Voltage Differencing Buffered Amplifier-Based Novel Truly Mixed-Mode Biquadratic Universal Filter with Versatile Input/Output Features

Abstract

In this paper, a first-of-a-kind mixed-mode universal filter employing three VDBAs and three passive components, is proposed. The filter operates in all four modes and provides all five filter responses, namely voltage-mode (VM), current-mode (CM), trans-impedance-mode (TIM), or trans-admittance-mode (TAM). Additionally, the same filter topology can also work as a CM single-input-multi-output (SIMO) filter. A state-of-the-art comparison of various ‘voltage differencing’ variants of the voltage differencing buffered amplifier (VDBA)-based SIMO/MISO (single-input-multi-output/multi-input-single-output)-type biquad filters further highlight the significance of the presented research. In the proposed no passive component matching is required for generating the filter responses. The filter circuit also provides inbuilt tunability of the quality factor independent of the pole frequency. The non-ideal frequency dependent gain and component sensitivity analyses of the filter were also performed. The Silterra Malaysia $0.18\mathsf{\mu }\mathrm{m}$ process design kit (PDK) is employed to design and validated the proposed VDBA-based filter using the Cadence design software. The simulation results closely follow the theoretical predictions. To further verify the practical feasibility of the proposed filter, an experimental evaluation is also completed. The VDBA-based filter is implemented using off-the-shelf operational transconductance amplifiers Intersil CA3080, Texas Instruments LF356 op-amp, and Analog Devices AD844s. The filter is designed for a characteristic frequency of 100 kHz. The time and frequency domain measurement results indicate the proper functioning of the filter.

1. Introduction

Analog frequency filters are an important component of signal processing system. They are employed in instrumentation systems, communication systems, speech processing, sensor data preprocessing, data acquisition systems, etc. [1,2,3]. The active element-based filters are the most employed as they have advantages in terms of chip area, low-power operation, tunability, and compatibility [1,2]. In present day complex signal processing systems, as the design complexity of the system is increasing to achieve high performance, both current-mode and voltage-mode signal processing circuits are employed in a single system. In order to connect the current-mode output to a voltage-mode circuit or vice versa, trans-admittance and trans-impedance stages are required to perform voltage to current (V-I) and I-V conversion. The mixed-mode filters will find application in such a scenario as it will perform the dual task of signal processing and signal conversion simultaneously. One such example is given in reference [4] of a three-way high-fidelity loudspeaker crossover network. The design of mixed-mode universal filters that can provide low-pass (LP), high-pass (HP), band-pass (BP), band-reject (BR), and all-pass (AP) filter responses in CM, VM, TAM, and TIM modes of operation are needed for the mixed signals system architecture [1,2,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. The popular analog building blocks (ABBs) that are used in the design of active filters include operational transconductance amplifier (OTA) [5], second-generation current conveyor (CCII) [6], differential voltage current conveyor (DVCC) [16], extra current conveyor transconductance amplifier (EXCCTA) [21], differential difference current conveyor (DDCCII) [18], fully differential current conveyor (FDCCII) [15], current differencing buffer amplifier (CDBA) [3], etc. The voltage differencing buffered amplifier (VDBA) is another popular ABB that is very simple in design and versatile in realizing numerous applications [3,22,23,24]. Various ‘voltage differencing’ variants of the VDBA are proposed, such as fully balanced voltage differencing buffered amplifier (FB-VDBA) [25], voltage differencing inverting buffered amplifier (VDIBA) [26,27], fully balanced voltage differencing inverting buffered amplifier (FB-VDIBA) [28], or voltage differencing differential input buffered amplifier (VD-DIBA) [29]. In Table 1 and Table 2, a comparative study is carried out to compare the state-of-the-art SIMO/MISO (single-input-multi-output/multi-input-single-output) voltage differencing unit (VDU)-based biquad filters [25,26,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53] with here proposed designs. The comparison is made based on the following relevant criteria:

(i)

Number of ABBs employed;

(ii)

Count of passive components used;

(iii)

A requirement of passive components matching condition;

(iv)

Application of negative input for response generation;

(v)

A requirement of double voltage input for response realization;

(vi)

Low output impedance in the case of VM and TIM filters;

(vii)

High output impedance in the case of CM and TAM filters;

(viii)

Mode of operation;

(ix)

Independent tunability of quality factor and filter frequency;

(x)

Can realize all five filter responses;

(xi)

Test frequency;

(xii)

Power dissipation;

(xiii)

Supply voltage;

(xiv)

Total harmonic distortion (THD).

Reported VDBA-based universal biquadratic filters have three major limitations that severely curtail their application spectrum, which are: (a) non-availability of all five filter responses, (b) the employment of floating passive components, and (c) passive component matching constraints. It can be inferred from the comparative study that out of the 30 designs available in the literature; only 15 can provide all five filter responses in either VM and CM mode [23,26,34,35,36,39,41,42,43,44,45,46,47,48,49,52]. Most importantly, none of the VDU-based filter structures can operate in mixed-mode configuration.

In this research, a first-of-a-kind VDBA-based MISO type mixed-mode universal filter is proposed that can work in all four modes of operation, providing all five filter responses. The proposed structure without any change in the core topology can also function as a SIMO filter providing CM output. The validation of the VDBA and filter is carried out in Cadence design software using $0.18\mathsf{\mu }\mathrm{m}$ Silterra Malaysia PDK. Both simulation and experimental results are in close agreement with the theoretical findings.

Table 1. Comparative study of various VDU-based SIMO-type biquad filter designs with the proposed filter (Note: NA—not applicable).

References	(i)	(ii)	(iii)	(iv)	(v)	(vi)	(vii)	(viii)	(ix)	(x)	(xi) (MHz)	(xii) (W)	(xiii) (V)	(xiv)
[25]	2-FB-VDBA	2C + 4R	Yes	NA	NA	Yes	NA	VM/CM	No	No	1	–	$\pm 5$	–
[28]	2-FB-VDIBA	2C + 4R	Yes	NA	NA	Yes	NA	VM	No	No	7.9	476 $\mathsf{\mu }$	$\pm 0.4$	–
[29]	2-VD-DIBA	2C	No	NA	NA	No	NA	VM	No	No	0.159	–	$\pm 5$	0.76% @ 1.07 V (for HP VM mode)
[33]	1-ZC-VDBA	2C	No	NA	NA	NA	No	CM	No	No	10	–	$\pm 0.9$	≤10% @ 25 μA (for LP VM mode)
[38]	1-VDBA	2C + 3R	No	NA	NA	Yes	NA	VM	No	No	1.59	–	$\pm 0.9$	–
[39]	1-VDBA	2C + 2R	No	NA	NA	NA	No	CM	No	Yes	0.78	–	$\pm 1.2$	–
[40]	3-VDBA	2C	No	NA	NA	Yes	NA	VM	No	No	0.0469	–	$\pm 2$	–
[53]	2-VD-DIBA	2C + 2R	No	NA	NA	No	NA	VM	Yes	No	0.1	–	$\pm 0.9$	≥1.8% @ 400 mV (for LP VM mode)
This work	3-VDBA	2C	No	NA	NA	NA	Yes except (HP)	CM/TAM	Yes	Yes	16.32	5.482 m	$\pm 1.25$	≤4% @ 300 mV (for HP VM mode)

Table 1. Comparative study of various VDU-based SIMO-type biquad filter designs with the proposed filter (Note: NA—not applicable).

References	(i)	(ii)	(iii)	(iv)	(v)	(vi)	(vii)	(viii)	(ix)	(x)	(xi) (MHz)	(xii) (W)	(xiii) (V)	(xiv)
[25]	2-FB-VDBA	2C + 4R	Yes	NA	NA	Yes	NA	VM/CM	No	No	1	–	$\pm 5$	–
[28]	2-FB-VDIBA	2C + 4R	Yes	NA	NA	Yes	NA	VM	No	No	7.9	476 $\mathsf{\mu }$	$\pm 0.4$	–
[29]	2-VD-DIBA	2C	No	NA	NA	No	NA	VM	No	No	0.159	–	$\pm 5$	0.76% @ 1.07 V (for HP VM mode)
[33]	1-ZC-VDBA	2C	No	NA	NA	NA	No	CM	No	No	10	–	$\pm 0.9$	≤10% @ 25 μA (for LP VM mode)
[38]	1-VDBA	2C + 3R	No	NA	NA	Yes	NA	VM	No	No	1.59	–	$\pm 0.9$	–
[39]	1-VDBA	2C + 2R	No	NA	NA	NA	No	CM	No	Yes	0.78	–	$\pm 1.2$	–
[40]	3-VDBA	2C	No	NA	NA	Yes	NA	VM	No	No	0.0469	–	$\pm 2$	–
[53]	2-VD-DIBA	2C + 2R	No	NA	NA	No	NA	VM	Yes	No	0.1	–	$\pm 0.9$	≥1.8% @ 400 mV (for LP VM mode)
This work	3-VDBA	2C	No	NA	NA	NA	Yes except (HP)	CM/TAM	Yes	Yes	16.32	5.482 m	$\pm 1.25$	≤4% @ 300 mV (for HP VM mode)

Table 2. Comparative study of various VDU-based MISO-type biquad filter designs with the proposed filter (Note: NA—not applicable).

References	(i)	(ii)	(iii)	(iv)	(v)	(vi)	(vii)	(viii)	(ix)	(x)	(xi) (MHz)	(xii) (W)	(xiii) (V)	(xiv)
[23]	2-VDBA	2C	No	Yes	No	Yes	NA	VM	No	Yes	1.19	970 $\mathsf{\mu }$	±1.5	≤1% @ 0.4 V (for BP VM mode)
[26]	1-VDIBA	2C + R	No	No	NA	No	NA	VM	No	Yes	1.34	–	–	–
[30]	2-VDBA	2C	No	No	NA	Yes	NA	VM	No	No	0.1	–	±0.2	>1.5% @ 50 mV (for VM mode)
[31]	2-VDIBA	2C	No	No	NA	No	NA	VM	Yes	No	2.06	–	±0.4	–
[32]	1-VDBA	2C + 2R	Yes	No	No	No	NA	VM	No	No	0.88	–	±0.9	–
[34]	2-VDIBA	2C	No	No	NA	Yes	NA	VM	No	Yes	12.9	2.8 m	±0.75	≤1% @ 85 mV (for VM mode)
[35]	2-VDIBA	2C + R	No	Yes	No	Yes	NA	VM	Yes	Yes	10.1	1.14 m	±0.6	0.4% @ 25 mV (for VM mode)
[36]	2-VDBA	2C	No	No	No	Yes	NA	VM	No	Yes	56	440.6 n	±0.7	–
[37]	2-VDBA	2C	No	No	No	Yes	NA	VM	No	No	47	–	–	–
[41]	1-VD-DIBA	2C + R	Yes	No	Yes	Yes	NA	VM	No	Yes	–	–	±2	–
[42]	1-VDIBA	2C	No	No	No	No	NA	VM	No	Yes	1.59	–	±0.9	3.15% @ 50 mV (for BP VM mode)
[43]	1-VDBA	2C	No	No	No	Yes	NA	VM	No	Yes	0.766	–	–	–
[44]	2-VDBA	2C	No	Yes	No	Yes	NA	VM	No	Yes	1.16	–	±1.5	>3.15% @ 0.8 V (for BP VM mode)
[45]	2-VDBA	2C	No	Yes	No	Yes	NA	VM	No	Yes	10.16	–	±1.5	≤4% @ 28 mV (for VM mode)
[46]	2-VD-DIBA	2C	No	No	Yes	Yes	NA	VM	No	Yes	0.1563	–	±5	–
[47]	2-VDBA	2C	No	Yes	No	Yes	NA	VM	No	Yes	22	750 $\mathsf{\mu }$	±0.75	≥2% @ 50 mV (for BP VM mode)
[48]	1-VDBA	2C + R	No	Yes	No	No	NA	VM	No	Yes	–	–	±1.5	–
[49]	1-VDBA	2C + R	No	Yes	No	No	NA	VM	Yes	Yes	19.49	360 $\mathsf{\mu }$	±0.75	–
[50]	2-VDIBA	2C + R	No	No	No	No	NA	VM	Yes	No	–	–	±0.6	–
[51]	2-VD-DIBA	2C + 2R	No	No	No	No	NA	VM	Yes	No	0.3093	–	±5	>4% @ 90 mV (for BP VM mode)
[52]	2-VDBA	2C	No	Yes	No	Yes	NA	VM	No	Yes	0.05	–	±5	2.98% @ 50 mV (for BP VM mode)
[53]	2-VD-DIBA	2C + 2R	Yes	No	No	Yes	NA	VM	Yes	Yes	0.1	–	–	–
[54]	3-VDBA	2C + 2R	No	No	No	Yes	Yes	VM, TAM	Yes	Yes	7.2	5.47 m	±1.25	≤6% @ 250 mV (for BP VM mode)
This work	3-VDBA	2C + R	No	No	No	Yes	Yes	VM, CM, TIM, TAM	Yes	Yes	16.34	5.482 m	±1.25	≤4% @ 350 mV (for HP VM mode)

Table 2. Comparative study of various VDU-based MISO-type biquad filter designs with the proposed filter (Note: NA—not applicable).

References	(i)	(ii)	(iii)	(iv)	(v)	(vi)	(vii)	(viii)	(ix)	(x)	(xi) (MHz)	(xii) (W)	(xiii) (V)	(xiv)
[23]	2-VDBA	2C	No	Yes	No	Yes	NA	VM	No	Yes	1.19	970 $\mathsf{\mu }$	±1.5	≤1% @ 0.4 V (for BP VM mode)
[26]	1-VDIBA	2C + R	No	No	NA	No	NA	VM	No	Yes	1.34	–	–	–
[30]	2-VDBA	2C	No	No	NA	Yes	NA	VM	No	No	0.1	–	±0.2	>1.5% @ 50 mV (for VM mode)
[31]	2-VDIBA	2C	No	No	NA	No	NA	VM	Yes	No	2.06	–	±0.4	–
[32]	1-VDBA	2C + 2R	Yes	No	No	No	NA	VM	No	No	0.88	–	±0.9	–
[34]	2-VDIBA	2C	No	No	NA	Yes	NA	VM	No	Yes	12.9	2.8 m	±0.75	≤1% @ 85 mV (for VM mode)
[35]	2-VDIBA	2C + R	No	Yes	No	Yes	NA	VM	Yes	Yes	10.1	1.14 m	±0.6	0.4% @ 25 mV (for VM mode)
[36]	2-VDBA	2C	No	No	No	Yes	NA	VM	No	Yes	56	440.6 n	±0.7	–
[37]	2-VDBA	2C	No	No	No	Yes	NA	VM	No	No	47	–	–	–
[41]	1-VD-DIBA	2C + R	Yes	No	Yes	Yes	NA	VM	No	Yes	–	–	±2	–
[42]	1-VDIBA	2C	No	No	No	No	NA	VM	No	Yes	1.59	–	±0.9	3.15% @ 50 mV (for BP VM mode)
[43]	1-VDBA	2C	No	No	No	Yes	NA	VM	No	Yes	0.766	–	–	–
[44]	2-VDBA	2C	No	Yes	No	Yes	NA	VM	No	Yes	1.16	–	±1.5	>3.15% @ 0.8 V (for BP VM mode)
[45]	2-VDBA	2C	No	Yes	No	Yes	NA	VM	No	Yes	10.16	–	±1.5	≤4% @ 28 mV (for VM mode)
[46]	2-VD-DIBA	2C	No	No	Yes	Yes	NA	VM	No	Yes	0.1563	–	±5	–
[47]	2-VDBA	2C	No	Yes	No	Yes	NA	VM	No	Yes	22	750 $\mathsf{\mu }$	±0.75	≥2% @ 50 mV (for BP VM mode)
[48]	1-VDBA	2C + R	No	Yes	No	No	NA	VM	No	Yes	–	–	±1.5	–
[49]	1-VDBA	2C + R	No	Yes	No	No	NA	VM	Yes	Yes	19.49	360 $\mathsf{\mu }$	±0.75	–
[50]	2-VDIBA	2C + R	No	No	No	No	NA	VM	Yes	No	–	–	±0.6	–
[51]	2-VD-DIBA	2C + 2R	No	No	No	No	NA	VM	Yes	No	0.3093	–	±5	>4% @ 90 mV (for BP VM mode)
[52]	2-VDBA	2C	No	Yes	No	Yes	NA	VM	No	Yes	0.05	–	±5	2.98% @ 50 mV (for BP VM mode)
[53]	2-VD-DIBA	2C + 2R	Yes	No	No	Yes	NA	VM	Yes	Yes	0.1	–	–	–
[54]	3-VDBA	2C + 2R	No	No	No	Yes	Yes	VM, TAM	Yes	Yes	7.2	5.47 m	±1.25	≤6% @ 250 mV (for BP VM mode)
This work	3-VDBA	2C + R	No	No	No	Yes	Yes	VM, CM, TIM, TAM	Yes	Yes	16.34	5.482 m	±1.25	≤4% @ 350 mV (for HP VM mode)

2. Voltage Differencing Buffered Amplifier (VDBA)

The VDBA simply is a cascade connection of a voltage buffer and an operational transconductance amplifier (OTA). The voltage-current relationship of the VDBA is presented in Equation (1) and the functional block representation is given in Figure 1a.

$$\left[\begin{array}{c}{I}_{\mathrm{P}}\\ I_{\mathrm{N}}\\ I_{\mathrm{Z}}\\ I_{\mathrm{ZC}+}\\ I_{\mathrm{ZC}-}\\ V_{\mathrm{W}}\end{array}\right]=\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ g_{\mathrm{m}}& -g_{\mathrm{m}}& 0\\ g_{\mathrm{m}}& {-g}_{\mathrm{m}}& 0\\ {-g}_{\mathrm{m}}& g_{\mathrm{m}}& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{V}_{\mathrm{P}}\\ V_{\mathrm{N}}\\ V_{\mathrm{Z}}\end{array}\right].$$

(1)

The VDBA is a six-terminal device, of which CMOS implementation is shown in Figure 1b. The first transconductance amplifier stage is built by the transistors M1–M14. The output current of the transconductance amplifier depends on the difference in voltage between P and N terminals. If operation in saturation region is assumed and $W/L$ ratio for transistors M1 and M2 are made identical then the output current $I_{\mathrm{Z}}$ of the OTA is given by Equation (2): The voltage follower forms the second stage of the VDBA designed using transistors M15–M21.

$$I_{\mathrm{Z}}=g_{\mathrm{m}}\left(V_{\mathrm{P}}-V_{\mathrm{N}}\right)=\left(\sqrt{2I_{\mathrm{Bias}}{K}_i}\right)\left(V_{\mathrm{P}}-V_{\mathrm{N}}\right),$$

(2)

where the transconductance parameter $K_i=\mu C_{\mathrm{ox}}W/2L$$(i=1,2)$, W is the effective channel width, L is the effective length of the channel, $C_{\mathrm{ox}}$ is the gate oxide capacitance per unit area, and $\mu$ is the carrier mobility.

3. Proposed Universal Filter

The proposed filter shown in Figure 2 utilizes three VDBAs and three passive components. The filter provides all five filter responses in all four modes of operation in MISO configuration. The filter can also be used in SIMO configuration wherein it provides CM responses. The MISO filter has the following features: (i) ability to operate in all four modes of operation, (ii) low output impedance for VM/TIM and high input impedance for CM/TAM, (iii) no passive component matching required, (iv) no need for inverting inputs for response realization, and (v) inbuilt tunability of quality factor independent of pole frequency.

3.1. Operation in VM and TAM Modes

In VM, the input voltage ($V_{\mathrm{IN}}$) is applied according to

Table 3. Input voltage excitation sequence.

Response	Inputs
	V1	V2	V3
LP	Vin	0	0
HP	0	Vin	0
BP	0	0	Vin
BR	Vin	Vin	0
AP	Vin	Vin	Vin

to obtain all five filter responses, namely LP, BP, HP, BR, and AP. Equations (3) and (4) give the transfer function of the VM and TAM, while Equations (5) and (6) give the expression for the characteristic frequency and quality factor. The input current ($I_{\mathrm{IN}}$) is set to zero.

$$V_{\mathrm{OUT}\left(\mathrm{VM}\right)}=\frac{s^2{C}_1{C}_2{V}_2-s{C}_1{g}_{\mathrm{m}1}{V}_3+{g_{\mathrm{m}1}{g}_{\mathrm{m}3}V}_1}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+g_{\mathrm{m}1}{g}_{\mathrm{m}3}},$$

(3)

$$I_{\mathrm{OUT}\left(\mathrm{TAM}\right)}={-g}_{\mathrm{m}2}\left[\frac{s^2{C}_1{C}_2{V}_2-s{C}_1{g}_{\mathrm{m}1}{V}_3+{g_{\mathrm{m}1}{g}_{\mathrm{m}3}V}_1}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+g_{\mathrm{m}1}{g}_{\mathrm{m}3}}\right],$$

(4)

$${\omega }_0=\sqrt{\frac{g_{\mathrm{m}1}{g}_{\mathrm{m}3}}{C_1{C}_2}},$$

(5)

$$Q=\frac{1}{g_{\mathrm{m}2}}\sqrt{\frac{g_{\mathrm{m}1}{g}_{\mathrm{m}3}{C}_2}{C_1}}.$$

(6)

3.2. Operation in Current- and Trans-Impedance-Modes

In CM mode, the input voltage ($V_{\mathrm{IN}}$) is set to zero and input currents are applied according to

Table 4. Input current excitation sequence.

Response	Inputs
	I1	I2	I3	I4
LP	Iin	0	0	0
HP	Iin	Iin	Iin	Iin
BP	0	Iin	0	0
BR	0	Iin	Iin	Iin
AP	Iin	2Iin	Iin	Iin

to obtain all five filter responses. Equations (7) and (8) give the transfer functions of the CM modes.

$$I_{\mathrm{OUT}\left(\mathrm{CM}\right)}=\frac{{(s}^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+g_{\mathrm{m}1}{g}_{\mathrm{m}3})I_3-s{C}_1{g}_{\mathrm{m}2}{I}_2-g_{\mathrm{m}1}{g}_{\mathrm{m}2}{I}_1}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+g_{\mathrm{m}1}{g}_{\mathrm{m}3}},$$

(7)

$$V_{\mathrm{OUT}\left(\mathrm{TIM}\right)}=R_1\left[\frac{{(s}^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+g_{\mathrm{m}1}{g}_{\mathrm{m}3})I_4-s{C}_1{g}_{\mathrm{m}2}{I}_2-g_{\mathrm{m}1}{g}_{\mathrm{m}2}{I}_1}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+g_{\mathrm{m}1}{g}_{\mathrm{m}3}}\right].$$

(8)

In the current- and trans-impedance-modes of operation, only three input currents will be used. For CM, currents $I_1$, $I_2$, $I_3$ and for TIM currents $I_1$, $I_2$, $I_4$ will be applied, respectively. In addition, to realize AP response $I_2$ with double magnitude is required. It can be easily generated by applying two currents of equal magnitude at the input node without requiring any additional hardware. Furthermore, the gain of the TIM response can be adjusted using the resistor $R_1$.

3.3. SIMO Filter Configuration

Figure 3 shows the SIMO filter topology. It can be seen from the figure that the core circuit remain unchanged and the resistor $R_1$ is no longer required leading to resistorless implementation. The only drawback is the availability of the HP output through the capacitor. The HP current can be sensed using a current follower. In the SIMO configuration, the filter can function in CM mode by providing all five filter responses.

For the current-mode of operation, $V_{\mathrm{IN}}$ is set to zero and current $I_{\mathrm{IN}}$ is applied to the filter topology. The transfer functions in the CM are given in Equations (9)–(13), while a corresponding quality factor and pole frequency are given in Equations (14) and (15).

$$\frac{I_{\mathrm{LP}}}{I_{\mathrm{IN}}}=\frac{g_{\mathrm{m}1}{g}_{\mathrm{m}3}}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+g_{\mathrm{m}2}{g}_{\mathrm{m}3}},$$

(9)

$$\frac{I_{\mathrm{HP}}}{I_{\mathrm{IN}}}=\frac{s^2{C}_1{C}_2}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+g_{\mathrm{m}2}{g}_{\mathrm{m}3}},$$

(10)

$$\frac{I_{\mathrm{BP}}}{I_{\mathrm{IN}}}=\frac{-s{C}_1{g}_{\mathrm{m}2}}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+g_{\mathrm{m}2}{g}_{\mathrm{m}3}}.$$

(11)

$$\frac{I_{\mathrm{BR}}}{I_{\mathrm{IN}}}=\frac{g_{\mathrm{m}1}{g}_{\mathrm{m}3}+s^2{C}_1{C}_2}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+g_{\mathrm{m}2}{g}_{\mathrm{m}3}},$$

(12)

$$\frac{I_{\mathrm{AP}}}{I_{\mathrm{IN}}}=\frac{g_{\mathrm{m}1}{g}_{\mathrm{m}3}-s{C}_1{g}_{\mathrm{m}2}+s^2{C}_1{C}_2}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+g_{\mathrm{m}2}{g}_{\mathrm{m}3}},$$

(13)

$${\omega }_0=\sqrt{\frac{g_{\mathrm{m}2}{g}_{\mathrm{m}3}}{C_1{C}_2}},$$

(14)

$$Q=\sqrt{\frac{g_{\mathrm{m}3}{C}_2}{{g_{\mathrm{m}2}C}_1}}.$$

(15)

Note that the BR and AP responses can be obtained by summing the LP, HP, and BP currents, $I_{\mathrm{BR}}=I_{\mathrm{LP}}+I_{\mathrm{HP}}$ and $I_{\mathrm{AP}}=I_{\mathrm{LP}}+I_{\mathrm{HP}}+I_{\mathrm{BP}}$.

4. Non-Ideal Analysis

The mismatch between current mirrors, process variation and the device mismatch between the MOS transistors results in variation in the frequency dependent voltage and current transfer gains of the VDBA. This change in the gain from the ideal value of unity results in the deviation in the center frequency and quality factor of the filter. The effect of frequency dependent non-deal voltage and current transfer gains is analyzed in this section. The ($\beta$) denotes the frequency dependent non-ideal voltage transfer gain and $\left(\gamma \right)$ represents the transconductance transfer gain of the OTA. Considering the effect of the non-ideal gains the V-I characteristics of the VDBA will be modified as given in Equations (16)–(18), where ${\beta }_m=1-{ϵ}_{\mathrm{v}m}$ and ${\gamma }_m=1-{ϵ}_{\mathrm{gm}}$, for $m=1,2$, which refers to the number of VDBAs. Here, ${ϵ}_{\mathrm{v}m}\left(\right|{ϵ}_{\mathrm{v}m}\left|\ll 1\right)$ denote voltage tracking error, and ${ϵ}_{\mathrm{gm}}\left(\right|{ϵ}_{\mathrm{gm}}\left|\ll 1\right)$ denote transconductance errors of the VDBA.

The modified transfer function and expressions for center frequency and quality factor including the non-ideal effect is given in Equations (19)–(24) for the MISO filter. The non-idealities result in deviations from the expected value.

$$I_{\mathrm{Z}}=I_{\mathrm{ZC}+}=\gamma g_{\mathrm{m}}(V_{\mathrm{P}}-V_{\mathrm{N}}),$$

(16)

$$I_{\mathrm{ZC}-}=\gamma {}^{\prime }{g}_{\mathrm{m}}(V_{\mathrm{P}}-V_{\mathrm{N}}),$$

(17)

$$V_{\mathrm{Z}}={\beta }_{\mathrm{m}}{V}_{\mathrm{W}}.$$

(18)

$$V_{\mathrm{OUT}\left(\mathrm{VM}\right)}={\beta }_1\left[\frac{s^2{C}_1{C}_2{V}_2-s{C}_1{g}_{\mathrm{m}1}{\gamma }_1{V}_3+{g_{\mathrm{m}1}{g}_{\mathrm{m}3}{\gamma }_1{\gamma }_{3}V}_1}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+{\gamma }_1{\gamma }_3{g}_{\mathrm{m}1}{g}_{\mathrm{m}3}}\right],$$

(19)

$$I_{\mathrm{OUT}\left(\mathrm{CM}\right)}=\left[\frac{{(s}^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+{{\gamma }_1{\gamma }_{3}g}_{\mathrm{m}1}{g}_{\mathrm{m}3})I_3-s{C}_1{g}_{\mathrm{m}2}{\gamma }_2{\beta }_1{I}_2-{{\gamma }_1{\gamma }_2{\beta }_{1}g}_{\mathrm{m}1}{g}_{\mathrm{m}2}{I}_1}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+{{\gamma }_1{\gamma }_{3}g}_{\mathrm{m}1}{g}_{\mathrm{m}3}}\right],$$

(20)

$$I_{\mathrm{OUT}\left(\mathrm{TAM}\right)}=-{\gamma }_2{\beta }_1{g}_{\mathrm{m}2}\left[\frac{s^2{C}_1{C}_2{V}_2-s{C}_1{g}_{\mathrm{m}1}{\gamma }_1{V}_3+{g_{\mathrm{m}1}{g}_{\mathrm{m}3}{\gamma }_1{\gamma }_{3}V}_1}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+{{\gamma }_1{\gamma }_{3}g}_1{g}_{\mathrm{m}3}}\right],$$

(21)

$$V_{\mathrm{OUT}\left(\mathrm{TIM}\right)}=R_1\left[\frac{{(s}^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+{{\gamma }_1{\gamma }_{3}g}_{\mathrm{m}1}{g}_{\mathrm{m}3})I_4-s{C}_1{g}_{\mathrm{m}2}{\gamma }_2{\beta }_1{I}_2-{{\gamma }_1{\gamma }_2{\beta }_{1}g}_{\mathrm{m}1}{g}_{\mathrm{m}2}{I}_1}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+{{\gamma }_1{\gamma }_{3}g}_{\mathrm{m}1}{g}_{\mathrm{m}3}}\right],$$

(22)

$${\omega }_0=\sqrt{\frac{{{\gamma }_1{\gamma }_{3}g}_{\mathrm{m}1}{g}_{\mathrm{m}3}}{C_1{C}_2}},$$

(23)

$$Q=\frac{1}{g_{\mathrm{m}2}}\sqrt{\frac{{{\gamma }_1{\gamma }_{3}g}_{\mathrm{m}1}{g}_{\mathrm{m}3}{C}_2}{C_1}}.$$

(24)

The non-ideal expressions of the filter transfer function for the CM SIMO filter are given as follows:

$$\frac{I_{\mathrm{LP}}}{I_{\mathrm{IN}}}=\frac{{\gamma }_1{\gamma }_3{g}_{\mathrm{m}1}{g}_{\mathrm{m}3}}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+{{\gamma }_1{\gamma }_{3}g}_{\mathrm{m}1}{g}_{\mathrm{m}3}},$$

(25)

$$\frac{I_{\mathrm{HP}}}{I_{\mathrm{IN}}}=\frac{s^2{C}_1{C}_2}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+{{\gamma }_1{\gamma }_{3}g}_{\mathrm{m}1}{g}_{\mathrm{m}3}},$$

(26)

$$\frac{I_{\mathrm{BP}}}{I_{\mathrm{IN}}}=\frac{-s{C}_1{g}_{\mathrm{m}2}{\gamma }_2}{s^2{C}_1{C}_2+s{C}_1{g}_{\mathrm{m}2}+{{\gamma }_1{\gamma }_{3}g}_{\mathrm{m}1}{g}_{\mathrm{m}3}}.$$

(27)

The sensitivities of ${\omega }_0$ and Q with respect to the non-ideal gain and passive elements are calculated. Equations (28)–(30) indicate identical sensitivities for the MISO mixed-mode universal filter and CM SIMO filter.

$$-S_{C_1}^{{\omega }_0}={-S}_{C_2}^{{\omega }_0}=S_{{\gamma }_1}^{{\omega }_0}=S_{{\gamma }_3}^{{\omega }_0}=S_{g_{\mathrm{m}1}}^{{\omega }_0}=S_{g_{\mathrm{m}3}}^{{\omega }_0}=\frac{1}{2},$$

(28)

$$-S_{C_1}^Q=S_{g_{\mathrm{m}1}}^Q=S_{g_{\mathrm{m}3}}^Q=S_{C_2}^Q=S_{{\gamma }_1}^Q=S_{{\gamma }_3}^Q=\frac{1}{2},$$

(29)

$${-S}_{g_{\mathrm{m}2}}^Q=1.$$

(30)

The sensitivities are not greater than one, which is desired.

5. Parasitic Analysis

The block diagram presented in Figure 4 shows the various parasitic impedance associated with different terminals of the VDBA. The parasitic resistances and capacitance appear in parallel with the P, N, and Z terminals. The low impedance W terminal has a resistance in series with the inductance. For the frequency of interest, the inductance effect can be ignored. The denominator of the filter transfer function is modified in the presence of the parasitic effect as given in Equation (31).

$$D^{\prime }\left(s\right)\cong s^2{C}_1^{\prime }{C}_2^{\prime }+{sC}_1^{\prime }{g}_{\mathrm{m}2}+{sC}_2^{\prime }{R}_{\mathrm{A}}^{\prime }+g_{\mathrm{m}2}{R}_{\mathrm{A}}^{\prime }+g_{\mathrm{m}1}{g}_{\mathrm{m}3}+R_{\mathrm{B}}{sC}_1^{\prime }+{R_{\mathrm{B}}R}_{\mathrm{A}}^{\prime }$$

(31)

where $R_{\mathrm{A}}^{\prime }\cong R_{\mathrm{P}1}\left|\right|R_{\mathrm{Z}3},R_1^{\prime }\cong R_1\left|\right|R_{\mathrm{Z}2},R_{\mathrm{B}}\cong R_{\mathrm{N}2}\left|\right|R_{\mathrm{Z}1}\left|\right|R_{\mathrm{Z}2},C_1^{\prime }\cong C_1+C_{\mathrm{P}1}+C_{\mathrm{Z}3}$ and $C_2^{\prime }\cong C_2+s{C}_{\mathrm{N}2}+C_{\mathrm{Z}1}+C_{\mathrm{Z}2}$.

$$V_{\mathrm{OUT}\left(\mathrm{VM}\right)}^{\prime }\cong \frac{{(s}^2{C_1^{\prime }{C}_2^{\prime }+R_{\mathrm{A}}^{\prime })V}_2-({sC}_1^{\prime }{+R_{\mathrm{A}}^{\prime })g}_{\mathrm{m}1}{V}_3+{g_{\mathrm{m}1}{g}_{\mathrm{m}3}V}_1}{s^2{C}_1^{\prime }{C}_2^{\prime }+C_1^{\prime }{g}_{\mathrm{m}2}+{sC}_2^{\prime }{R}_{\mathrm{A}}^{\prime }+g_{\mathrm{m}2}{R}_{\mathrm{A}}^{\prime }+g_{\mathrm{m}1}{g}_{\mathrm{m}3}+R_{\mathrm{B}}{sC}_1^{\prime }+{R_{\mathrm{B}}R}_{\mathrm{A}}^{\prime }}$$

(32)

$$I_{\mathrm{OUT}\left(\mathrm{CM}\right)}^{\prime }\cong \frac{(s^2{C}_1^{\prime }{C}_2^{\prime }+{sC}_1^{\prime }{g}_{\mathrm{m}2}+{sC}_2^{\prime }{R}_{\mathrm{A}}^{\prime }+g_{\mathrm{m}2}{R}_{\mathrm{A}}^{\prime }+g_{\mathrm{m}1}{g}_{\mathrm{m}3})I_3-({sC}_1^{\prime }{+R_{\mathrm{A}}^{\prime })g}_{m2}{I}_2-{g_{\mathrm{m}1}{g}_{\mathrm{m}2}I}_1}{s^2{C}_1^{\prime }{C}_2^{\prime }+{sC}_1^{\prime }{g}_{\mathrm{m}2}+{sC}_2^{\prime }{R}_{\mathrm{A}}^{\prime }+g_{\mathrm{m}2}{R}_{\mathrm{A}}^{\prime }+g_{\mathrm{m}1}{g}_{\mathrm{m}3}+R_{\mathrm{B}}{sC}_1^{\prime }+{R_{\mathrm{B}}R}_{\mathrm{A}}^{\prime }}$$

(33)

$$Q^{\prime }\cong \sqrt{\frac{g_{\mathrm{m}2}{R}_{\mathrm{A}}^{\prime }+g_{\mathrm{m}1}{g}_{\mathrm{m}3}+{R_{\mathrm{B}}R}_{\mathrm{A}}^{\prime }}{C_1^{\prime }{C}_2^{\prime }}\times {\left(\frac{C_1^{\prime }{C}_2^{\prime }}{C_1^{\prime }{g}_{\mathrm{m}2}+C_2^{\prime }{R}_{\mathrm{A}}^{\prime }+R_{\mathrm{B}}{C}_1^{\prime }}\right)}^2}$$

(34)

$${\omega }_0^{\prime }\cong \sqrt{\frac{g_{\mathrm{m}2}{R}_{\mathrm{A}}^{\prime }+g_{\mathrm{m}1}{g}_{\mathrm{m}3}+{R_{\mathrm{B}}R}_{\mathrm{A}}^{\prime }}{C_1^{\prime }{C}_2^{\prime }}}$$

(35)

If $R_{\mathrm{P}1}$ and $R_{\mathrm{Z}3}$ are made greater, the $R_{\mathrm{A}}^{\prime }\cong 0$ the expression for $Q^{\prime }$ and ${\omega }_0^{\prime }$ will be simplified as given below.

$$Q^{\prime }\cong \frac{1}{g_{\mathrm{m}2}+R_{\mathrm{B}}}\sqrt{\frac{C_2^{\prime }\left(g_{\mathrm{m}1}{g}_{\mathrm{m}3}\right)}{C_1^{\prime }}}$$

(36)

$${\omega }_0^{\prime }\cong \sqrt{\frac{g_{\mathrm{m}1}{g}_{\mathrm{m}3}}{C_1^{\prime }{C}_2^{\prime }}}$$

(37)

6. Simulation Results

To validate the performance of the designed VDBA-based mixed-mode universal filter, it was designed and simulated in Silterra Malaysia $0.18\mathsf{\mu }\mathrm{m}$ technology using Cadence Virtuoso software. The supply voltages ±1.25 V are used. The width and length of the MOS transistors in Figure 1b are given in

Table 5. Width and length of the MOS transistors.

Transistor	Width ($\mathsf{\mu }$m)	Length ($\mathsf{\mu }$m)
M1–M4, M10–M16	1.8	0.36
M5–M9	5.4	0.36
M17–M18	1.2	0.36
M19–M20	4.8	0.36
M21	2.4	0.36

, while the design metrics of the VDBA active block are listed in

Table 6. Performance metrics of the VDBA.

Parameters	Values
Parasitics at nodes P and N @ 1 kHz:
$R_{\mathrm{P}}=R_{\mathrm{N}}$	25 G$\mathsf{\Omega }$
Parasitics at W node: $R_{\mathrm{W}}$, $L_{\mathrm{W}}$	140.89 $\mathsf{\Omega }$, 0.923 $\mathsf{\mu }$H
Parasitics at nodes Z, ZC + ZC−:
$R_{\mathrm{Z}}=R_{\mathrm{ZC}+}=R_{\mathrm{ZC}-}$, $C_{\mathrm{Z}}=C_{\mathrm{ZC}+}=C_{\mathrm{ZC}-}$	64.4 k$\mathsf{\Omega }$, 26.3 fF
Voltage gain: $V_{\mathrm{W}}/V_{\mathrm{Z}}$	0.985
Voltage transfer bandwidth: $V_{\mathrm{W}}/V_{\mathrm{Z}}$	3.0262 GHz
DC voltage range: $V_{\mathrm{Z}}-V_{\mathrm{W}}$	±900 mV
Static power dissipation	1.618 mW

.

The developed filter is designed for a pole frequency of 16.631 MHz by selecting component values as $C_1=C_2=10\mathrm{pF}$, $R_1=1\mathrm{k}\mathsf{\Omega }$, and $g_{\mathrm{m}(1-3)}=1.045\mathrm{mA}/\mathrm{V}$. It must be mentioned that results provided for the filter are pre-layout results considering the nominal values as provided in the Silerra Malaysia PDK. The proposed filter is suitable for wide variety of applications in industrial signal processing and wireless communication, etc. The frequency-domain responses of the filter in all four modes are presented in Figure 5, Figure 6, Figure 7 and Figure 8. To test the quality factor tuning independent of the frequency BP response is plotted for different values of the bias current $I_{\mathrm{Bias}1}$. It can be inferred from Figure 9 that the quality factor can be tuned without disturbing the frequency.

As the OTA offset current can cause frequency and phase deviation in the designed filter, Monte Carlo analysis is carried out for 200 runs to obtain an accurate measure of the offset current at the (Z, ZC + ) terminals of the OTA. The $I_{\mathrm{Bias}}$ of OTA is set at 120 $\mathsf{\mu }$A. The results show minimum offset current $=1.08\mathsf{\mu }$A, maximum offset current $=18.131\mathsf{\mu }$A, mean offset current $=10.87\mathsf{\mu }$A and standard deviation $=4.20\mathsf{\mu }$A. To verify the signal processing capability of the filter, transient analysis is performed for BP responses in the VM and CM mode. In VM, a sinusoidal signal of 16.6 MHz frequency and 200 mV peak-to-peak is applied at the input and the output waveform is observed as given in Figure 10a. In CM, a sinusoidal signal of 16.6 MHz frequency and 100 $\mathsf{\mu }$A peak-to-peak is applied and the output waveform is presented in Figure 10b. It can be observed that the filter functions correctly.

To study the effect of process spread on the designed filter, Monte Carlo analysis is done for 200 runs for VM BP and CM AP configurations as presented in Figure 11a,b. It can be deduced from the figures that there is no large variation in the pole frequency of the filter due to process variations.

The THD of the proposed filter for LP, HP, and BP responses is plotted for different input signal amplitudes for VM, as shown in Figure 12a. The THD plot for CM-BP/LP is presented in Figure 12b. As per the IEEE Std 519-2014 [55] the THD of the filter remains within acceptable limits (≤5%) for a considerable input signal range. Moreover, the THD performance of the filter is at par with other reported mixed-mode filters [10,11,13,14,15,19].

The reduction in the frequency of the filter due to the increase in temperature can be ascribed to the decrease in the transconductance of the OTA. The major factors affecting the transconductance are carrier mobility ($\mu$) and threshold voltage ($V_t$). The carrier mobility dependence on temperature can be modeled by Equation (38):

$${\mu }_{\mathrm{N}}\left(T\right)={\mu }_{\mathrm{N}}\left(T_{\mathrm{O}}\right){\left(\frac{T}{T_{\mathrm{O}}}\right)}^{{\alpha }_{\mu }},$$

(38)

where ${\alpha }_{\mu }$ stands for the mobility temperature exponent, it is considered constant roughly equal to 1.5. The threshold voltage $V_t$ can be approximated as a linear function of temperature [56,57] given by Equation (39):

$$V_t\left(T\right)=V_t\left(T_{\mathrm{O}}\right) + {\alpha }_{V_t}\left(T-T_{\mathrm{O}}\right),$$

(39)

here, ${\alpha }_{V_t}$ denotes the threshold voltage temperature coefficient, which varies from −1 mV/${}^{\circ }$C to −4 mV/${}^{\circ }$C and $T_{\mathrm{O}}$ is the reference temperature (300 K). These two Equations exhibit negative temperature dependence and this correlates with the decrease in the filter frequency with temperature as observed in Figure 13. The effect of noise on the performance of the proposed filter is also analyzed. The thermal and flicker noise are present in the bulk CMOS devices, and they effect the performance of the designed filter. Figure 14 gives the plot of the input and output noise for the BP VM filter configuration. At the pole frequency of the filter the input and output noises are found to be 36.2 nV/$\sqrt{\mathrm{Hz}}$ and 36.48 nV/$\sqrt{\mathrm{Hz}}$, respectively. It can be seen from the figure that the input and output noise are well within the acceptable limits.

To verify the CM SIMO filter, it is designed with the exact specifications of the MISO filter. The frequency responses of the filter are shown in Figure 15.

The time domain and THD analysis for the SIMO current-mode filter are presented in Figure 16 and Figure 17. The results validate the correct functioning of the designed filter.

The Monte Carlo analysis results for the designed CM BP filter response are presented in Figure 18. The frequency response and the static variations in the designed frequency are under acceptable limits.

To highlight the advantages of the designed filter, it is compared with some exemplary designs of mixed-mode filters, as shown in

Table 7. Comparison of the proposed filter with other similar topologies.

References	No. of ABBs	No. of PassiveComponents	IndependentTuning of Q	All Five Filter Responses Available in Four Operation Modes	Low Output Impedance for VM and TIM	No Requirement for Double/Negative Input Signals Voltage	In-BuiltTunability	TestFrequency(MHz)	Power Dissipation (W)	Supply Voltage (V)	THD
[5]/2003	6-OTA	2C	No	No	No	Yes	Yes	–	–	–	–
[6]/2004	7-CCII	2C + 8R	No	Yes	No	Yes	No	–	–	–	–
[7]/2006	3-CCII	3C + 4R + 2-switch	No	Yes	No	Yes	No	–	–	±12	–
[8]/2008	4-OTA	2C	No	No	No	Yes	Yes	2.25	–	–	–
[9]/2010	5-OTA	2C	No	Yes	No	No	Yes	1.59	–	±1.25	0.777% @ 0.4 VP-P (for LP VM mode)
[10]/2010	2-MOCCCII	2C + 2R	Yes	Yes	No	Yes	Yes	1.27	–	±2.5	≤3% @ 100 μA (for BP CM mode)
[11]/2013	4-MOCCCII	2C	No	Yes	Yes	No	Yes	–	–	±1.25	≥0.5% @ 150 μA
[12]/2013	1-FDCCII	2C + 2R	No	No	No	Yes	No	10	–	±0.9	–
[13]/2013	2-VDTA	2C	Yes	No	No	Yes	Yes	1	–	±1.5	≤3% @ 400 mV (for BP VM mode)
[14]/2010	1-CFOA	2C + 3R	Yes	No	No	No	No	12.7	2.53 m	±1.25	≥4% @ 40 μA (for BP CM mode)
[15]/2016	1-FDCCII +1-DDCC	2C + 6R	Yes	Yes	No	No	No	1.59	–	±0.9	≤4% @ 400 mV (for AP VM mode)
[16]/2018	5-DVCC	2C + 5R	Yes	Yes	No	Yes	No	1	471 $\mathsf{\mu }$	±0.8	–
[17]/2019	5-OTA	2C	Yes	Yes	No	Yes	Yes	3.39	191.7 $\mathsf{\mu }$	±0.9	–
[18]/2020	3-DDCCII	2C + 4R	No	Yes	No	Yes	No	3.978	–	±1.25	–
[19]/2016	1-MCCTA	2C + 2R	Yes	Yes	No	Yes	Yes	12.16	–	–	≤3% @ 70 μA (for BP CM mode)
[20]/2018	4-CCII	2C + 4R	Yes	No	No	Yes	No	31.8	–	–	–
This work	3-VDBA	2C + R	Yes	Yes	Yes	Yes	Yes	16.32	5.482 m	±1.25	≤4% @ 350 mV (for HP VM mode)

. By analyzing the comparison table, it can be observed that the proposed filter structure holds certain advantages over the other similar designs and also performs at par with other designs in terms of power dissipation, supply voltage, and total harmonic distortion, in addition to being the first truly mixed-mode filter based on the VDBA. The authors would like to point out that the recently reported VDBA-based mixed-mode filter designs [54,58] are not truly mixed-mode as they cannot provide all five filter responses in all four modes of operation. Furthermore, in [58] the output currents are not available from high-impedance nodes; hence extra current followers will be needed to extract the currents.

7. Experimental Validation

To further verify the correct functioning of the proposed filter circuit and to complement the theoretical and simulation results, detailed experimental analysis is carried out for MISO VM and TAM modes and SIMO CM configuration. The VDBA is built with available integrated circuits (ICs), the Intersil CA3080 OTAs and Texas Instruments LF356 op-amp, as shown in Figure 19. The supply voltages are set ±5 V.

To design the filter for a pole frequency of $f_0=$ $\omega$${}_0/2\pi$ = 100.27 kHz and $Q=1$, the active component values are selected as $g_{\mathrm{m}}=g_{\mathrm{m}i}$$(g_{\mathrm{m}}$ of i-th VDBA, i= 1, 2, 3) = 0.63 mA/V (I${}_{\mathrm{B}}$ = 31.5 $\mathsf{\mu }$A), where $g_{\mathrm{m}}=\frac{I_{\mathrm{B}}}{2V_{\mathrm{T}}}$ and $V_{\mathrm{T}}$ is thermal voltage ≅ 25 mV at 27 ${}^{\circ }$C. In all measurements, the passive components are chosen as $R_1=1\mathrm{k}\mathsf{\Omega }$, and $C_1=C_2=1\mathrm{nF}$. The measured LP, HP, BP, BR, and AP frequency response results of the VM MISO configuration in Figure 2 are given in Figure 20. Figure 21 also presents the measured time-domain responses for LP, HP, BP, and BR filters, when the sinusoidal input signal of an amplitude 100 mV peak-to-peak at 100 kHz is applied. In addition, the measurement of input and output voltage waveforms of the VM AP filter and the FFT analysis results at the $V_{\mathrm{OUT}}$ output terminal are given in Figure 22, respectively.

For obtaining the TAM and CM SIMO filter results, two additional Analog Devices AD844s and a converting resistor ($R_{\mathrm{C}}$) are employed to covert current to voltage. The circuit is shown in Figure 23, where the value of $R_{\mathrm{C}}$ is equal to 1 k$\mathsf{\Omega }$. Figure 24 shows the measured TAM filtering responses with the same component values as described above for $f_0=$ 100.27 kHz and $Q=1$. Next, Figure 25 shows the time-domain responses of the proposed TAM operation for LP, BP, HP, and BR filters. In Figure 26, the measured input and output voltage waveforms of the TAM AP filter and its FFT spectrum analysis are, respectively, given.

In the same way, the LP, HP, and BP filter responses of the CM SIMO filter in Figure 3 are presented in Figure 27. In this case, the circuit components are the same as that used in the above design to have the following filter characteristics: $f_0=$ 100.27 kHz and $Q=1$. As expected, the experimental results of the CM SIMO configuration are close to the theoretical results.

From the experimental results, it is evident that the proposed filter topologies are practically realizable. The deviation in the measurement results is mainly due to the breadboard circuit implementation. It is expected that, when the filter circuit is fabricated, the behavior of the proposed filter will be very close to the simulation results.

8. Conclusions

In this research, a truly mixed-mode universal filter based on VDBA is proposed. The filter requires three VDBAs, two capacitors, and a resistor for implementation. It provides all five filter responses in all four modes of operation in MISO configuration. A SIMO resistorless CM universal filter can also be derived from the same core arrangement. In MISO configuration, the VM/TIM outputs are available from low impedance nodes and CM/TAM outputs are available from high impedance node leading to cascadability. The filter has a feature of inbuilt tunability as well. The detailed theoretical analysis, non-ideal, and sensitivity analyses are performed to establish the correct functioning of the filter. The VDBA-based filter is designed and validated in Cadence Virtuoso software using Silterra Malaysia $0.18\mathsf{\mu }\mathrm{m}$ PDK. The filter is designed for a characteristic frequency of 16.66 MHz with a ±1.25 V supply. The Monte Carlo analysis shows that the frequency deviation is within acceptable limits. Additionally, the THD is within 5% for a substantial voltage/current input signal range. The experimental validation of the proposed filter is also carried out. The filter is constructed using commercially available ICs. The frequency responses and time-domain results of the filter confirm the correct functioning. The simulation and experimental results are found consistent with the theoretical predictions.