Single VDCC-Based Mixed-Mode First-Order Universal Filter and Applications in Bio-Signal Processing Systems

Abstract

This paper presents a compact mixed-mode first-order universal filter based on a single voltage differencing current conveyor (VDCC), which can function in all four possible operation modes, i.e., voltage mode (VM), trans-admittance mode (TAM), current mode (CM), and trans-impedance mode (TIM). The proposed configuration requires only two grounded resistors and one floating capacitor, which contributes to a low component count, facilitates integration, and allows for the electronic tunability of the pole frequency through the transconductance gain of the VDCC. This work also demonstrates two practical biomedical applications: an electrocardiogram (ECG) acquisition system utilizing the VM low-pass filter for noise suppression and a bioimpedance (BioZ) measurement system employing the proposed configuration-based CM oscillator circuit as a sinusoidal excitation source. The performance validation confirms the accuracy of impedance extraction and the preservation of waveforms using tissue-equivalent models. The results demonstrate that the proposed VDCC-based filter offers a compact, power-efficient, and versatile analog signal-processing solution suitable for modern biomedical instrumentation.

1. Introduction

The design of continuous-time analog filters remains a vital and challenging topic for research. Recently, universal active filter designs that provide the simultaneous implementation of several filtering functions—specifically low-pass (LP), high-pass (HP), and all-pass (AP) filters from a single topology—have garnered significant interest. These filters are widely utilized in instrumentation and control systems, sensor interfaces, and low-power electronic systems. Furthermore, they are very useful in bio-signal processing applications, such as electrocardiogram (ECG) acquisition systems, bioimpedance (BioZ) analyzers, and phase-sensitive detectors, owing to their versatility across different circuit configurations. In the design of high-order active filters of odd order, first-order universal filters are necessary. Consequently, considerable efforts have been aimed at the development of first-order universal filters utilizing various contemporary analog active building blocks [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27].

The work given in [1] simultaneously realized LP, HP, and AP filter functions in voltage mode (VM) using two second-generation current conveyors (CCIIs), two floating resistors, two grounded resistors, and one grounded capacitor. For the realization of an AP filter, the circuit had to maintain an equal resistor state to ensure independent control of the pole frequency (f_p). In [2], a single fully differential current conveyor (FDCCII), three resistors, and one grounded capacitor were employed to implement three different first-order filter designs. These designs had voltage inputs and voltage and current outputs, and they operated in VM and trans-admittance mode (TAM). The design in [3] described a versatile first-order current mode (CM) universal filter composed of two multiple-output CCIIs (MO-CCIIs), one grounded resistor, and one grounded capacitor. The given filter comprised one grounded capacitor, making it appropriate for integration technology. However, it did not feature electronic adjustment of its f_p. A single differential voltage current conveyor (DVCC) containing two resistors and one grounded capacitor was utilized to implement a VM first-order universal filter, as detailed in [4]. There were numerous matching requirements for this circuit in the AP realization. Once more, in [5], a DVCC-based VM first-order universal filter structure using two DVCCs, one grounded resistor, and one grounded capacitor were reported. A first-order CM AP filter with amplitude equalization based on only one multi-output operational transconductance amplifier (MO-OTA) was described in [6]. Nonetheless, the circuits were incapable of providing all three first-order filter functions. The CM first-order universal filter in [7] was realized with one dual-X second-generation multi-output current conveyor (DX-MOCCII) and four passive elements. It still lacked the ability to electronically modify the f_p. The previous comparable circuit in [8] suggested a CM first-order filter configuration employing two MO-CCIIs and all three grounded passive components to achieve low-input and high-output impedance features. The constraints on element matching were needed to facilitate the implementation of all three first-order filter functions. The construction of the VM first-order universal filter topology with one DVCC, one floating resistor, and one grounded capacitor was proposed in [9]. By choosing suitable input voltages, it could achieve all three first-order filter functions without necessitating component matching. As reported in [10], a first-order VM universal filter with digital programmability using a digitally controlled current conveyor (DPCCII) was developed. The implementation required three identical resistors and one grounded capacitor. According to [11], a CM first-order multifunction filter circuit was realized using a single current differencing buffered amplifier (CDBA), two resistors, and one grounded capacitor, which could synthesize LP and HP filter functions simultaneously. This structure did not utilize the full capacity of the CDBA device, as it did not utilize the terminal n. Furthermore, the circuit of [12] employed two dual-output CCIIs (DO-CCIIs), a floating resistor, and a grounded capacitor to develop the CM first-order universal filter. For this circuit, no matching constraint were used to derive LP, HP, and AP responses. In [13], a single configuration work for both inverting and non-inverting CM first-order LP, HP, and AP filters were presented using two inverting CCIIs (ICCIIs), one electronic MOS resistor, and a floating capacitor. The first-order CM and VM universal filters described in [14] and [15], respectively, required one active element and two passive grounded components. However, they possessed complicated internal architecture that included a minimum of 40 MOS transistors and a compensating capacitor and resistor. The electronic tunability of these circuits was also unfeasible. In [16], two different first-order VM filter structures were introduced. Each consisted of two voltage subtractors, one floating resistor, and one grounded capacitor. They needed no component matching constraints, but they lacked electronic control. A first-order CM filter structure, which was made up of a single extra-X current-controlled conveyor (EX-CCCII) and a single grounded capacitor, was introduced in [17]. The design provided low-input and high-output impedance while concurrently generating three current filter functions. None of the three implemented filter functions required matching requirements. The research in [18] described a first-order universal filter that could be controlled electronically. It had two operational transconductance amplifiers (OTAs), a grounded resistor, and a grounded capacitor, with both input and output impedances being ideal and infinite. The work, however, achieved VM filter functionality only for AP filters. Two circuit topologies for first-order filters were suggested in [19]. The first employed one multiple-output dual-X current conveyor transconductance amplifier (MO-DXCCTA), three identical transconductors, and one capacitor to carry out CM filter functions. The second filter required a MOSFET, a grounded capacitor, and one DXCCTA to perform three TAM filter functions. Based on a single modified DXCCTA, a first-order generic CM filter circuit has recently been presented in [20]. The circuit featured electronic tunability, easy cascadability, and low-voltage operation. However, it was non-canonical with respect to the capacitors. The resistorless implementation in [21] addressed the first-order CM universal filter with a differential difference dual-X second-generation current conveyor (DD-DXCCII), a grounded capacitor, and four MOSFETs. It required component-matching conditions for the implementation of all three CM filter responses. First-order LP, HP, and AP filters operating in CM were introduced in [22] and [23], each utilizing two active components, a resistor, and a capacitor. The work in [22] used MO-CCIIs as the active components, whereas [23] employed plus-type inverting current conveyors (ICCII+s) for its active components. Conversely, a configuration from [24] involved designing a VM electrically tunable first-order universal filter using the readily available LT1228 IC. It comprised a single LT1228 IC along with two floating resistors and a floating capacitor. In [25], five designs of first-order universal filters were presented, consisting of two current feedback operational amplifiers (CFOAs), along with three or four resistors and a grounded capacitor. Two of the five circuits needed specific criteria to achieve HP function, whereas all five circuits needed matching criteria for realizing the AP function. The presented filters provided filtering functionality in all four modes; however, the filter parameters were not electronically modifiable. As demonstrated in the fully differential configuration from [26], it used only one multiple-output current differencing transconductance amplifier (MO-CDTA) and one capacitor to implement first-order LP, HP, and AP filter current responses. A recent report in [27] described a mixed-mode first-order universal filter with electronic tunability. The realization required three OTAs and one grounded capacitor to obtain all three first-order generic filter functions across four operation modes.

The voltage differencing current conveyor (VDCC) has emerged as a promising active building block that enhances the functionality of conventional current conveyors. It offers increased adaptability for analog signal processing applications, including filters, oscillators, and impedance converters [28]. Owing to its high bandwidth, low power consumption, and ability to process both voltage and current, the VDCC is particularly well-suited for implementing compact, electronically tunable analog building blocks. Although various VDCC-based filters and oscillators have been reported, the realization of a simple mixed-mode first-order universal filter using only one VDCC and minimal passive components has not been sufficiently explored. Therefore, the above critical review inspired the authors to develop a minimum-component mixed-mode first-order universal filter based on a single VDCC. The filter supports VM, CM, TAM, and trans-impedance mode (TIM) operations while employing only two grounded resistors and one capacitor, yielding an easy layout for integrated circuit fabrication. By relying on a single active element, the design simplifies the overall topology while retaining full multi-mode functionality, which is rare in comparable designs. The pole frequency can be electronically controlled through the VDCC transconductance gain, which enhances flexibility in practical design. To validate the usefulness of the proposed configuration, two biomedical applications are demonstrated: an ECG acquisition system using the VM low-pass filter for noise reduction and a BioZ measurement interface utilizing the CM oscillator configuration as a sinusoidal excitation source. Both PSPICE simulation results based on 0.13-μm IBM process parameters and practical measurement scenarios confirm the accuracy, robustness, and low-power performance of the proposed design.

Accordingly, to explicitly summarize the main technical contributions of the proposed work, the following can also be highlighted:

(i)

The development of a mixed-mode first-order universal filter that utilizes only a single VDCC along with a minimum number of passive components.

(ii)

The capability of a single topology to simultaneously facilitate VM, TAM, CM, and TIM operations.

(iii)

The electronic tunability of the pole frequency via VDCC transconductance without requiring component matching in both VM and TAM modes.

(iv)

The exploration of practical biomedical applications, including ECG signal conditioning and BioZ excitation.

The remainder of this paper is structured as follows: Section 2 introduces the proposed mixed-mode first-order universal filter and presents its theoretical formulation along with the analyses of non-ideal factors; Section 3 provides simulation results generated using the PSPICE program; Section 4 demonstrates a dual-mode sinusoidal oscillator circuit derived from the proposed filter; Section 5 explores the application of the proposed circuit in the ECG and BioZ measurement systems; and, finally, Section 6 concludes the key findings of this work.

2. The Proposed Mixed-Mode First-Order Universal Filter Configuration

In the proposed design, the VDCC served as an active component. The symbolic circuit representation of the VDCC is illustrated in Figure 1, with the corresponding description matrix expressed as:

$$\left[\begin{array}{c}{i}_p\\ i_n\\ i_z\\ v_x\\ i_{wp}\\ i_{wn}\end{array}\right]=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ g_m& -g_m& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\\ 0& 0& 0& -1\end{array}\right]\left[\begin{array}{c}{v}_p\\ v_n\\ v_z\\ i_x\end{array}\right].$$

(1)

The parameter g_m in Equation (1) represents the transconductance gain of the amplifier, which is generally regulated through electronic methods. Based on the definition matrix of Equation (1), the implementation of the VDCC using the CMOS technology is given in Figure 2. The realized g_m of the CMOS VDCC can be electronically modified using the balanced output OTA (M₁–M₈). This adjustment is determined in the following manner [29]:

$$g_m=\sqrt{K_n\left({\displaystyle \frac{W}{L}}\right)I_B},$$

(2)

where K_n = μ_nC_ox, μ_n denotes the channel carrier mobility, C_ox indicates the per-unit-area gate-oxide capacitance, and I_B represents the external DC bias current. Additionally, (W/L) refers to the width-to-length ratio of transistors M₁ and M₂.

Utilizing the VDCC as an active element, the proposed mixed-mode first-order universal filter can be implemented with two grounded resistors and one capacitor as depicted in Figure 3. It is important to note that, with the appropriate selection of input and output signals, the circuit can operate as a mixed-mode, first-order multi-function filter with the same circuit design. Assuming ideal circumstances and disregarding tracking errors and parasitic impedances of the VDCC, the circuit analysis of Figure 3 provides the following details for VM, TAM, CM, and TIM.

2.1. VM and TAM First-Order Universal Filters

To generate VM and TAM filter responses, the input currents i₁, i₂, and i₃ were set at zero (open circuit). The two input voltages v₁ and v₂ were set as detailed in

Table 1. Voltage signal excitation for VM and TAM filter realizations.

Applied Signal Voltage		Filter Type	Matching Condition	Passband Gain
v1	v2			VM	TAM
vin (input voltage)	0	LP	no	1	1/R1
0	vin	HP	no	1	1/R1
vin	−vin	AP	no	1	1/R1

. The filter outputs were derived from v_out1 for VM and i_out for TAM. The transfer functions for the VM and TAM of the two-input two-output first-order multi-function filter can be expressed as follows:

$$\mathrm{VM};\hspace{1em}\hspace{1em}\hspace{1em}{v}_{out1}={\displaystyle \frac{s{C}_1{v}_2+g_m{v}_1}{s{C}_1+g_m}},$$

(3)

and

$$\mathrm{TAM};\hspace{1em}\hspace{1em}\hspace{1em}{i}_{out}=\left({\displaystyle \frac{1}{R_1}}\right)\left[{\displaystyle \frac{s{C}_1{v}_2+g_m{v}_1}{s{C}_1+g_m}}\right].$$

(4)

Therefore, the corresponding pole frequency (ω_p) of the realized filter in Figure 3 can be given by:

$${\omega }_p=2\pi f_p={\displaystyle \frac{g_m}{C_1}}.$$

(5)

Further examination of Equations (3) and (4) indicates that all three standard first-order filters, i.e., LP, HP, and AP, can be obtained in both VM and TAM with passband gains of unity and (1/R₁), respectively. Additionally, the relationship outlined in Equation (5) describes that the frequency ω_p of the proposed filter is electronically controllable through the transconductance gain (g_m) of the VDCC. In both realizations, there was no need for matching circuit components.

2.2. CM and TIM First-Order Universal Filters

The proposed mixed-mode first-order universal filter circuit in Figure 3 can also be operated in CM and TIM by setting v₁ = v₂ = 0 (ground potential connected). The CM filter output is taken from the i_out terminal, whereas the output for the TIM filter is obtained from the v_out2 terminal. The signal currents i₁, i₂, and i₃ are injected into the filter as specified in

Table 2. Current signal excitation for CM and TIM filter realizations.

Mode	Applied Signal Current			Filter Type	Matching Condition	Passband Gain
	i1	i2	i3
CM	iin (input current)	0	0	LP	gmR1 = 1	1
	−iin	iin	0	HP
	−iin/2	iin	0	AP
TIM	iin	0	0	LP	gmR1 = 1	R2
	iin	0	iin	HP
	−iin/2	0	iin	AP

. Consequently, this configuration produces two distinct output responses for the CM and TIM, respectively:

$$\mathrm{CM};\hspace{1em}\hspace{1em}\hspace{1em}{i}_{out}={\displaystyle \frac{\left(s{C}_1+g_m\right)i_2+g_m{i}_1}{s{C}_1+g_m}},$$

(6)

and

$$\mathrm{TIM};\hspace{1em}\hspace{1em}\hspace{1em}{v}_{out2}=R_2\left[{\displaystyle \frac{\left(s{C}_1+g_m\right)i_3-g_m{i}_1}{s{C}_1+g_m}}\right].$$

(7)

Table 2 demonstrates that the proposed circuit achieved the CM filter functions with a passband gain of unity. In contrast, the TIM filter functions for LP, HP, and AP first-order responses exhibited a passband gain of R₂. For both operational modes, it was necessary to keep a simple component matching constraint of g_mR₁ = 1.

2.3. Non-Ideal Gain Effects

In case of the non-ideal behavior, the characteristic equation of the VDCC was modified as follows:

$$\left[\begin{array}{c}{i}_p\\ i_n\\ i_z\\ v_x\\ i_{wp}\\ i_{wn}\end{array}\right]=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ \alpha g_m& -\alpha g_m& 0& 0\\ 0& 0& \beta & 0\\ 0& 0& 0& {\gamma }_p\\ 0& 0& 0& -{\gamma }_n\end{array}\right]\left[\begin{array}{c}{v}_p\\ v_n\\ v_z\\ i_x\end{array}\right],$$

(8)

where α represents the non-ideal transconductance gain, β denotes the non-ideal transfer voltage gain, and γ_p and γ_n indicate the non-ideal transfer current gains of the VDCC. Ideally, these transfer gains are all equal to unity (α = β = γ_p = γ_n = 1). Thus, when analyzing the filter transfer functions with these non-ideal gains taken into consideration, the output voltages and currents of the proposed circuit depicted in Figure 3 would be altered in each mode to:

$$\mathrm{VM};\hspace{1em}\hspace{1em}\hspace{1em}{v}_{out1}=\beta \left({\displaystyle \frac{s{C}_1{v}_2+\alpha g_m{v}_1}{s{C}_1+\alpha g_m}}\right),$$

(9)

$$\mathrm{TAM};\hspace{1em}\hspace{1em}\hspace{1em}{i}_{out}=\left({\displaystyle \frac{\beta {\gamma }_p}{R_1}}\right)\left[{\displaystyle \frac{s{C}_1{v}_2+\alpha g_m{v}_1}{s{C}_1+\alpha g_m}}\right],$$

(10)

$$\mathrm{CM};\hspace{1em}\hspace{1em}\hspace{1em}{i}_{out}={\displaystyle \frac{\left(s{C}_1+\alpha g_m\right)i_2+\left(\beta {\gamma }_p{g}_m\right)i_1}{s{C}_1+\alpha g_m}},$$

(11)

and

$$\mathrm{TIM};\hspace{1em}\hspace{1em}\hspace{1em}{v}_{out2}=R_2\left[{\displaystyle \frac{\left(s{C}_1+\alpha g_m\right)i_3-\left(\beta {\gamma }_n{g}_m\right)i_1}{s{C}_1+\alpha g_m}}\right].$$

(12)

Equations (9)–(12) indicate that the non-ideal transfer gains of the VDCC directly influence the derived transfer functions of the proposed circuit. Consequently, the non-ideal dependencies for each filter mode can be summarized in

Table 3. Non-ideal parameters of the proposed mixed-mode first-order universal filter in Figure 3.

Operational Mode	Filter Type	Transfer Function	Matching Condition	Passband Gain
VM	LP	${\displaystyle \frac{v_{out1}}{v_{in}}}={\displaystyle \frac{\beta \left(\alpha g_m\right)}{D_n(s)}}$	no	β
	HP	${\displaystyle \frac{v_{out1}}{v_{in}}}={\displaystyle \frac{\beta \left(s{C}_1\right)}{D_n(s)}}$
	AP	${\displaystyle \frac{v_{out1}}{v_{in}}}={\displaystyle \frac{\beta \left(s{C}_1-\alpha g_m\right)}{D_n(s)}}$
TAM	LP	${\displaystyle \frac{i_{out}}{v_{in}}}=\left({\displaystyle \frac{\beta {\gamma }_p}{R_1}}\right)\left[{\displaystyle \frac{\alpha g_m}{D_n(s)}}\right]$	no	${\displaystyle \frac{\beta {\gamma }_p}{R_1}}$
	HP	${\displaystyle \frac{i_{out}}{v_{in}}}=\left({\displaystyle \frac{\beta {\gamma }_p}{R_1}}\right)\left[{\displaystyle \frac{s{C}_1}{D_n(s)}}\right]$
	AP	${\displaystyle \frac{i_{out}}{v_{in}}}=\left({\displaystyle \frac{\beta {\gamma }_p}{R_1}}\right)\left[{\displaystyle \frac{s{C}_1-\alpha g_m}{D_n(s)}}\right]$
CM	LP	${\displaystyle \frac{i_{out}}{i_{in}}}={\displaystyle \frac{\beta {\gamma }_p{g}_m}{D_n(s)}}$	gmR1 = 1, α = βγp	1
	HP	${\displaystyle \frac{i_{out}}{i_{in}}}={\displaystyle \frac{s{C}_1}{D_n(s)}}$
	AP	${\displaystyle \frac{i_{out}}{i_{in}}}={\displaystyle \frac{s{C}_1-\alpha g_m}{D_n(s)}}$
TIM	LP	${\displaystyle \frac{v_{out2}}{i_{in}}}=-R_2\left[{\displaystyle \frac{\beta {\gamma }_n{g}_m}{D_n(s)}}\right]$	gmR1 = 1, α = βγn	R2
	HP	${\displaystyle \frac{v_{out2}}{i_{in}}}=R_2\left[{\displaystyle \frac{s{C}_1}{D_n(s)}}\right]$
	AP	${\displaystyle \frac{v_{out2}}{i_{in}}}=R_2\left[{\displaystyle \frac{s{C}_1-\alpha g_m}{D_n(s)}}\right]$

Note: $D_n\left(s\right)=s{C}_1+\alpha g_m$.

. As described in the four transfer functions, the modified pole frequency of the universal filter affected by the non-ideal gains can be expressed as:

$${{\omega }^{\prime }}_p=2\pi {f^{\prime }}_p={\displaystyle \frac{\alpha g_m}{C_1}}.$$

(13)

It can be concluded that the pole frequency of the filter shows a slight deviation from the theoretical value derived from the non-ideal parameter α. Also note that this deviation can be mitigated and adjusted through the pre-distortion value of g_m.

2.4. Parasitic Element Effects

Next, the proposed mixed-mode first-order universal filter shown in Figure 3 was analyzed in terms of the effects of VDCC terminal parasitics. In the CMOS VDCC structure in Figure 2, a low-value parasitic resistance (R_x) was connected in series with the x terminal, while a high-value parasitic resistance (R_wp) and a low-value parasitic capacitance (C_wp) were arranged in parallel between the w_p terminal and the ground [28]. Additionally, high-value resistance (R_wn) and low-value capacitance (C_wn) were also configured in parallel between the w_n terminal and the ground. Furthermore, a grounded high-value parasitic resistance (R_z) was located at the z terminal. Figure 4 presents the proposed filter configuration, which accounts for VDCC terminal parasitics.

Considering the effect of the VDCC parasitic impedance on the proposed mixed-mode first-order filter shown in Figure 4, the expression of the non-ideal pole frequency (ω″_p) in this case was determined as:

$${{\omega }^{″}}_p=2\pi {f^{″}}_p={\displaystyle \frac{g_m+\frac{1}{R_z}}{C_1}}.$$

(14)

Moreover, the impact of the low-serial parasitic resistance R_x can be absorbed with the external resistor R₁. Additionally, at the terminal w_n, the resistor R₂ was connected in parallel with a high-value parasitic resistance R_wn. As a result, the merging of R_wn with R₂ eliminated its influence. Therefore, we could significantly reduce the influence of parasitic elements by adhering to the following component selections:

$$\min \left\{g_m\right\}>>{\displaystyle \frac{1}{R_z}},$$

(15)

min {R₁} >> parasitic resistance R_x,

(16)

and

max {R₂} << parasitic resistance R_wn.

(17)

The presence of these parasitics has also introduced two undesirable dominant poles that limited the effective frequency range of the filter. The non-ideal pole frequencies of the proposed mixed-mode first-order universal filter circuit in Figure 3 have been evaluated and are described as follows:

$${\omega }_1={\displaystyle \frac{1}{R_z{C}_1}},$$

(18)

and

$${\omega }_2={\displaystyle \frac{1}{\left(R_2//R_{wn}\right)C_{wn}}}.$$

(19)

To achieve the proper frequency operation, the filter circuit should function at a frequency that is greater than ω₁ and less than ω₂. Therefore, the useful frequency region for the suggested filter circuit in Figure 3 was defined as follows:

$$\max \left\{{\omega }_1\right\}<<\omega <<\min \left\{{\omega }_2\right\}.$$

(20)

3. Performance Verification

In this section, the proposed circuit in Figure 3 was subjected to performance verification through simulation using the PSPICE program, which employed 0.13-μm IBM model parameters. The simulation included the CMOS VDCC shown in Figure 2 with the transistor aspect ratios specified in

Table 4. Transistor aspect ratios of the CMOS VDCC in Figure 2.

Transistor	W/L (μm/(μm)
M1, M2, M9, M10	0.35/0.13
M3–M6, M11–M17	5/0.13
M7, M8	3/0.13
M18-M22	1/0.13

. The symmetrical supply voltages, +V and −V, used for biasing the VDCC were set to ±0.5 V.

The expected and simulated results are shown in Figure 5, Figure 6, Figure 7 and Figure 8. The proposed filter was designed for a pole frequency of f_p = 987 kHz using the following components: g_m = 124 μA/V (I_B = 10 μA), R₁ = 8 kΩ, R₂ = 1 kΩ, and C₁ = 20 pF. Figure 5 illustrates the transient and frequency responses of the proposed VM filter, including LP, HP, and AP responses, whereas Figure 6 depicts the frequency response for the proposed TAM filter. The slight deviation from the exact unity gain observed in Figure 5c is mainly attributed to the non-ideal characteristics of the VDCC, including finite transconductance accuracy, non-unity voltage and current transfer gains, and the influence of parasitic elements inherent in the CMOS implementation. These effects were explicitly analyzed in Section 2.3 and Section 2.4. Importantly, the all-pass phase response, which was the primary functional objective of the AP filter, remained in close agreement with theoretical expectations. For transient response analysis, a sinusoidal signal with a peak voltage of 50 mV at 987 kHz was applied to the filter. In contrast, Figure 7 and Figure 8 present the proposed filter responses in cases of the CM and TIM, respectively. The close alignment between simulation results and theoretical predictions validated the practical performance of the circuit. As measured in simulation, the proposed circuit showed a maximum power consumption of 0.25 mW when the bias current was set to I_A = I_B = 10 μA.

To evaluate the linearity performance of the proposed VDCC-based VM filter, a total harmonic distortion (THD) analysis was carried out. Time-domain simulations were performed using a sinusoidal input signal at the pole frequency with various input voltage amplitudes. The THD values were extracted and provided in

Table 5. THD versus input signal amplitude for the proposed VM LP filter at f = f_p.

Input Amplitude (mVp-p)	THD (%)
20	0.32
40	0.67
60	1.01
80	1.60
100	1.92

. For a peak-to-peak input amplitude of 20 mV, the simulated THD was found to be approximately 0.32%, indicating a highly linear operation. When the input amplitude was increased to 60 mV (p-p), the THD increased slightly to 1.10%, while for 100 mV(p-p) it reached 1.92%. These results demonstrated that the proposed filter maintained good linearity over a practical input signal range.

The proposed AP filter in VM depicted in Figure 3 was also simulated for various transconductance values of g_m = 124 μA/V, 196 μA/V, and 304 μA/V (I_B = 10 μA, 25 μA, and 60 μA), which ideally correspond to pole frequency values of f_p = 987 kHz, 1.56 MHz, and 2.42 MHz, respectively. The resultant phase responses are shown in Figure 9, with the simulated f_p values recorded at 1.03 MHz, 1.68 MHz, and 2.51 MHz. These values reflected relative deviations of 4.26%, 7.75%, and 3.97%, respectively, in comparison to the theoretical values.

To evaluate the performance of the proposed circuit in relation to process variations, a Monte Carlo (MC) statistical analysis was conducted with 200 simulation runs, focusing on the 5% deviation in values of g_m, R₁, R₂, and C₁. The histogram resulting from the MC simulation for the VM LP gain response is presented in Figure 10, while the histogram for the VM HP gain response is illustrated in Figure 11. The findings of the MC analysis indicated the robustness of the proposed configuration in the presence of mismatches.

A further investigation was conducted into the influences of temperature variations on filter performance. In order to achieve this, a simulation of the suggested filter was performed using ambient temperature fluctuations varying from 0 °C to 100 °C in increments of 25 °C. Figure 12 shows the variations in the gain response for both LP and HP filters during the VM operation. According to the findings, the passband gain for the LP filter varied from 0.902 dBV to 0.893 dBV at varying temperatures, while for the HP filter, it spanned from 0.181 dBV to 0.228 dBV.

4. Dual-Mode Sinusoidal Oscillator Realization Using the Proposed Mixed-Mode First-Order Universal Filter

Figure 13 presents a simple circuit realization of the dual-mode sinusoidal oscillator, which simultaneously generates both a voltage output (v_osc) and a current output (i_osc). This configuration comprises the cascade connection of two identical mixed-mode first-order universal filters, as shown in Figure 3. The characteristic equation can be expressed in the following form:

$$s^2+\left({\displaystyle \frac{g_{m1}}{C_1}}-{\displaystyle \frac{g_{m2}}{C_2}}\right)s+\left({\displaystyle \frac{g_{m1}{g}_{m2}}{C_1{C}_2}}\right)=0.$$

(21)

In this context, g_mi (where i = 1, 2) denotes the transconductance parameter g_m associated with the i-th VDCC. As evident from (21), the conditions for oscillation (CO) and the frequency of oscillation (FO) are derived from the dual-mode second-order oscillator as follows:

$$\mathrm{CO}:\hspace{1em}\hspace{1em}\hspace{1em}{g}_{m1}{C}_2=g_{m2}{C}_1,$$

(22)

and

$$\mathrm{FO}:\hspace{1em}\hspace{1em}\hspace{1em}{\omega }_{osc}=2\pi f_{osc}=\sqrt{{\displaystyle \frac{g_{m1}{g}_{m2}}{C_1{C}_2}}}$$

(23)

The presented oscillator circuit in Figure 13 was tested through simulation with the following parameters: g_m1 = g_m2 = 316 μA/V (I_B1 = I_B2 = 65 μA), R₁ = 3.16 kΩ, R₂ = 1 kΩ, and C₁ = C₂ = 1 nF. For this configuration, the ideal value of f_osc was determined to be 50.29 kHz. The simulated time-domain responses of output voltage and current waveforms, designated as v_osc and i_osc, together with the spectral analysis are shown in Figure 14 and Figure 15, respectively. The observed frequencies (FOs) for both v_osc and i_osc were found to be 47.85 kHz in this particular case. The total harmonic distortion (THD) values of oscillated signals were recorded at only 5.20%.

5. Applications in Bio-Signal Processing Systems

Some applications of the proposed mixed-mode first-order universal filter in Figure 3 were further explored in bio-signal processing systems. The circuit was employed as an essential section in both the ECG acquisition system and the BioZ analyzer circuit. These applications demonstrated the practicality of the proposed circuit, which exhibited signal clarity and accuracy in biomedical diagnostics. Detailed descriptions of the circuits were provided as follows.

5.1. Application in the ECG Acquisition System

Electrocardiogram (ECG) signals play a crucial role in biomedical engineering for diagnosing and monitoring various heart conditions. Figure 16 shows an analog front-end block diagram for the acquisition and processing of ECG signals. The ECG system comprises a pre-amplifier, an LP filter, a post-amplifier, and an analog-to-digital converter (ADC). To filter out unwanted signals from the ECG, the proposed VM LP filter from Figure 3 was implemented as a filtering stage. This filter employed R₁ = 8 kΩ, R₂ = 1 kΩ, C₁ = 100 nF, and g_m = 152 μA/V (I_B = 15 μA). The resulting pole frequency was obtained at f_p = 242 Hz, with the output-referred noise of approximately 20.20 nV/(√Hz) in the 0.01–100 Hz range, as shown in Figure 17. This indicated a low internal noise contribution from the circuit.

In practical ECG acquisition systems, low-noise instrumentation amplifiers are typically employed for initial signal amplification, followed by band-limiting filters to reduce noise. This work proposes a mixed-mode universal filter designed for the signal conditioning stage. Furthermore, the voltage gain of the proposed filter can be adjusted by passive component ratios and electronically controlled transconductance parameters if additional amplification is required.

To evaluate the proposed LP filter for ECG signal processing, an ECG input signal (shown in the channel A of Figure 18) was intentionally combined with a 0.2 mV noise signal at 300 Hz to simulate electrical interference common in real ECG recordings, e.g., from power lines or muscle artifacts. The resulting noisy signal, shown in channel B, was subsequently processed through the proposed LP filter. The filtered output, which represents the clean ECG waveform, is shown in the channel C of Figure 18. Figure 19 also illustrates a wave comparison of the ECG input signal and the filtered output signal from Figure 18. It is clear that the filtered ECG closely reproduced the morphology of the clean input, with noticeable suppression of the 300 Hz interference.

Additionally, the results of filtering ECG signal were compared to those of the normal ECG signal in terms of wave amplitude [30] and timing characteristics [31], as summarized in

Table 6. Wave amplitude of ECG signals.

Wave Type	ECG Input Signal (Channel A in Figure 18) (mV)	Filtered Output Signal (Channel C in Figure 18) (mV)	Normal ECG Signal [30] (mV)
P-wave	0.249	0.245	0.250
R-wave	1.626	1.532	1.600
Q-wave	−0.315	−0.305	25% of R-wave
T-wave	0.370	0.366	0.1–0.5

and

Table 7. Timing values of ECG signals.

Wave Type	ECG Input Signal (Channel A in Figure 18) (s)	Filtered Output Signal (Channel C in Figure 18) (s)	Normal ECG Signal [31] (s)
PR-wave	0.200	0.200	0.12–0.20
QRS-wave	0.251	0.251	>0.10
ST-wave	0.133	0.133	0.05–0.15

, respectively. The results showed that the proposed filter effectively suppressed high-frequency noise (300 Hz) while preserving key ECG waveform features, such as the P-QRS-T complex. The minimal amplitude attenuation (<6% difference for R-wave) and identical timing values suggested that the filter maintained signal fidelity and did not introduce phase distortion. Therefore, the proposed circuit effectively enhanced the signal-to-noise ratio and diagnostic reliability of ECG measurements.

5.2. Application in the Bioimpedance Measurement System

The bioimpedance (BioZ) measurement is extensively used to evaluate characteristics of biological tissues, particularly for distinguishing between intra- and extracellular fluid compositions. Figure 20 shows the block diagram of the general BioZ measurement system, which employs a four-electrode configuration to minimize the influence of electrode-tissue impedance (ETI). In this approach, an alternating stimulus current (i_inject) was driven through a pair of outer electrodes, while the resulting voltage across tissue impedance (v_measure) was sensed through the inner electrode pair using a high-gain instrumentation amplifier (IA). To generate the sinusoidal excitation current, the proposed mixed-mode first-order universal filter was configured as a CM sinusoidal oscillator, as described in Section 4. The oscillator was designed to operate at an oscillation frequency of f_osc ≅ 251 kHz, which lies within the frequency range typically used in impedance spectroscopy, where the capacitive behavior of cell membranes becomes significant. The design parameters for the oscillator circuit were selected as: g_m1 = g_m2 = 316 μA/V (I_B1 = I_B2 = 65 μA), R₁ = 3.16 kΩ, R₂ = 1 kΩ, and C₁ = C₂ = 0.2 nF.

The electrical model of biological tissue employed for verification is shown in Figure 21, consisting of extracellular fluid resistance (R_e), intracellular fluid resistance (R_i), and cell membrane capacitance (C_m) [32,33]. For validation testing, the tissue model parameters were set to R_e = R_i = 100 Ω and C_m = 220 nF, consistent with established tissue-equivalent models [34]. A generated sinusoidal current (i_osc) from the oscillator was injected into this model, while the IA measured the voltage v_measure developed across the tissue impedance.

Figure 22 presents the transient responses of i_inject, v_measure, and the extracted BioZ magnitude (Z_BioZ). The injected current (i_inject = i_osc) exhibited a clean sinusoidal waveform with stable amplitude, indicating that the oscillator provided a stable and distortion-free excitation source. The voltage v_measure was properly synchronized with i_inject and maintained as an amplitude consistent with the expected Z_BioZ. At 251 kHz, the capacitive reactance of C_m is X_C = (1/2πfC_m) ≅ 2.88 Ω, which is much smaller than R_e and R_i (each 100 Ω). Therefore, the total impedance is dominated by the resistive path, giving Z_BioZ = R_e//R_i ≅ 50 Ω, which closely matches with the obtained value in Figure 22. These findings validated that the proposed mixed-mode first-order universal filter, when performed as a CM sinusoidal oscillator, enables an effective, compact, and low-power solution for BioZ measurement. The system provided stable AC excitation, accurate voltage sensing, and reliable impedance extraction, highlighting its suitability for portable or wearable biomedical sensing platforms.

5.3. Practical Implementation Considerations in Bio-Signal Processing Applications

In practical bio-signal processing applications, component tolerances, process variations, and temperature dependence may lead to slight deviations in the pole frequency and gain of the proposed VDCC-based mixed-mode universal filter. However, since the pole frequency can be electronically tuned through the VDCC transconductance, these variations can be effectively compensated by adjusting the bias current. This capability is particularly beneficial in integrated implementations. Simulation results under varying temperature conditions indicate only minor fluctuations in gain, suggesting that the system demonstrates adequate robustness for ECG and BioZ applications.

In ECG acquisition systems, non-ideal factors such as variations in electrode skin impedance, motion artifacts, and external interference can adversely affect signal quality. The proposed VM LP filter, characterized by high input impedance and a tunable pole frequency, effectively suppresses high-frequency noise while preserving essential ECG waveform features. In BioZ measurement systems, the stability of the excitation signal and parasitic effects of the active devices can influence measurement accuracy, especially at high frequencies. Nevertheless, the low distortion and parasitic-aware design presented in this work ensure reliable sinusoidal excitation and precise impedance extraction within the typical biomedical frequency range.

In conclusion, despite inherent non-idealities in real biomedical environments, the proposed filter topology offers sufficient tunability, robustness, and compactness to serve as an effective analog front-end building block for ECG acquisition and BioZ measurement systems.

6. Conclusions

This work presented a compact mixed-mode first-order universal filter based on a single VDCC and employing only two grounded resistors and one floating capacitor. Owing to its simple structure and electronically tunable pole frequency, the proposed scheme supports four operation modes—VM, TAM, CM, and TIM—without the need for additional active components. Theoretical derivations, non-ideal analysis, and PSPICE simulation results verify that the filter achieves high accuracy and stable frequency characteristics and that it is well-suited for low-voltage, low-power analog signal processing systems. To demonstrate its practical utility, the proposed filter was applied to two biomedical signal-processing tasks. The VM low-pass response was used to implement an ECG acquisition filter capable of effective noise suppression and waveform preservation. In addition, the filter-based CM oscillator configuration was utilized as a sinusoidal excitation source in a bioimpedance (BioZ) measurement system, resulting in stable current generation and precise impedance extraction from tissue-equivalent models. These application results verified that the proposed topology provides reliable performance across different operation modes, all while maintaining compactness and low power consumption. The fabrication and experimental characterization of the proposed circuit will be considered in future work.