A Novel Low-Power Mixed-Mode Universal Filter Design Using Multiple-Input Operational Transconductance Amplifiers

Abstract

This study introduces an innovative mixed-mode universal biquad filter implemented using multiple-input operational transconductance amplifiers (MI-OTAs). Based on the advantage of OTAs, which possess multiple inputs, the proposed mixed-mode universal filter using MI-OTAs can implement both non-inverting and inverting standard filtering functions such as low-pass, high-pass, band-pass, band-stop, and all-pass filters in voltage-mode, transadmittance-mode, current-mode, and transimpedance-mode, which is the maximum capability of mixed-mode universal filters. The natural frequency of all filtering functions can be electronically controlled. Based on the multiple-input bulk-driven MOS transistor (MOST) technique, the OTA can also operate at very low supply voltage and provide wide-input voltage swing. The technique of MOST, operating in the weak inversion region, is used to achieve the low-power consumption of OTA. The MI-OTA circuit and mixed-mode universal filter were designed and simulated using Cadence Virtuoso, utilizing TSMC’s 65-nm CMOS technology. At a 0.5 V supply voltage, the filter demonstrated a simulated power consumption of 450 nW at a natural frequency of 156 Hz. In these ranges of power consumption and natural frequency, it can be expected that the proposed filter can be built as an versatile integrated circuit for low-frequency applications such as bio-signal processing. The design parameters were successfully validated through both post-layout extractions and discrete hardware prototyping utilizing commercially available LM13700N ICs.

1. Introduction

Universal filters are defined by their capacity to provide five distinct frequency responses—namely low-pass (LPF), high-pass (HPF), band-pass (BPF), band-stop (BSF), and all-pass (APF)—out of a solitary network. Concurrently, mixed-mode analog configurations are highly valued for their ability to navigate voltage-mode (VM), current-mode (CM), transadmittance-mode (TAM), and transimpedance-mode (TIM) operating domains within a single architectural layout. A circuit configuration maps to a VM filter when its foundational transfer functions track voltage ratios, whereas a CM filter evaluates current ratios. In a similar manner, TAM blocks bridge driving voltages to output currents, while TIM topologies convert driving currents into output voltages. By functioning across these multi-regime spaces, these filters serve as highly efficient, direct interfaces between distinct voltage- and current-driven subsystems, entirely removing the need for auxiliary I-V or V-I converter blocks [1]. Consequently, a comprehensively versatile mixed-mode universal filter must theoretically deliver a collection of 20 unique transfer functions.

There are many mixed-mode universal filters available in the literature; for example, see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]. These mixed-mode universal filters are implemented based on different active devices such as current conveyors [1,2,3,4,5,6,7,8,9,10,11,12], the Operational Transconductance Amplifier (OTA) [13,14,15,16,17,18,19], Voltage Differencing Transconductance Amplifier (VDTA) [20,21], Voltage Differencing Buffered Amplifier (VDBA) [22,23], Current Conveyor Transconductance Amplifier (CCTA) [24,25,26,27,28,29], Voltage Differencing Gain Amplifier (VDGA) [30,31], Differential Transconductance Amplifier (DDTA) [32,33], Differential Difference Current Conveyor Transconductance Amplifier (DDCCTA) [34], and Multiple-Input Multiple-Output Operational Transconductance Amplifier (MI-OTA) [35,36]. Several reported filters employ a minimum number of active elements; however, some of these mixed-mode universal filters suffer from the following drawbacks:

• lack of electronic tunability [1,2,3,4,5];
• applying the input signal for VM via the capacitor or resistor [3,4,5,6,7,8,13,20,22,23,26,27,28,29,30];
• employment of floating passive components [2,3,5,6,7,8,20,22,23,26,27,28,29,30];
• suffer from active or passive component matching condition [1,2,3,5,6,7,8,9,10,13,14,16,17,18,19,24,25,26,27,28,29,30];
• suffer from input signal matching condition or require minus-type input signal [1,2,3,4,5,8,13,16,17,18,22,25,30];
• supplying the output current via the capacitor or resistor [22,30,31].

None of the mixed-mode universal filters reported in [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31] can provide both non-inverting and inverting transfer functions in VM, CM, TAM, and TIM modes for LPF, HPF, BPF, BSF, and APF responses within a single topology.

The mixed-mode universal filters reported in [32,33,34,35,36] can provide various transfer functions in VM, CM, TIM, and TAM modes corresponding to LPF, HPF, BPF, BSF, and APF responses. However, input matching conditions are required for realizing some filtering functions such as CM and TIM operations. The need for multiple input signals necessitates additional active elements.

Therefore, a novel mixed-mode universal filter that enriches the filtering functions is proposed in this paper. The enrichment of many filtering functions is possible using multiple-input operational transconductance amplifiers (MI-OTA-based filter). Both non-inverting and inverting standard filtering functions such as low-pass, high-pass, band-pass, band-stop, and all-pass filters of voltage-mode, transadmittance-mode, current-mode, and transimpedance-mode converge into a single topology. The natural frequency of all filtering functions can be electronically controlled. The technique of MOST operating in the weak inversion region is used to achieve the low-power consumption of OTA. The multiple input of OTA can be obtained using the multiple-input bulk-driven MOS transistor (MOST) technique. Based on this technique, the OTA can also operate at a very low supply voltage and provide wide-input voltage swing. The MI-OTA circuit and mixed-mode universal filter were designed and simulated using Cadence Virtuoso, utilizing TSMC’s 65-nm (1P9M) CMOS technology.

The proposed filter is designed to operate at a natural frequency of 156 Hz, which is suitable for low-frequency applications such as bio-signal processing. At a natural frequency of 156 Hz and a supply voltage of 0.5 V, the filter demonstrated a simulated power consumption of 450 nW. Post-layout simulations confirmed the expected performance, and experimental validation was carried out using discrete-component MI-OTA-based circuits built with LM13700N, confirming the filter’s correct operation.

2. Proposed Circuit

This section consists of two subsections: the proposed multiple-input operational transconductance amplifier (MI-OTA) and the proposed mixed-mode universal filter.

2.1. Multiple-Input Operational Transconductance Amplifier

Figure 1a shows the electrical symbol of the proposed multiple-input MI-OTA with three inputs. In an ideal case, its current–voltage relationship can be expressed as follows:

$$I_o=g_m\left(V_{1+}+V_{2+}+V_{3+}-V_{1-}-V_{2-}-V_{3-}\right),$$

(1)

where $I_o$ represents the output current, $g_m$ denotes the transconductance, and $V_{+}$ and $V_{-}$ refer to the non-inverting and inverting input voltages, respectively. As indicated by Equation (1), the output current is directly proportional to the differential sum of the input voltages applied to the OTA terminals.

Figure 1b presents the conventional method for implementing a multiple-input OTA, which involves using several transconductors with their outputs connected together. This approach leads to an increased chip area, higher power consumption, and greater design complexity. In contrast, the proposed MI-OTA uses a single core OTA, with multiple inputs realized through passive components, as will be described later.

Figure 2 presents the CMOS implementation of the proposed MI-OTA, optimized for the target application. The corresponding layout with a total silicon area of 148 μm × 89 μm is presented in Figure 3. The circuit utilizes a current mirror OTA architecture, incorporating input-stage linearization (transistors M₁, M₂, M₁₁, M₁₂) as reported in [37]. This linearization strategy has been adapted for use with bulk-driven (BD) MOS transistors operating in the subthreshold regime, enabling efficient operation under a low supply voltage and ultra-low power conditions.

Transistors M₁₁ and M₁₂, biased in the triode region, form part of a linearized differential input pair in conjunction with M₁ and M₂. This input stage is current biased via sources M_7/7c and M_8/8c. The remaining transistors—specifically M_3/3c through M_10/10c, and M_13/13c—are configured in self-cascode (SC) structures to enhance the output resistance, thereby improving the overall voltage gain of the OTA.

Multiple-input capability is realized through capacitive voltage division at the input nodes, using coupling capacitors denoted as C_B. This technique introduces no additional static power consumption [38,39]. To ensure proper DC biasing, each input path includes a high-resistance element implemented using MOS transistors (M_R) biased in the cutoff region, with their gate and source terminals shorted (i.e., $V_{GS}=$ 0).

Although similar OTA topologies have previously been demonstrated using 0.18 µm CMOS technology [39], the proposed design is implemented in a 65 nm CMOS process, leveraging its advanced device scaling capabilities. In particular, the self-cascode structures utilize different transistor flavors offered by the used technology, namely, low-threshold voltage (LVT) transistors ($V_{TH}=$ +266 mV/−268 mV) as the upper cascode devices, while standard-threshold transistors ($V_{TH}=$ +410 mV/−406 mV) serve as the lower (main) transistors [40]. This configuration ensures that the lower devices in each SC pair operate with a drain-source voltage ($V_{DS}$) of approximately 100 mV, placing them near the edge of saturation, thereby approximating classical cascode behavior.

This technique mitigates the inherently low intrinsic gain of bulk-driven MOS transistors in the 65 nm technology node, an issue further exacerbated by the use of capacitive input division. By carefully biasing the SC stages, the design compensates for gain limitations while maintaining low-voltage operation.

The large-signal quasi-static current–voltage (I–V) characteristic of a single differential input pair ($V_{i+}$, $V_{i-}$, for $i$ = 1, 2, 3), with all other inputs grounded, can be expressed as [39]:

$$I_{out}={2I}_{set}tanh\left(\beta \eta {\displaystyle \frac{V_{i+}-V_{i-}}{2n_p{U}_T}}-{tanh}^{-1}\left\{{\displaystyle \frac{1}{4m+1}}tanh\left(\beta \eta {\displaystyle \frac{V_{i+}-V_{i-}}{2n_p{U}_T}}\right)\right\}\right)$$

(2)

where $n_p$ is the subthreshold slope factor for PMOS transistor,$\eta =\left(n_p-1\right)$ is the bulk to gate transconductance ratio for the transistors M₁ and M₂ at operating point, $U_T$ is the thermal potential, $m$ = (W₁₁/L₁₂)/(W₁/L₁) and $\beta$ is the voltage gain of the input capacitive divider. For optimal linearity, the coefficient $m$ should be set to 0.5, which corresponds to the optimal value for a gate-driven counterpart of this circuit [39]. The coefficient $\beta$ is equal to 0.33 for three identical capacitors $C_B$, neglecting the impact of other parasitic capacitances.

Based on Equation (2), the small-signal transconductance of the MI-OTA is expressed as:

$$g_m=\beta \eta \left({\displaystyle \frac{4m}{4m+1}}\right){\displaystyle \frac{I_{set}}{n_p{U}_T}}$$

(3)

Substituting $\beta$ = 0.33 and $m$ = 0.5 yields:

$$g_m=0.22\eta {\displaystyle \frac{I_{set}}{n_p{U}_T}}$$

(4)

Thus, the small-signal transconductance $g_m$ is a linear function of the bias current $I_{set}$ and can be easily regulated. The low-frequency voltage gain is:

$$A_{VO}\cong g_m{r}_{out}$$

(5)

where the output resistance of the OTA $r_{out}$ can be approximated as:

$$r_{out}\cong \left(g_{m9}{r}_{ds9}{r}_{ds9c}\right)\left|\right|\left(g_{m6}{r}_{ds6}{r}_{ds6c}\right)$$

(6)

Notably, the self-cascode topology significantly enhances the output resistance and, consequently, the voltage gain, particularly when both transistors in each SC pair are biased near the edge of saturation. This helps to compensate for gain reduction caused by the input capacitive voltage divider. Although the capacitive divider also increases the input-referred noise, the input signal amplitude is scaled by the same factor, thereby preserving the dynamic range (DR). A key advantage of the proposed design is its ability to maintain a high DR while operating at very low supply voltages—enabled by techniques such as the multiple-input OTA architecture and bulk-driven transistor operation. A detailed analysis of the noise performance for this OTA topology is provided in [39].

2.2. Proposed Mixed-Mode Universal Filter

The mixed-mode universal filter employing MI-OTAs is illustrated in Figure 4. The circuit comprises seven transconductances, denoted as $g_{m1}$ to $g_{m7}$, and two grounded capacitors, $C_1$ and $C_2$. The transconductance $g_{m1}$ together with $C_2$ realizes the first integrator, while $g_{m2}$ in conjunction with $C_2$ implements the second integrator. The transconductances $g_{m3}$, $g_{m4}$, and $g_{m5}$ perform the adder/subtractor voltage operation with a unity gain. Thus, $g_{m3}$, $g_{m4}$, and $g_{m5}$ are out of the transfer functions. It can be observed that adder/subtractor voltage is readily achieved without the need for passive resistors, unlike operational amplifier-based circuits, and is efficiently realized using MI-OTA-based implementations. The transconductance $g_{m6}$ operates as both a voltage follower and a current-to-voltage converter, whereas $g_{m7}$ functions as a voltage-to-current converter. When $g_{m6}$ operates as a current-to-voltage converter, terminals $V_1$ and $V_2$ should be grounded.

•

Voltage-mode

The transconductance $g_{m6}$ operates as a voltage follower ($V_i=V_1-V_2$), whereas $g_{m7}$ remains unused. In addition, the inputs $I_1$ and $I_2$ are not applied. The variant filter responses can be expressed as follows:

$$V_{o1}={\displaystyle \frac{g_{m1}{g}_{m2}}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}\left(V_2-V_1\right)$$

(7)

$$V_{o2}={\displaystyle \frac{s^2{C}_1{C}_2}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}\left(V_1-V_2\right)$$

(8)

$$V_{o3}={\displaystyle \frac{s{C}_1{g}_{m2}}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}\left(V_1-V_2\right)$$

(9)

$$V_{o4}={\displaystyle \frac{s^2{C}_1{C}_2+g_{m1}{g}_{m2}}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}\left(V_1-V_2\right)$$

(10)

$$V_{o5}={\displaystyle \frac{s^2{C}_1{C}_2-s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}\left(V_1-V_2\right)$$

(11)

Both non-inverting and inverting VM transfer functions of LPF, HPF, BPF, BSF, and APF can be realized by appropriately applying the inputs $V_1$ and $V_2$.

•

Transimpedance-mode

The transconductance $g_{m6}$ operates as a current-to-voltage converter ($V_i=\left(I_1-I_2\right)/g_{m6}$), whereas $g_{m7}$ remains unused. In addition, the inputs $V_1$ and $V_2$ are grounded. The variant filter responses can be expressed as follows:

$$V_{o1}={\displaystyle \frac{1}{g_{m6}}}{\displaystyle \frac{g_{m1}{g}_{m2}}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}\left(I_2-I_1\right)$$

(12)

$$V_{o2}={\displaystyle \frac{1}{g_{m6}}}{\displaystyle \frac{s^2{C}_1{C}_2}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}\left(I_1-I_2\right)$$

(13)

$$V_{o3}={\displaystyle \frac{1}{g_{m6}}}{\displaystyle \frac{s{C}_1{g}_{m2}}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}\left(I_1-I_2\right)$$

(14)

$$V_{o4}={\displaystyle \frac{1}{g_{m6}}}{\displaystyle \frac{s^2{C}_1{C}_2+g_{m1}{g}_{m2}}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}\left(I_1-I_2\right)$$

(15)

$$V_{o5}={\displaystyle \frac{1}{g_{m6}}}{\displaystyle \frac{s^2{C}_1{C}_2-s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}\left(I_1-I_2\right)$$

(16)

Both non-inverting and inverting TIM transfer functions of LPF, HPF, BPF, BSF, and APF can be realized by appropriately applying the inputs $I_1$ and $I_2$. In this case, an inverting current input signal is required. However, this requirement involves only a single input signal without the need for dual inputs or input matching conditions, i.e., $I_{in}$= $-{2I}_1$.

•

Transadmittance-mode:

The transconductance $g_{m6}$ operates as a voltage follower ($V_i=V_1-V_2$), whereas $g_{m7}$ functions as a voltage-to-current converter. The inputs $I_1$ and $I_2$ are not applied. From Figure 4, the current $I_{CM}$ can be given as $I_{CM}=g_{m7}\left(V_{o5}+V_3+V_4-V_5\right)$. Substituting $V_{o5}$ from (11), the terminal $I_{CM}$ provides the output current, which can be expressed by

$$I_{CM}=g_{m7}\left({\displaystyle \frac{\left(s^2{C}_1{C}_2-s{C}_1{g}_{m2}+g_{m1}{g}_{m2}\right)\left(V_1-V_2\right)}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}+\left(V_3+V_4-V_5\right)\right)$$

(17)

The various filter responses can be expressed under the following conditions (Appendix A):

LPF: $V_3$ is connected to $V_{o3}$, $V_4$ is grounded, $V_5$ is connected $V_{o2}$.

$$I_{LPF}=I_{CM}=g_{m7}{\displaystyle \frac{g_{m1}{g}_{m2}\left(V_1-V_2\right)}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}$$

(18)

HPF: $V_3$ is connected to $V_{o3}$, $V_4$ is connected to $V_{o1}$, $V_5$ is grounded.

$$I_{HPF}=I_{CM}=g_{m7}{\displaystyle \frac{s^2{C}_1{C}_2\left(V_1-V_2\right)}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}$$

(19)

BPF: $V_3$ is connected to $V_{o1}$, $V_4$ is grounded, $V_5$ is connected to $V_{o2}$.

$$I_{BPF}=I_{CM}=g_{m7}{\displaystyle \frac{s{C}_1{g}_{m2}\left(V_2-V_1\right)}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}$$

(20)

BSF: $V_3$ is connected to $V_{o3}$, $V_4$ and $V_5$ are grounded.

$$I_{BSF}=I_{CM}=g_{m7}{\displaystyle \frac{\left(s^2{C}_1{C}_2+g_{m1}{g}_{m2}\right)\left(V_1-V_2\right)}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}$$

(21)

APF: $V_3$, $V_4$ and $V_5$ are grounded.

$$I_{APF}=I_{CM}=g_{m7}{\displaystyle \frac{\left(s^2{C}_1{C}_2-s{C}_1{g}_{m2}+g_{m1}{g}_{m2}\right)\left(V_1-V_2\right)}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}$$

(22)

Both non-inverting and inverting TIM functions of LPF, HPF, BPF, BSF, and APF can be realized by appropriately applying the inputs $V_1$ and $V_2$.

•

Current-mode

The transconductance $g_{m6}$ operates as a current-to-voltage converter ($V_i=\left(I_1-I_2\right)/g_{m6}$), whereas $g_{m7}$ functions as a voltage-to-current converter. The inputs $V_1$ and $V_2$ are grounded. The outputs of the current-mode filter can be expressed by

$$I_{CM}={\displaystyle \frac{g_{m7}}{g_{m6}}}\left({\displaystyle \frac{\left(s^2{C}_1{C}_2-s{C}_1{g}_{m2}+g_{m1}{g}_{m2}\right)\left(I_1-I_2\right)}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}+(V_3+V_4-V_5)\right)$$

(23)

The various filter responses can be expressed under the following conditions:

LPF: $V_3$ is connected to $V_{o3}$, $V_4$ is grounded, $V_5$ is connected $V_{o2}$.

$$I_{CM}=I_{LPF}={\displaystyle \frac{g_{m7}}{g_{m6}}}{\displaystyle \frac{g_{m1}{g}_{m2}\left(I_1-I_2\right)}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}$$

(24)

HPF: $V_3$ is connected to $V_{o3}$, $V_4$ is connected to $V_{o1}$, $V_5$ is grounded.

$$I_{CM}=I_{HPF}={\displaystyle \frac{g_{m7}}{g_{m6}}}{\displaystyle \frac{s^2{C}_1{C}_2\left(I_1-I_2\right)}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}$$

(25)

BPF: $V_3$ is connected to $V_{o1}$, $V_4$ is grounded, $V_5$ is connected to $V_{o2}$.

$$I_{CM}=I_{BPF}={\displaystyle \frac{g_{m7}}{g_{m6}}}{\displaystyle \frac{s{C}_1{g}_{m2}\left(I_2-I_1\right)}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}$$

(26)

BSF: $V_3$ is connected to $V_{o3}$, $V_4$ and $V_5$ are grounded.

$$I_{CM}=I_{BSF}={\displaystyle \frac{g_{m7}}{g_{m6}}}{\displaystyle \frac{\left(s^2{C}_1{C}_2+g_{m1}{g}_{m2}\right)\left(I_1-I_2\right)}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}$$

(27)

APF: $V_3$, $V_4$ and $V_5$ are grounded.

$$I_{CM}=I_{APF}={\displaystyle \frac{g_{m7}}{g_{m6}}}{\displaystyle \frac{\left(s^2{C}_1{C}_2-s{C}_1{g}_{m2}+g_{m1}{g}_{m2}\right)\left(I_1-I_2\right)}{s^2{C}_1{C}_2+s{C}_1{g}_{m2}+g_{m1}{g}_{m2}}}$$

(28)

Both non-inverting and inverting TAM responses of LPF, HPF, BPF, BSF, and APF can be realized by appropriately applying the input signals to $I_1$ and $I_2$.

The summary of forty transfer functions for VM, CM, TIM, and TAM corresponding to LPF, HPF, BPF, BSF, and APF responses is given in

Table 1. Obtaining variant filtering functions of mixed-mode universal filter.

Mode	Filtering Function		Input	Output	Condition
VM	LPF	Non-inverting	$V_2$	$V_{o1}$	$V_1$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
		Inverting	$V_1$	$V_{o1}$	$V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
	HPF	Non-inverting	$V_1$	$V_{o2}$	$V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
		Inverting	$V_2$	$V_{o2}$	$V_1$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
	BPF	Non-inverting	$V_1$	$V_{o3}$	$V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
		Inverting	$V_2$	$V_{o3}$	$V_1$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
	BSF	Non-inverting	$V_1$	$V_{o4}$	$V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
		Inverting	$V_2$	$V_{o4}$	$V_1$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
	APF	Non-inverting	$V_1$	$V_{o5}$	$V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
		Inverting	$V_2$	$V_{o5}$	$V_1$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
TIM	LPF	Non-inverting	$I_2$	$V_{o1}$	$V_1$ = $V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = 0
		Inverting	$I_1$	$V_{o1}$	$V_1$ = $V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_2$ = 0
	HPF	Non-inverting	$I_1$	$V_{o2}$	$V_1$ = $V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_2$ = 0
		Inverting	$I_2$	$V_{o2}$	$V_1$ = $V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = 0
	BPF	Non-inverting	$I_1$	$V_{o3}$	$V_1$ = $V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_2$ = 0
		Inverting	$I_2$	$V_{o3}$	$V_1$ = $V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = 0
	BSF	Non-inverting	$I_1$	$V_{o4}$	$V_1$ = $V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_2$ = 0
		Inverting	$I_2$	$V_{o4}$	$V_1$ = $V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = 0
	APF	Non-inverting	$I_1$	$V_{o5}$	$V_1$ = $V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_2$ = 0
		Inverting	$I_2$	$V_{o5}$	$V_1$ = $V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = 0
TAM	LPF	Non-inverting	$V_1$	$I_{CM}=I_{LPF\left(non\right)}$	$V_2$ = 0, $V_3$ = $V_{o3}$, $V_4$ = 0, $V_5$ = $V_{o2}$, $I_1$ = $I_2$ = 0
		Inverting	$V_2$	$I_{CM}=I_{LPF\left(in\right)}$	$V_1$ = 0, $V_3$ = $V_{o3}$, $V_4$ = 0, $V_5$ = $V_{o2}$, $I_1$ = $I_2$ = 0
	HPF	Non-inverting	$V_1$	$I_{CM}=I_{HPF\left(non\right)}$	$V_2$ = 0, $V_3$ = $V_{o3}$, $V_4$ = $V_{o1}$, $V_5$ = 0, $I_1$ = $I_2$ = 0
		Inverting	$V_2$	$I_{CM}=I_{HPF\left(in\right)}$	$V_1$ = 0, $V_3$ = $V_{o3}$, $V_4$ = $V_{o1}$, $V_5$ = 0, $I_1$ = $I_2$ = 0
	BPF	Non-inverting	$V_2$	$I_{CM}=I_{BPF\left(non\right)}$	$V_1$ = 0, $V_3$ = $V_{o1}$, $V_4$ = $0$, $V_5$ = $V_{o2}$, $I_1$ = $I_2$ = 0
		Inverting	$V_1$	$I_{CM}=I_{BPF\left(in\right)}$	$V_2$ = 0, $V_3$ = $V_{o1}$, $V_4$ = $0$, $V_5$ = $V_{o2}$, $I_1$ = $I_2$ = 0
	BSF	Non-inverting	$V_1$	$I_{CM}=I_{BSF\left(non\right)}$	$V_2$ = 0, $V_3$ = $V_{o3}$, $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
		Inverting	$V_2$	$I_{CM}=I_{BSF\left(in\right)}$	$V_1$ = 0, $V_3$ = $V_{o3}$, $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
	APF	Non-inverting	$V_1$	$I_{CM}=I_{APF\left(non\right)}$	$V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
		Inverting	$V_2$	$I_{CM}=I_{APF\left(in\right)}$	$V_1$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = $I_2$ = 0
CM	LPF	Non-inverting	$I_2$	$I_{CM}=I_{LPF\left(non\right)}$	$V_1$ = $V_2$ = 0, $V_3$ = $V_{o3}$, $V_4$ = 0, $V_5$ = $V_{o2}$, $I_1$ = 0
		Inverting	$I_1$	$I_{CM}=I_{LPF\left(in\right)}$	$V_1$ = $V_2$ = 0, $V_3$ = $V_{o3}$, $V_4$ = 0, $V_5$ = $V_{o2}$, $I_2$ = 0
	HPF	Non-inverting	$I_1$	$I_{CM}=I_{HPF\left(non\right)}$	$V_1$ = $V_2$ = 0, $V_3$ = $V_{o3}$, $V_4$ = $V_{o1}$, $V_5$ = 0, $I_2$ = 0
		Inverting	$I_2$	$I_{CM}=I_{HPF\left(in\right)}$	$V_1$ = $V_2$ = 0, $V_3$ = $V_{o3}$, $V_4$ = $V_{o1}$, $V_5$ = 0, $I_1$ = 0
	BPF	Non-inverting	$I_2$	$I_{CM}=I_{BPF\left(non\right)}$	$V_1$ = $V_2$ = 0, $V_3$ = $V_{o1}$, $V_4$ = $0$, $V_5$ = $V_{o2}$, $I_1$ = 0
		Inverting	$I_1$	$I_{CM}=I_{BPF\left(in\right)}$	$V_1$ = $V_2$ = 0, $V_3$ = $V_{o1}$, $V_4$ = $0$, $V_5$ = $V_{o2}$, $I_2$ = 0
	BSF	Non-inverting	$I_1$	$I_{CM}=I_{BSF\left(non\right)}$	$V_1$ = $V_2$ = 0, $V_3$ = $V_{o3}$, $V_4$ = $V_5$ = 0, $I_2$ = 0
		Inverting	$I_2$	$I_{CM}=I_{BSF\left(in\right)}$	$V_1$ = $V_2$ = 0, $V_3$ = $V_{o3}$, $V_4$ = $V_5$ = 0, $I_1$ = 0
	APF	Non-inverting	$I_1$	$I_{CM}=I_{APF\left(non\right)}$	$V_1$ = $V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_2$ = 0
		Inverting	$I_2$	$I_{CM}=I_{APF\left(in\right)}$	$V_1$ = $V_2$ = $V_3$ = $V_4$ = $V_5$ = 0, $I_1$ = 0

. Unlike the mixed-mode universal filters reported in [32,33,34,35,36], the proposed mixed-mode universal filter can realize the variant transfer functions for VM, CM, TIM, and TAM corresponding to LPF, HPF, BPF, BSF, and APF responses using a single input signal, similar to a SIMO filter, without requiring input matching conditions such as $V_{in}=V_{in1}= V_{in2}$ in [32], or $I_{in}=I_{in1}= I_{in2}$ in [34,35]. Moreover, compared with [32,33,34,35,36], the proposed mixed-mode universal filter can provide both non-inverting and inverting VM, CM, TIM, and TAM corresponding to LPF, HPF, BPF, BSF, and APF responses.

The parameters ${\omega }_o$ and $Q$ of LPF, HPF, BPF, BSF and APF in the case of VM, CM, TAM, and TIM configuration can be expressed as

$${\omega }_o=\sqrt{{\displaystyle \frac{g_{m1}{g}_{m2}}{C_1{C}_2}}}$$

(29)

$$Q=\sqrt{{\displaystyle \frac{g_{m1}{C}_2}{g_{m2}{C}_1}}}$$

(30)

The parameter ${\omega }_o$ can be controlled through the transconductance $g_{m1}$ and $g_{m2}$, where $g_{m1}=g_{m2}$, while the parameter $Q$ is determined by the capacitor ratio $C_2/C_1$. For practical applications, the quality factor $Q$ should be determined first, after which the transconductances $g_{m1}$ and $g_{m2}$ can then be tuned to achieve the desired natural frequency ${\omega }_o$. With this feature, the filter parameters can be controlled orthogonally.

2.3. Non-Idealities Analysis

As illustrated in Figure 4, the initial lossless integrator in the mixed-mode universal filter is established by transconductance $g_{m1}$ and capacitor $C_1$, while the second lossless integrator is formed by transconductance $g_{m2}$ and capacitor $C_2$.

Two integrators constitute the core components of the proposed filter, and their formulation includes the non-ideal effects of the transconductance elements. In the vicinity of the cut-off frequency, the non-ideal transconductance $g_{m1}$ and $g_{m2}$ ($g_{mnj}$) can be described as follows [41]:

$$g_{mnj}\left(s\right)\cong g_{mj}\left(1-T_{oj}s\right)$$

(31)

where $T_{oj}=1/{\omega }_{gmj}$ and ${\omega }_{gmj}$ represents the first pole frequency of $g_{mj}$ ($j=1,2)$.

The transconductances $g_{m3}$ and $g_{m4}$ function as summing amplifiers. The arithmetic summing and subtracting network is realized via transconductances $g_{m3}$ and $g_{m4}$, yielding an input-to-output voltage relationship expressed as follows:

$$V_o={\beta }_{+1j}{V}_{+1}+{\beta }_{+2j}{V}_{+2}-{{\beta }_{-1j}V}_{-1}$$

(32)

where the voltage tracking errors are represented by ${\beta }_{+1j}$, ${\beta }_{+2j}$, and ${\beta }_{-1j}$. For a perfectly matched circuit, these gains optimally reach a nominal value of one for $g_{mj}$ ($j=3, 4)$.

The transconductance $g_{m5}$ operates as summing and differencing amplifiers to realize the APF response. Transconductance $g_{m6}$ serves as a voltage follower in VM operation and as a current-to-voltage converter in CM, whereas $g_{m7}$ functions as a voltage-to-current converter for CM and TAM. These transconductances can be omitted, as they do not influence the denominator of the transfer functions.

Considering the non-idealities in (31) for $g_{m1}$ and $g_{m2}$, the non-idealities can be approximated as $g_{mn1}\left(s\right)\cong g_{m1}\left(1-T_{o1}s\right)$ and $g_{mn2}\left(s\right)\cong g_{m2}\left(1-T_{o2}s\right)$, and the relationship between the input and output voltages in (32); the denominator $\left(D\left(s\right)\right)$ of the transfer functions can be then written as follows:

$$\begin{gathered} D\left(s\right)=s^2{C}_1{C}_2\left(1-{\displaystyle \frac{{C_1{g}_{m2}{\beta }_{+13}T}_{o2}-g_{m1}{g}_{m2}{\beta }_{+23}{T}_{o1}{T}_{o2}}{C_1{C}_2}}\right) \\ +s{C}_1{g}_{m2}{\beta }_{+13}\left(1-{\displaystyle \frac{g_{m1}{\beta }_{+23}\left(T_{o1}+T_{o2}\right)}{C_1{\beta }_{+13}}}\right)+g_{m1}{g}_{m2}{\beta }_{+23} \end{gathered}$$

(33)

Based on Equation (33), the non-idealities associated with transconductances $g_{m1}$ and $g_{m2}$ and the subtraction/addition amplifiers can be successfully compensated for by establishing the following constraints:

$$\left.\begin{array}{c}{\displaystyle \frac{{C_1{g}_{m2}{\beta }_{+13}T}_{o2}-g_{m1}{g}_{m2}{\beta }_{+23}{T}_{o1}{T}_{o2}}{C_1{C}_2}}\ll 1\\ {\displaystyle \frac{g_{m1}{\beta }_{+23}\left(T_{o1}+T_{o2}\right)}{C_1{\beta }_{+13}}}\ll 1\end{array}\right\}$$

(34)

These constraints are satisfied by scaling $g_{m1}$, $g_{m2}$, and the capacitive elements $C_1$ and $C_2$ to ensure the primary time constants are substantially greater than the secondary time constants introduced by circuit non-idealities.

The non-idealities associated with the summing and differencing amplifiers implemented using $g_{m4}$, $g_{m5}$, and $g_{m6}$ influence the magnitude of the transfer functions.

The non-ideal parameters ${\omega }_{on}$ and $Q_n$ for all filter responses can be expressed as:

$${\omega }_{on}=\sqrt{{\displaystyle \frac{g_{m1}{g}_{m2}{\beta }_{+23}}{C_1{C}_2}}}$$

(35)

$$Q_n={\displaystyle \frac{1}{{\beta }_{+13}}}\sqrt{{\displaystyle \frac{g_{m1}{C}_2{\beta }_{+23}}{g_{m2}{C}_1}}}$$

(36)

The prior non-ideal analysis operates under the assumption of low-frequency operation, neglecting the parasitic components of the MI-OTA. Nevertheless, when moving into high-frequency ranges, these parasitic resistances and capacitances must be factored into the non-ideal formulations. Figure 4 demonstrates how the natural frequency of the system is altered by the output parasitic impedances of $g_{m1}$ and $g_{m2}$. Specifically, the parameters $C_{o1}$ and $C_{o2}$ signify the output parasitic capacitances, whereas $R_{o1}$ and $R_{o2}$ capture the output parasitic resistances of $g_{m1}$ and $g_{m2}$.

When the $C_{o1}$ and $C_{o2}$ are taken into account, the effective capacitances become $C_1^{\prime }$ = $C_1+C_{o1}$ and $C_2^{\prime }$ = $C_2+C_{o2}$, respectively. Consequently, the pole frequencies of the filter are given by $g_{m1}/C_1^{\prime }$, $g_{m2}/C_2^{\prime }$, $1/\left(R_{o1}{C}_1^{\prime }\right)$, and $1/\left(R_{o2}{C}_2^{\prime }\right)$. In the high-frequency region, the pole frequencies $g_{m1}/C_1^{\prime }$ and $g_{m2}/C_2^{\prime }$ govern the filter’s cut-off frequency, as the poles $1/R_{o1}{C}_1^{\prime }$ and $1/R_{o2}{C}_2^{\prime }$ occur at significantly higher frequencies. However, the parasitic capacitances $C_{o1}$ and $C_{o2}$ introduce deviations in the natural frequency. This influence can be compensated by tuning $g_{m1}$ and $g_{m2}$, or mitigated by selecting $C_1\gg C_{o1}$ and $C_2\gg C_{o2}$.

3. Results

3.1. Simulation Result

To evaluate performance, the proposed configuration was designed and simulated within the Cadence Virtuoso suite using standard 65-nm TSMC CMOS process node parameters (Taiwan Semiconductor Manufacturing Company, Hsinchu, Taiwan). The targeted component details and design constraints are structured in

Table 2. Transistor Dimensions for the MI-OTA.

Component	W/L (µm/µm)
M1,2	2 × 30/3
M11,12	30/3
M3–6, M3c–6c	10/5
M7–10, M13	15/5
M7c–10c, M13c	2 × 15/5
MR	6/5
CB = 0.4 pF

. Operating from a scaled supply rail of 0.5 V, the architecture prioritizes minimal energy consumption, rendering it exceptionally appropriate for power-constrained implementations. From these simulation trials, the MI-OTA consumes a power footprint of only 25 nW under a biasing current fixed at 10 nA.

To implement the ultra-low-frequency poles for the proposed mixed-mode universal filter without consuming excessive silicon area, the two core integration grounded capacitors are chosen as $C_1$ = $C_2$ = 20 pF, realized via high-density on-chip MOS capacitors. The total layout footprint occupied by these capacitors is 5324 µm². Post-layout parasitic extraction indicates a routing and junction parasitic capacitance of 132 fF and 155 fF at the respective integration nodes, which contributes a negligible deviation (less than 0.8%) from the ideal nominal behavior and is easily compensated via bias current tuning.

Selected simulation results are presented to demonstrate the performance of the proposed filters. Figure 5 and Figure 6 show the frequency characteristics of gains and phases for the VM and CM filter, respectively, for the following configurations: LPF (a), HPF (b), BPF (c), BSF (d), and APF (e). While $I_{set3-7}$ was fixed at 20 nA, $I_{set\mathrm{1,2}}$ was varied (10, 20 and 40 nA) to adjust the cutoff frequency to 43 Hz, 82 Hz and 156 Hz, respectively.

To confirm the robustness of the design against process, voltage, and temperature (PVT) variations, an analysis was performed for the VM-LPF, as shown in Figure 7. The results demonstrate that, across various MOS transistor process corners, including slow-slow (SS), slow-fast (SF), fast-slow (FS), fast-fast (FF), and typical-typical (TT), as well as a ±10% deviation in supply voltage and temperature variations of −10 °C and 60 °C, the frequency response curves remain closely aligned. This overlap confirms the reliability and proper functionality of the circuit under PVT variations.

To evaluate the sensitivity and robust operation of the proposed multi-input operational transconductance amplifier filter against manufacturing imperfections, a 200-run Monte Carlo statistical simulation was performed at 27 degrees Celsius. The analysis evaluated both global process variations and local transistor mismatch across typical-typical, fast-fast, and slow-slow corners for the voltage-mode and current-mode low-pass configurations targeting a 156 Hz center frequency and a quality factor of 0.707.

In the nominal typical-typical corner, the voltage-mode filter exhibits a mean natural frequency of 155.4 Hz with an 11.19 percent three-sigma spread, while the quality factor and passband gain show tight three-sigma spreads of 6.38 percent and 2.70 percent, respectively. Across all worst-case corners, the maximum three-sigma frequency variation remains bounded within 11.69 percent, with the mean shifting to a maximum of 164.9 Hz in the fast-fast corner and a minimum of 144.5 Hz in the slow-slow corner. Meanwhile, the quality factor and passband gain maintain excellent structural stability across all corners, with maximum three-sigma spreads staying strictly under 6.8 percent and 4.0 percent, respectively.

These results demonstrate that while subthreshold operation introduces an expected 11 percent frequency variation due to random threshold voltage fluctuations in the bulk-driven input transistors, the quality factor and passband gain remain highly stable because they depend on closely matched layout ratios. Consequently, any manufacturing-induced center frequency shifts can be easily compensated for post-fabrication by applying minor electronic tuning adjustments to the internal bias currents without causing any passband peaking or transfer function distortions.

The transient analysis of the VM-LPF is shown in Figure 8. When a sine wave input signal with an amplitude of 50 mV and a frequency of 10 Hz is applied, the output sine wave exhibits a total harmonic distortion (THD) of approximately 1%.

Figure 9 plots the equivalent output voltage noise spectral density for the VM-LPF. Over a frequency band spanning from 1 Hz to 156 Hz, the integrated output noise is evaluated at 494 µV, which provides a dynamic range of 37 dB.

3.2. Applications

Conventional biosignals, including EEG, ECG, and EMG, generally possess low frequencies and very low amplitudes. Consequently, an amplification stage is necessary before subsequent signal processing. Instrumentation amplifiers are fundamental front-end circuits used to amplify low-level biosignals, and continuous-time filtering is essential in subsequent processing, where low-pass, band-pass, and band-stop filters are employed to suppress high-frequency noise, select the desired frequency band, and eliminate 50/60-Hz power-line interference, respectively. Several instrumentation amplifiers have been reported in the open literature [42,43,44,45,46,47,48,49]. The circuit in [42] operates in the voltage mode, where both the input and output signals are in voltage form. The circuits in [43,44] operate in the current mode, where both the input and output signals are in current form. The circuits in [45,46] operate in the transadmittance mode, in which the input signal is in voltage form while the output signal is in current form. The circuits in [47,48] operate in the transimpedance mode, where the input signal is in current form and the output signal is in voltage form. The circuit in [49] supports multi-mode operation, in which either the input or output signal can be in voltage or current form. From these operating modes, the output signal of an instrumentation amplifier can be either in voltage or current form and can be supplied to subsequent filter stages. It should be noted that the proposed mixed-mode universal filter satisfies this requirement, as it can accept both voltage and current signals at its input. Moreover, the proposed filter operates with a low supply voltage, consumes low power, and is suitable for low-frequency biosignal applications.

To demonstrate its real-world utility in suppressing out-of-band interference, the multi-regime universal filter was evaluated using physiological signals. An ECG signal corrupted by an unwanted 500-Hz interference component was routed through the TAM LPF configuration, which was set to a 156-Hz corner frequency. The performance of this signal conditioning step is illustrated in Figure 10, where the input signal containing a 5 mV/500-Hz noise artifact is plotted in (a), and the reconstructed output is displayed in (b). As shown, the 5 mV/500-Hz noise component is successfully suppressed.

In practical biomedical systems, this filter is highly useful because its mixed-mode design lets it connect directly to various types of front-end sensors without needing extra, power-hungry signal conversion blocks. When placed after a standard low-noise instrumentation amplifier, the weak bio-signals are lifted well above the filter’s noise floor, minimizing overall system noise degradation. Furthermore, the filter’s wide linear input range prevents signal clipping or saturation caused by sudden patient motion artifacts, while the input capacitors provide complete DC isolation to stop unwanted offset voltages from propagating through the signal chain.

3.3. Experimental Result

To practically validate the filter’s functionality, a hardware prototype was constructed and experimentally evaluated. This test circuit was assembled utilizing commercially available LM13700N integrated circuits [50], where the multi-input OTA (MI-OTA) structure was realized through the parallel combination of discrete operational transconductance amplifiers, as shown in Figure 1b. Because of structural differences between the transistor-level CMOS MI-OTA topology and this discrete macro-model approach, these discrete-IC measurements serve as a functional proof-of-concept validation rather than a direct, exact copy of the integrated circuit layout.

Figure 11 illustrates the benchmark test setup used for the universal filter. The discrete prototype was energized by symmetric power rails of $V_{DD}$ = ${-V}_{SS}$ = 5 V, and both the sinusoidal driving signals and the resulting output responses were acquired via a KEYSIGHT DSOX1204G oscilloscope. Fixing $R_{bias}$ = 51 kΩ set the active transconductances $g_{m1}$ and $g_{m2}$ to 1.384 mS, while the discrete capacitors $C_1$ and $C_2$ were selected as 220 nF. Concurrently, the auxiliary transconductances $g_{m3}$, $g_{m4}$, $g_{m5}$, and $g_{m6}$ were fixed at 0.496 mS by employing biasing resistors of $R_{const}$ = 150 kΩ. Given these design parameters, the universal filter targeted a nominal corner frequency of $f_o$ = 1.0 kHz.

To initiate the performance evaluation, a bias resistor of $R_{bias}$ = 51 kΩ was applied to fix the transconductance values at $g_{m1}$ = $g_{m2}$ = 1.384 mS. The resulting experimental magnitude and phase profiles for the LPF, HPF, BPF, BSF, and APF are plotted in Figure 12, tracking a mutual center frequency of $f_o$ = 1.0 kHz alongside a quality factor ($Q$) closely approaching unity ($Q$ $\approx$ 1).

For the second test, the transconductances $g_{m1}$ and $g_{m2}$ were varied to 0.712 mS, 1.384 mS, and 2.796 mS, by adjusting $R_{bias}$ to 100 kΩ, 51 kΩ, and 25 kΩ, respectively. Figure 13 illustrates the measured magnitude responses of the LPF, HPF, BPF, BSF, and APF for different transconductance values $g_m$, where $g_{m1}$ = $g_{m2}$ = $g_m$. The experimental results validate the functionality of the proposed filter. For transconductance values of 0.712 mS, 1.384 mS, and 2.796 mS, the corresponding natural frequencies of approximately 515 Hz, 1.0 kHz, and 2.02 kHz, respectively, are obtained.

Figure 14 illustrates the transient responses of the APF output voltages to a sinusoidal input signal with a peak-to-peak amplitude of 10 mV at a frequency of 1 kHz. This result clearly demonstrates the operation for a 180º degree phase difference for the APF response.

4. Discussion and Comparison

Table 3. Comparison of the proposed mixed-mode universal filter with some previous works.

Factor	Proposed	[17] 2020	[19] 2025	[22] 2021	[25] 2017	[29] 2025	[31] 2025
Number of active devices	7-MI-OTA	5-OTA	10-OTA	2-VDBA	3-CCCCTA	2-DVCCTA	1-VDGA
Realization	65 nm CMOS	0.35 µm CMOS	0.18 µm CMOS	0.18 µm CMOS	0.18 µm CMOS	0.18 µm CMOS	0.18 µm CMOS
Passive components	2-C	2-C	2-C	2-C, 2-R	2-C	2-C, 6-R	2-C
Number of offered responses	40	20	5	17	18	20	13
Offer five standard responses of VM, TAM, CM, TIM	Yes	Yes	Yes	No	No	Yes	No
All grounded passive components	Yes	Yes	Yes	No	Yes	No	No
High input impedances for VM	Yes	Yes	Yes	No	Yes	No	Yes
Electronic tunning capability	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Natural frequency (Hz)	156	3.39 × 106	50.6–1270	1.44 × 106	3.183 × 106	3.98 × 106	1.59 × 106
Power supply (V)	0.5	±0.9	0.5–1.2	±0.75	±0.9	±0.9	±0.9
Power dissipation (W)	450 × 10−9	-	48 × 10−9	0.373 × 10−3	1.99 × 10−3	4.69 × 10−3	2.84 × 10−3
THD ([%]@mV)	1@50	-	0.93@50	2.2@100	2.16@200	<6@120	-
Dynamic range (dB)	37	-	53.46	-	-	-	-
Verification of result	Sim/Exp	Sim/Post-Layout	Sim/Post-Layout	Sim/Exp	Sim/Post-Layout	Sim/Post-Layout	Sim/Exp
Application area	Bio.	Comm.	Bio.	Comm.	Comm.	Comm.	Comm.

Note: Bio = Biomedical systems, Comm. = Communication systems.

compares the proposed universal filters with several previously reported designs. The mixed-mode universal filters in [17,19,22,25,29,31] are selected for comparison. Compared with these reported universal filters, the proposed mixed-mode universal filter offers maximum transfer functions of VM, TAM, TIM, and CM of both non-inverting and inverting for LPF, HPF, BPF, BSF, and APF responses. The filter in [22,29] applies to some input voltages via either capacitor or resistor and supplies some output currents through either resistor or capacitor; this means that additional buffer circuits are required.

Again, the proposed mixed-mode universal filter is compared with previous works in [32,33,34,35,36], as summarized in

Table 4. Comparison of the proposed filter with previous low-voltage mixed-mode filters.

Factor	Proposed	[32] 2022	[33] 2023	[34] 2024	[35] 2024	[36] 2024
Number of active devices	7-MI-OTA	5-DDTA	2-MO-OTA, 2-MIMO-OTA	2-DDTA, 2 MO-DDTA	3-MIMO-DDCCTA	3-MI-OTA, 1-MIMO-OTA
Realization	65 nm CMOS	0.18 µm CMOS	0.18 µm CMOS	0.18 µm CMOS	0.18 µm CMOS	0.18 µm CMOS
Passive components	2-C	2-C	2-C	2-C	2-C, 3-R	2-C, 1-R
Number of offered responses	40	36	35	61	179	40
Offer five standard responses of VM, TAM, CM, TIM	Yes	Yes	Yes	Yes	Yes	Yes
Offer both non-inverting and inverting transfer functions	Yes	No	No	No	Yes	Yes
Without dual/triple input current signals	Yes	Yes	No	No	No	No
Natural frequency (Hz)	156	1.04 × 103	114	211	1.59 × 103	5.95 × 103
Power supply (V)	0.5	1.2	0.5	0.5	1	1
Power dissipation (W)	450 × 10−9	330 × 10−6	58 × 10−9	281 × 10−9	374 × 10−3	156.8 × 10−6
THD ([%]@mV)	1@50	1.09@325	1@85	1@150	0.983@170	1@220
Dynamic range (dB)	37	63.69	53.2	58.23	57.7	40.2

Note: MI = multiple-input, MO = multiple-output, MIMO = multiple-input multiple-output.

. These filters operate in mixed mode, employ low supply voltages, and consume low power. These topologies offer electronic tuning capability, employ only grounded passive components, provide five standard responses in VM, TAM, CM, and TIM modes, and are free from active and passive matching conditions, similar to the proposed mixed-mode universal filter. However, the filters in [32,33,34] do not provide both non-inverting and inverting transfer functions for the five standard responses in VM, TAM, CM, and TIM modes. Although the filters in [35,36] can realize both non-inverting and inverting transfer functions for all five standard responses, they require dual/triple input current signals, which complicate practical implementation. In contrast, the proposed mixed-mode universal filter satisfies all of the aforementioned features. Based on their operating frequencies, the filters in [32,33,34,35,36] and the proposed filter are suitable for bio-signal processing applications.

In practice, the mode reconfiguration on chip can be implemented using analog switches or control logic circuits. However, the additional control devices introduce parasitic resistance and capacitance, which may affect the natural frequency and bandwidth of the filter, especially at nodes $V_{o1}$ and $V_{o3}$. In addition, the switching/control network used for input and output mode selection may increase the overall noise of the filter.

To critically evaluate the proposed universal filter from a practical application standpoint, several key design trade-offs and operational boundaries must be addressed:

•

Sensitivity to Process and Temperature Variations: Because the transistors operate in the subthreshold region, the circuit is inherently sensitive to temperature-induced exponential current variations. However, for targeted biomedical applications (such as wearable or implantable medical devices), the ambient temperature environment remains highly stable. To verify robustness against unpredictable variations, the design functionality was thoroughly validated across rigorous Process–Voltage–Temperature (PVT) corners, with a specific focus on temperature corners, proving stable filter operation under realistic deployment conditions.

•

Scalability to Higher Frequencies: The proposed circuit is specifically optimized for low-frequency biomedical applications (ranging from sub-Hertz up to 10 kHz). In this low-frequency domain, the small bulk-driven transconductance ($g_{mb}$) is highly beneficial for achieving ultra-low cutoff frequencies without requiring excessively large capacitors. If scaling to higher operating frequencies is required for other applications, the multiple-input (MI) technique can be readily adapted to a conventional gate-driven MOS architecture to leverage its higher transconductance ($g_m$).

•

Noise Performance: The bulk-driven architecture experiences a higher input-referred noise floor compared to conventional gate-driven topologies due to the lower value of $g_{mb}$. However, the capacitive division of the multiple-input network simultaneously expands the linear input voltage range by the exact same scaling ratio. As a result, the signal-handling capacity increases proportionally with the noise floor, ensuring that the overall Dynamic Range (DR) remains unaffected and fully compliant with system requirements.

•

Limitations Associated with Bulk-Driven MOS Transistors: While the reduced transconductance ($g_{mb}$) of bulk-driven devices relative to gate-driven devices is traditionally viewed as a limitation, it serves as a core design advantage in this application. Minimizing the filter cutoff frequency (f_c) fundamentally requires establishing an exceptionally low transconductance-to-capacitance ratio ($g/C$). Utilizing the smaller $g_{mb}$ offers an ideal architectural solution, enabling sub-Hertz pole realization while maintaining highly manageable on-chip capacitance values.

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Implementation Complexity in Integrated Circuits: The proposed design exhibits lower overall circuit complexity compared to conventional highly linearized low-frequency filters. Although the multiple-input (MI) capacitive network marginally increases the silicon area of the input stage, it uses the exact same compact core amplifier circuit. By using a single differential pair combined with the MI network rather than complex multi-stage distortion cancellation techniques, the structural complexity of the integrated circuit is significantly minimized.

5. Conclusions

In summary, an innovative low-voltage, ultra-low-power universal filter framework utilizing MI-OTAs has been presented. The primary architecture verifies that SIMO filter topologies built around MI-OTAs can successfully deliver diverse transfer functions without the need for any passive resistors. This multi-input terminal behavior is achieved through multiple-input bulk-driven MOS technology, an approach that allows for low DC supply operation alongside a significantly extended linear input range. Furthermore, the core transconductance block consumes power strictly within the nanowatt domain. By incorporating a single auxiliary MI-OTA, the foundational universal filter expands into a dual-mode system operating across both the voltage and transimpedance regimes, successfully providing all forty variations of inverting and non-inverting LPF, HPF, BPF, BSF, and APF characteristics. Electronic control over the filter’s natural frequency adds a critical layer of design adaptability. These performance benchmarks render the network highly optimized for processing biological signals and other ultra-low-frequency analog subsystems. Comprehensive validation was established through post-layout extractions and backed by physical laboratory measurements of a discrete prototype realized with commercial LM13700 components.