}$$

(6)

Thus, the proposed filter offers both non-inverting and inverting first-order transfer functions of HP and LP filters. The current gains of the HP and LP filters can be controlled by k₁ and k₂, respectively, where k₁ = I_a1/I_b1, k₂ = I_a2/I_b2, and I_a1, I_a2, I_b1, I_b2 are the bias currents of the current mirrors with an adjustable gain of the CCCIIs. The non-inverting first-order AP filter (phase lag) can be obtained by connecting I_o2 and I_o3 (I_o2 + I_o3) and the inverting first-order AP filter (phase lead) can be obtained by connecting I_o1 and I_o4 (I_o1 + I_o4). Their transfer functions can be expressed by

$$\frac{I_{AP+}}{I_{in}}=\frac{I_{o2}+I_{o3}}{I_{in}}=k\frac{1-s{C}_1{R}_{x2}}{1+s{C}_1{R}_{x2}}=-k\frac{s{C}_1{R}_{x2}-1}{s{C}_1{R}_{x2}+1}$$

(7)

$$\frac{I_{AP-}}{I_{in}}=\frac{I_{o1}+I_{o4}}{I_{in}}=k\frac{s{C}_1{R}_{x2}-1}{s{C}_1{R}_{x2}+1}$$

(8)

where k₁ = k₂ = k. Thus, the current gains of the AP filters can be controlled by k (k = I_a1/I_b1 = I_a2/I_b2).

Equations (5)–(8) confirm that that the proposed filter offers six transfer functions of LP, HP, and AP filters from a single topology.

The pole frequency of all filters can be calculated as

$${\omega }_o=\frac{1}{s{C}_1{R}_{x2}}$$

(9)

Thus, the pole frequency can be electronically controlled by R_x2 through the dc bias current I_set2 of the CCCII₂. It should be noted that the pole frequency can be adjusted by the single bias current I_set2 without matching conditions for any parameter during the tuning process.

3. Non-Ideality Analysis

The relationship of the voltages and currents by taking the non-idealities of the translinear current conveyor with controlled current gain can be described as

$$\left(\begin{array}{c}\begin{array}{c}{I}_y\\ V_x\\ I_z\end{array}\\ I_{kz}\end{array}\right)=\left(\begin{array}{c}\begin{array}{ccc}0& 0& 0\\ \alpha & R_x& 0\\ 0& \pm \beta & 0\end{array}\begin{array}{c}0\\ 0\\ 0\end{array}\\ \begin{array}{ccc}0& \pm {\beta }_{k}k& 0\end{array}0\end{array}\right)=\left(\begin{array}{c}\begin{array}{c}{V}_y\\ I_x\\ V_z\end{array}\\ V_{kz}\end{array}\right)$$

(10)

where $\alpha$= 1 − ε_v and ε_v (ε_v « 1) is the voltage tracking error from y- to x-terminals, ${\beta }_1$ = 1 − ε_i and ε_i (ε_i « 1) is the output current tracking error from x- to z-terminals, ${\beta }_2$ = 1 − ε_ik and ε_ik (ε_ik « 1) is the output current tracking error from x- to kz-terminals.

The various parasitic elements in the non-ideal CCCII symbol are shown in Figure 3. It shows that the x-terminal illustrates limited parasitic serial resistance R_x, the y-terminal illustrates high-value parasitic resistance R_y in parallel with low-value parasitic capacitance C_y, the z-terminal illustrates high-value parasitic resistance R_z in parallel with low-value parasitic capacitance C_z, and the kz-terminal illustrates high-value parasitic resistance R_kz in parallel with low-value parasitic capacitance C_y.

Using (10) and Figure 3, the current outputs I_o1, I_o2, I_o3, and I_o4 can be rewritten as

$$I_{o1}=-I_{o2}={{\beta }_{k1}k}_1\left(\frac{{\beta }_1\left({sC}_T{R}_{x2}+G_T{R}_{x2}\right)}{\left({sC}_T{R}_{x2}+G_T{R}_{x2}\right)+{{\beta }_1{\beta }_2\alpha }_2}\right)I_{in}$$

(11)

$$I_{o3}=-I_{o4}={\beta }_{k2}{k}_2\left(\frac{{{\beta }_1{\beta }_2\alpha }_2}{\left({sC}_T{R}_{x2}+G_T{R}_{x2}\right)+{{\beta }_1{\beta }_2\alpha }_2}\right)I_{in}$$

(12)

The transfer functions of APFs become

$$\frac{I_{AP+}}{I_{in}}=\frac{I_{o2}+I_{o3}}{I_{in}}=-\frac{{\beta }_1{{\beta }_{k1}k}_1\left({sC}_T{R}_{x2}+G_T{R}_{x2}\right)-{{\beta }_1{\beta }_2\alpha }_2{\beta }_{k2}{k}_2}{\left({sC}_T{R}_{x2}+G_T{R}_{x2}\right)+{{\beta }_1{\beta }_2\alpha }_2}$$

(13)

$$\frac{I_{AP-}}{I_{in}}=\frac{I_{o1}+I_{o4}}{I_{in}}=\frac{{\beta }_1{{\beta }_{k1}k}_1\left({sC}_T{R}_{x2}+G_T{R}_{x2}\right)-{{\beta }_1{\beta }_2\alpha }_2{\beta }_{k2}{k}_2}{\left({sC}_T{R}_{x2}+G_T{R}_{x2}\right)+{{\beta }_1{\beta }_2\alpha }_2}$$

(14)

where C_T = C₁ + C_z1 + C_y2, G_T = (1/R_z1)//(1/R_y1).

All filters have a pole frequency that can be calculated as

$${\omega }_o=\frac{{{\beta }_1{\beta }_2\alpha }_2}{{sC}_T{R}_{x2}+G_T{R}_{x2}}$$

(15)

It should be noted that the impact of the parasitic capacitances C_z1 + C_y2 can be eliminated if the large value of C₁ is used, and the impact of the parasitic resistances R_z1//R_y1 can be eliminated if the low value of R_x2 is given. However, the voltage and current gains of CCCIIs change the pole frequency.

4. Application to Quadrature Oscillator

Figure 4 shows the application of the proposed versatile filter as a current-mode quadrature oscillator. The current-mode high-pass filter has been selected, and it cascaded with a current-mode lossy integrator. When the circuit is connected as a feedback loop, the characteristic equation of the system can be stated by

$$k_1\left(\frac{s{C}_1{R}_{x2}}{s{C}_1{R}_{x2}+1}\right)\left(\frac{1}{s{C}_2{R}_{x3}+1}\right)=0$$

(16)

The characteristic equation of the oscillator can be stated by

$$s^2{C}_1{C}_2{R}_{x2}{R}_{x3}+s\left(C_1{R}_{x2}+C_2{R}_{x3}-k_1{C}_1{R}_{x2}\right)+1=0$$

(17)

The system will generate the sinusoidal signal under the condition of oscillation (CO) as

$$k_1=\frac{C_1{R}_{x2}+C_2{R}_{x3}}{C_1{R}_{x2}}$$

(18)

Letting C₁ = C₂ and R_x2 = R_x3, the CO becomes

$$k_1=2$$

(19)

where R_x2 and R_x3 are, respectively, the parasitic resistances at x-terminals of CCCII₂ and CCCII₃, k₁ is the current gain of CCCII₁.

The frequency of oscillation (FO) is

$${\omega }_o=\frac{1}{\sqrt{C_1{C}_2{R}_{x2}{R}_{x3}}}$$

(20)

The CO is controlled by current gain k₁ and the FO is controlled by R_x2 and R_x3 (R_x2 = R_x3). Thus, the CO and FO can be controlled electronically and independently.

Consider Figure 4, the CCCII₂ and C₂ work as a lossless integrator, and the input is I_z- where I_z- = −kI_o1. Thus, the relationship of I_o1 and I_o2 can be given by

$$I_{o2}=\frac{k_1}{k_2}\left(\frac{1}{{sC}_1{R}_{x2}}\right)I_{o1}$$

(21)

Thus, the phase difference between I_o1 and I_o2 is 90°, the phase difference between I_o2 and I_o3 is 180°, and the phase of I_o2 leads the phase of I_o1 for 90°. Therefore, the proposed current-mode quadrature oscillator provides three output currents with a phase shift of 90°.

It could be noted that output currents I_o1, I_o2, and I_o3 are supplied from z-terminals of CCCII, so they have a high impedance level that can be fed to the load without the use of buffer circuits.

5. Simulation Results

SPICE simulations were performed to verify the characteristics of the proposed versatile filter in Figure 2. The CCCII in Figure 1 was performed with the transistor model parameters of AT&T’s ALA400 CBIC-R process [43]. The DC supply voltage was ±2.5 V, and the capacitors C₁ and C₂ were 10 nF. The bias currents I_set1 and I_bi were equal to 25 μA, and the bias current I_ai was used to control the current gain k_i (i = 1, 2). The summarized performance of the CCCII used in this paper is shown in

Table 1. Summarized performances of used CCCII.

Parameters	Value
Supply voltage	±2.5 V
Technology	BJT (ALA400 CBIC-R)
DC voltage range	−1.7 V to 1.7 V
Voltage gain	0.999
Current gain:
Iz-/Ix	1.01
Ikz+/Ix (k = 1)	1.02
−3 dB bandwidth VF	37.4 MHz
−3 dB bandwidth CF:
Iz-/Ix	14.6 MHz
Ikz+/Ix (k = 1)	14.6 MHz
Power consumption (Iset = Ia = Ib = 25 μA)	1.84 mW
Rx (Ib = 1–100 μA)	13.27 kΩ–0.134 kΩ
Ry//Cy	1.48 MΩ//5 pF
Rz-//Cz-	375 kΩ//6 pF
Rkz+//Ckz+	373.7 kΩ//4.2 pF

. Figure 5 illustrates the magnitude (a) and phase (b) responses of the LP and HP filters when the bias current I_set2 was given as 10 μA, and the bias currents I_a1 and I_a2 were given 25 μA. The simulated pole frequency was 12.8 kHz, and the power consumption was 2.72 mW, whereas the theoretical value of the pole frequency was 12.24 kHz. Thus, the percent error of simulated pole frequency was 1.96%. The high-frequency limitation of the filter is approximately 10 MHz, and the magnitude of filters such as HP and AP responses will be slowly decreased when the frequency is higher than appropriately 5 MHz.

Figure 6 shows the magnitude and phase responses of the AP filters. Figure 6a shows the magnitude and phase responses of the non-inverting AP filter (phase lag) obtained by summing up I_o2 and I_o3, and Figure 6b shows the magnitude and phase responses of the inverting AP filter (phase lead) obtained by summing up I_o1 and I_o4. It is clear from Figure 5 and Figure 6 that the proposed filter can provide both non-inverting and inverting transfer functions of LP, HP, and AP filters in the same topology.

The non-inverting AP filter has been used by applying the input frequency of 1 kHz and varying the amplitude to test the linearity of the proposed filter. The total harmonic distortion (THD) with different amplitudes of I_in is shown in Figure 7, which shows that the THD was 1% for the amplitude of 40 μA_p-p.

Figure 8 showed the frequency responses when the pole frequency was varied by R_x2 via the bias current I_set2. Figure 8a shows the variant magnitude frequency response of the LP filter, (b) variant magnitude frequency response of the HP filter, (c) variant phase frequency response of the non-inverting AP filter (phase-lag), (d) phase frequency response of the inverting AP filter (phase-lead), when the bias current I_set2 was changed as 5 μA, 10 μA, 25 μA, 50 μA, and 100 μA and the obtaining pole frequency were, respectively, 6.33 kHz, 12.8 kHz, 31.13 kHz, 60.98 kHz, and 117.61 kHz. This result is used to confirm that the proposed filter can tune the pole frequency using the single bias current I_set2 without matching conditions for other parameters.

Figure 9 shows the magnitude frequency responses for (a) LP filter, (b) HP filter, and (c) AP filter when the gains were varied by k₁ and/or k₂ via the bias currents I_a1 and/or I_a2 (I_b1 and I_b2 were set to 25 μA). The current gains were −0.36 dB, 0.3 dB, 6.1 dB, 9.6 dB, and 11.8 dB when the bias currents I_a1 and/or I_a2 were set to 15 μA (k = 0.6), 25 μA (k = 1), 50 μA (k = 2), 75 μA (k = 3), and 100 μA (k = 4), respectively.

The simulated magnitude frequency responses of the LP, HP, and AP filters for process, voltage, and temperature (PVT) corners were investigated. Figure 10 and Figure 11 show, respectively, the results of the Monte-Carlo (MC) analysis were variations of the beta ($\beta$) in BJT by 10% (LOT tolerance) and supply voltages by ±10%. Figure 12 shows the magnitude frequency responses when the temperature was changed from −20 to 85 °C. It can be noted that the magnitude frequency responses were slightly changed when the process, voltage, and temperature were varied. From Figure 10, the maximum variations of passband gains of LP, HP, and AP filters were, respectively, about 0.07 dB, 0.15 dB, and 0.06 dB, while the maximum variations of the passband gains of LP, HP, and AP filters were respectively about 0.14 dB, 0.11 dB, and 0.19 dB for Figure 11, and the maximum variations of passband gains of LP, HP, and AP filters were, respectively, about 0.32 dB, 0.69 dB, 0.53 dB for Figure 12. Since temperature also affects the pole frequency via R_x1 and R_x2 (2), considering the temperatures of −20° and 85°, the pole frequencies were respectively 14.37 kHz and 11.14 kHz, which differed by 3.23 kHz.

The LP response was simulated by setting 5% tolerances of the capacitor C₁ at the pole frequency of 12.8 kHz and 200 Gaussian distribution runs. Figure 13 shows the derived histogram of the cut-off frequency, which expressed that the standard deviation ($\sigma$) of f_o was 0.631 kHz, and the maximum and minimum values of f_o were, respectively, 14.496 kHz and 11.518 kHz. It is worth noting that thanks to the electronic tunability of the filter, the deviation of the cut-off frequency and the gain could be easily readjusted by the I_set2 and I_a, respectively.

The comparison of the proposed filter with the previous works is in

Table 2. Comparison with previous first-order filters.

Features	Proposed	[10] 2022	[11] 2021	[24] 2017	[26] 2019	[29] 2022	[34] 2023
Active and passive elements	2 CCCII, 2 C	1 LT1228, 2 R, 1 C	2 CVCII, 1 C, 2 R (Figure 2)	2 ICCII, 1 C, 1 MOS	1 DXCCTA, 2 C	1 MOCDTA, 1 C	1 VDGA, 1 C, 1 R
Realization	BJT process (ALA400 CBIC-R)	Commercial IC	CMOS structure (0.18 μm)	CMOS structure (0.13 μm)	CMOS structure (0.18 μm)	CMOS structure (0.13 μm)	CMOS structure (0.18 μm)
Mode operation	CM	VM	CM, TIM	CM	CM	CM	MM
Type of filter	SIMO	MISO	SIMO	SIMO	SIMO	MIMO	MIMO
Number of filtering functions	6 (LP+, LP-, HP+, HP-, AP+, AP-)	4 (LP+, HP+, AP+, AP-)	2 (LP+, AP+)	6 (LP+, LP-, HP+, HP-, AP+, AP-)	4 (LP-, HP+, AP-)	3 (LP+, HP+, AP+)	3 (LP-, HP+, AP-)
Electronic control of gain	Yes	LP+, HP+	Yes	No	No	No	Yes
Low-input and high-output impedance	Yes	-	No	No	Yes	Yes	No
Using grounded capacitor/resistor	Yes	No	No	No	Yes	Yes	No
Pole frequency (kHz)	12.3	90	89–1000	2600	10,000	1590	1590
$\mathrm{Electronic} \mathrm{control} \mathrm{of} \mathrm{parameter} {\omega }_o$	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Total harmonic distortion (%)	1@40 μApp	1@200 mVpp	2@30 μApp	<1.5@90 μApp	-	-	-
Power supply voltages (V)	±2.5	±5	±0.9	±0.75	±1.25	±1	±0.9
Power consumption (mW)	2.72	57.6	1.057	4.08	1.75	2.5	1.31
Verification of result	Sim.	Exp.	Sim./Exp.	Sim.	Sim./Exp.	Sim./Exp.	Sim./Exp.

Note: MOCDTA = multiple-output current differencing transconductance amplifier, DXCCTA = dual-X current conveyor transconductance amplifier, VDGA = voltage differencing gain amplifier, CVCII = Electronically controllable second-generation voltage conveyors, TIM = trans-impedance mode, SIMO = single-input multiple-output, MISO = multiple-input single-output, MIMO = multiple-input multiple-output, MM = mixed-mode.

. The VM first-order filter in [10], mixed-mode (MM) first-order filters [11,34], and CM first-order filters in [11,24,26,29] have been used to compare. Compared with [10,11,26,29], the proposed filter offers six transfer functions similar to [24], but for the filter in [24], the gain of the transfer functions cannot be controlled. The MM first-order filter in [34] offers VM, trans-admittance mode (TAM), CM, and trans-impedance mode (TIM) operation from the same circuit structure, but each operation mode provides only three transfer functions of LP, HP, and AP filters whereas the proposed filter offers six transfer functions of LP, HP, AP filters. Compared to [10,11,24,34], this realization uses only grounded capacitors and does not require a passive resistor. Finally, compared to [11,24,34], the proposed current-mode filter offers low-input and high-output impedances.

The current-mode quadrature oscillator in Figure 4 was simulated, and the CCCII with controlled current gain in Figure 1a was used. The bias current I_b1 and I_b2 of CCCII₁ and CCCII₂ were set to 25 μA, and the bias current I_a1 of CCCII₁ was 36 μA for controlling the condition of oscillation. Figure 14 shows the simulated outputs of the oscillator when C₁ and C₂ were set to 10 nF, the bias current I_set1 of CCCII₁ and the bias current I_set3 of CCCII₂ were given as 25 μA, and the bias current I_set2 of CCCII₂ was given as 10 μA. The oscillating frequency of 20.8 kHz was obtained, whereas the theoretical value of the oscillating frequency was 19.35 kHz. It could be noted that the amplitudes of output currents I_o1, I_o2, and I_o3 were almost equal. In this case, the bias current I_a2 of CCCII₂ of 50 μA was used to control the currents I_o2 and I_o3. It can also be noted that when the condition of oscillation was varied by R_x2 and R_x3 and led to the difference of amplitudes of I_o1 and I_o2, I_o3, the problem can be solved by adjusting k₂ of CCCII₂ via the bias current I_a2 to achieve the same amplitudes. This option of tuning is available thanks to the advantage of the CCCII circuit with controlled gain.

6. Conclusions

A new current-mode first-order versatile filter using two translinear current conveyors with controlled current gain and one grounded capacitor is presented in this paper. The proposed filter offers the following features: (1) realizations of non-inverting and inverting transfer functions of low-pass, high-pass, and all-pass filters into single topology, (2) control of the current gain for all transfer functions of the filters, (3) electronic control of a pole frequency, (4) no requirement of component-matching conditions for realizing all filter responses, (5) low-input impedance and high-output impedance. The proposed first-order filter has been applied to realize the current-mode quadrature sinusoidal oscillator. The proposed filter and its application were simulated with SPICE to confirm characteristics and workability.