Synthesis of High-Input Impedance Electronically Tunable Voltage-Mode Second-Order Low-Pass, Band-Pass, and High-Pass Filters Based on LT1228 Integrated Circuits

This paper introduces two new high-input impedance electronically tunable voltage-mode (VM) multifunction second-order architectures with band-pass (BP), low-pass (LP), and high-pass (HP) filters. Both proposed architectures have one input and five outputs, implemented employing three commercial LT1228 integrated circuits (ICs), two grounded capacitors, and five resistors. Both proposed architectures also feature one high-impedance input port and three low-impedance output ports for easy connection to other VM configurations without the need for VM buffers. The two proposed VM LT1228-based second-order multifunction filters simultaneously provide BP, LP, and HP filter transfer functions at Vo1, Vo2, and Vo3 output terminals. The pole angular frequencies and the quality factors of the two proposed VM LT1228-based second-order multifunction filters can be electronically and orthogonally adjusted by the bias currents from their corresponding commercial LT1228 ICs, and can be independently adjusted in special cases. In addition, both proposed VM LT1228-based second-order multifunction filters have two independent gain-controlled BP and LP filter transfer functions at Vo4 and Vo5 output terminals, respectively. Based on the three commercial LT1228 ICs and several passive components, simulations and experimental measurements are provided to verify the theoretical predictions and demonstrate the performance of the two proposed high-input impedance electronically tunable VM LT1228-based second-order multifunction filters. The measured input 1-dB power gain compression point (P1dB), third-order IMD (IMD3), third-order intercept (TOI) point, and spurious-free dynamic range (SFDR) of the first proposed filter were −7.1 dBm, −48.84 dBc, 4.133 dBm, and 45.02 dBc, respectively. The measured input P1dB, IMD3, TOI, and SFDR of the second proposed filter were −7 dBm, −49.65 dBc, 4.316 dBm, and 45.88 dBc, respectively. Both proposed filters use a topology synthesis method based on the VM second-order non-inverting/inverting HP filter transfer functions to generate the BP, LP and HP filter transfer functions simultaneously, making them suitable for applications in three-way crossover networks.


Introduction
Electronically tunable active filters and oscillators designed with active components are widely used in sensor applications such as electrocardiography systems [1], biosensors [2], electronically tunable LC oscillators [3], and phase-sensitive detection [4]. Especially in the electronic sensor systems, electronically tunable active filters are used to filter out noise in the sensor systems [5]. An interesting dual-output MOSFET-only filter without any passive components is also presented in [6]. It has proven to be an effective solution for high frequency ranges. Electronically tunable voltage-mode (VM) high-pass filter (HPF), band-pass filter (BPF), and low-pass filter (LPF) topologies suitable for integrated circuit (IC) structures have been a constant endeavor of circuit designers, and have become very important architecture circuits in sensors, analog systems, electrical and electronic engineering works. The choice of active building blocks (ABBs) plays an important role in (i) The filter can simultaneously generate HPF, BPF, and LPF second-order transfer functions, and is suitable for three-way crossover networks. (ii) The parameters of the filter, ω o and Q, permit for electronic and orthogonal controllability. (iii) The filter parameter Q has independent and electronic tuning capability. (iv) The filter provides a high-impedance input suitable for cascading voltage input stages.
(v) The HPF, BPF, and LPF responses provide low-impedance outputs suitable for cascading voltage output stages. (vi) Passive components do not require matching conditions. (vii) The passband gains of the LPF and BPF responses can be controlled effectively and independently without affecting the filter parameters ω o and Q. (viii) Synthesis methods of the filter topologies based on VM non-inverting/inverting HPF second-order transfer functions.
In addition to the three advantages (i) to (iii) realized in [33], these two new circuits provide the functions (iv) to (viii). In Table 1, the main characteristics of the two proposed LT1228-based electronically tunable VM second-order multifunction filters are compared with previous VM second-order multifunction filters implemented using commercially available ICs technology. As shown in Table 1, the two proposed LT1228-based electronically tunable VM second-order multifunction filters have independent gain-controlled LPF and BPF functions and satisfy all the main (i) to (viii) advantages. Both proposed filters use a topology synthesis method based on the VM second-order non-inverting/inverting HPF transfer functions to generate the BPF, LPF, and HPF transfer functions simultaneously, making them suitable for applications in three-way crossover networks [33]. To confirm the circuit performances of both proposed VM multifunction filters, PSpice simulation, measurement and theoretical calculation results are performed using three LT1228 ICs and several passive components.

First Proposed Synthesis Principle and Analysis Theory Based on Inverting HPF Transfer Function
To synthesize the first proposed VM second-order multifunction filter design system block, the VM inverting HPF (IHPF) second-order transfer function with two integrator time constants τ 1 and τ 2 and a voltage passband gain k 1 can be considered as the following function.
V IHPF V in = −k 1 s 2 s 2 + s k 1 τ 1 + 1 where V IHPF is one of the output voltages of the first proposed filter, and V in is the input voltage signal of the circuit.
To decompose the VM IHPF second-order transfer function into the VM non-inverting LPF (NLPF) and non-inverting BPF (NBPF) transfer functions, the terms of Equation (1) can be cross-multiplied first, and then divided by s 2 to obtain Rearranging Equation (2) can be rewritten as This indicates that the NBPF signal can be achieved by cascading the IHPF signal with an inverting loss integrator, and Equation (3) becomes Let V NLPF = 1 sτ 2 V NBPF (6) This means that the NLPF signal can be achieved by cascading the NBPF signal with a non-inverting loss integrator, and Equation (6) becomes According to Equations (4), (6), and (7), the first proposed VM second-order multifunction filter system structure can be synthesized. The output signals of NLPF and NBPF, and the first filter parameters of ω o and Q can be derived as follows.
V NLPF V in = k 1 1 τ 1 τ 2 s 2 + s k 1 τ 1 + 1 τ 1 τ 2 (9) ω o = 1 τ 1 τ 2 (10) Equations (10) and (11) indicate that the parameter Q can be independently tuned by adjusting the voltage gain building block of k 1 without affecting the parameter ω o . In the special case of τ 1 = τ 2 = τ, the parameter ω o can also be independently tuned by τ without affecting the parameter Q. Based on the DC bias current I B of the corresponding LT1228, the first proposed filter parameters of ω o and Q can be controlled electronically and orthogonally.
In Equation (1), the VM IHPF second-order transfer function is decomposed into the VM NLPF and NBPF second-order transfer functions, and the synthesis of the system block diagram can be achieved. Equations (4), (6), and (7) can be rearranged as Equation (12) in the form of an input-output matrix, and the system block diagram synthesis for the first proposed VM LT1228-based filter design is shown in Figure 1. It uses one input voltage node and three output voltage nodes, and consists of a non-inverting lossless integrator, an inverting lossless integrator, and a voltage gain building block. In Figure 1, taking the system blocks of τ1 = C1/gm1, τ2 = C2/gm2 and k1 = gm3R, Equation (12) can be rewritten as In Figure 1, taking the system blocks of τ 1 = C 1 /g m1 , τ 2 = C 2 /g m2 and k 1 = g m3 R, Equation (12) can be rewritten as where C 1 and C 2 are two capacitors, g m1 , g m2 , and g m3 are three LT1228 transconductance amplifiers, and R is a resistor. Solving Equation (13), the parameters ω o and Q of the first filter and the three VM second-order transfer functions of the NBPF, NLPF and IHPF can be obtained as follows.
V NBPF V in = sC 2 g m1 g m3 R s 2 C 1 C 2 + sC 2 g m1 g m3 R + g m1 g m2 (14) V NLPF V in = g m1 g m2 g m3 R s 2 C 1 C 2 + sC 2 g m1 g m3 R + g m1 g m2 (15) V IHPF V in = −s 2 C 1 C 2 g m3 R s 2 C 1 C 2 + sC 2 g m1 g m3 R + g m1 g m2 (16) Equations (17) and (18) indicate that the parameter Q can be independently tuned by adjusting g m3 and/or R without affecting the parameter ω o . In the special case of C 1 = C 2 , and g m1 = g m2 = g m , the parameter ω o can also be independently tuned by g m without affecting the parameter Q. Based on the DC bias current I B of the corresponding LT1228, the filter parameters of ω o and Q can be controlled electronically and orthogonally. Based on Figure 1 and Equation (13), Section 2.2 discusses the first proposed high-input impedance electronically tunable VM one-input five-output second-order multifunction filter based on three LT1228 ICs.

First Proposed VM LT1228-Based Second-Order Multifunction Filter
The LT1228 contains a g m transconductance amplifier with a DC bias current I B and a wide range of voltage-gain [33,49]. Figure 2a,b show the circuit symbol for the commercial LT1228 IC and the package for the 8-pin IC configuration, respectively. In Figure 2b, the g m transconductance differential voltages of V+ and V− have high-input impedance, the current output at Y terminal has high-output impedance, and the voltage at X terminal follows the voltage at Y terminal. The W terminal voltage has good linearity and can be directly connected to an external low resistance value. Therefore, the W terminal of the commercial LT1228 IC is suitable for driving low-impedance loads such as loudspeakers and cables. The supply voltages of V CC and V EE are the positive and negative supply voltages of the commercial LT1228 IC. The port factors of the LT1228 with high-input impedance V+ and V−, low-output impedance W and high-output impedance Y are important in the design of any analog circuits. Figure 3 shows the equivalent circuit of a commercial LT1228 IC, whose ideal property relations can be described by [32,33]: where R T is the transresistance gain of LT1228 and ideal value of R T is close to infinity. The transconductance g m of LT1228 depends on the I B and the g m -value can be described as [32,49] where R B is the bias current control resistor.
where RT is the transresistance gain of LT1228 and ideal value of RT is close to infinity. The transconductance gm of LT1228 depends on the IB and the gm-value can be described as [32,49] where RB is the bias current control resistor.   Based on the synthesis of the system block diagram in Figure 1, the first proposed VM LT1228-based second-order multifunction filter configuration using three commercial LT1228s, five resistors, and two capacitors connected to the ground is shown in Figure 4. The nodal analysis of the first proposed VM LT1228-based second-order multifunction filter configuration can be written as follows.    Based on the synthesis of the system block diagram in Figure 1, the first proposed VM LT1228-based second-order multifunction filter configuration using three commercial LT1228s, five resistors, and two capacitors connected to the ground is shown in Figure 4. The nodal analysis of the first proposed VM LT1228-based second-order multifunction filter configuration can be written as follows. the corresponding W terminal of each LT1228 to provide low output impedance. If C1 C2 = C, gm1 = gm2 = 10IB1 and gm3 = 10IB3, the parameters ωo and Q in Equations (17) and (18 can be rewritten as

1
In this particular case, the parameter ωo can be tuned electronically and inde pendently by the bias current IB1 of LT1228 without affecting the parameter Q, and th parameter Q can also be tuned electronically and independently by the bias current IB3 o LT1228 without affecting the parameter ωo.

Second Proposed Synthesis Principle and Analysis Theory Based on Non-Inverting HPF Transfer Function
To synthesize the second proposed VM second-order multifunction filter design sys tem block, the VM non-inverting HPF (NHPF) second-order transfer function with tw integrator time constants τ3 and τ4 and a voltage passband gain k2 can be considered a the following function.  Equations (21)-(23) can be rearranged in the form of an input-output matrix equation as follows.  Equation (26) is the same as Equation (13), if we let the outputs V o1 = V NBPF , V o2 = V NLPF , and V o3 = V IHPF . Therefore, the first proposed VM LT1228-based second-order multifunc-  Figure 4 simultaneously provides the NBPF, NLPF, and IHPF transfer functions at the V o1 , V o2 , and V o3 outputs, respectively, as shown in Equations (27)- (29). V o1 V in = sC 2 g m1 g m3 R s 2 C 1 C 2 + sC 2 g m1 g m3 R + g m1 g m2 (27) V o2 V in = g m1 g m2 g m3 R s 2 C 1 C 2 + sC 2 g m1 g m3 R + g m1 g m2 (28) V o3 V in = −s 2 C 1 C 2 g m3 R s 2 C 1 C 2 + sC 2 g m1 g m3 R + g m1 g m2 (29) Based on Equations (27)- (29), the first proposed filter parameters of ω o and Q are the same as Equations (17) and (18). According to Equations (24) and (25), the first proposed VM LT1228-based second-order multifunction filter has two independent gain-controlled BPF and LPF transfer functions at V o4 and V o5 output terminals, respectively, as shown in Equations (30) and (31).
g m1 g m2 g m3 R s 2 C 1 C 2 + sC 2 g m1 g m3 R + g m1 g m2 (31) In Equations (30) and (31), the first filter has two independent gain-controlled BPF and LPF transfer functions at the V o4 and V o5 outputs, and its four resistors of R 1 , R 2 , R 3 and R 4 can be tuned to independent gain control without affecting the design parameters of ω o and Q. In Figure 4, the three output voltage nodes V o3 , V o4 , and V o5 are connected to the corresponding W terminal of each LT1228 to provide low output impedance. If C 1 = C 2 = C, g m1 = g m2 = 10I B1 and g m3 = 10I B3 , the parameters ω o and Q in Equations (17) and (18) can be rewritten as In this particular case, the parameter ω o can be tuned electronically and independently by the bias current I B1 of LT1228 without affecting the parameter Q, and the parameter Q can also be tuned electronically and independently by the bias current I B3 of LT1228 without affecting the parameter ω o .

Second Proposed Synthesis Principle and Analysis Theory Based on Non-Inverting HPF Transfer Function
To synthesize the second proposed VM second-order multifunction filter design system block, the VM non-inverting HPF (NHPF) second-order transfer function with two integrator time constants τ 3 and τ 4 and a voltage passband gain k 2 can be considered as the following function.
where V NHPF is one of the output voltages of the second proposed filter, and V in is the input voltage signal of the circuit To decompose the VM NHPF second-order transfer function into the VM inverting LPF (ILPF) and NBPF transfer functions, the terms of Equation (34) can be cross-multiplied first, and then divided by s 2 to obtain Rearranging Equation (35) can be rewritten as This indicates that the NBPF signal can be achieved by cascading the NHPF signal with a non-inverting loss integrator, and Equation (37) becomes Let This means that the ILPF signal can be achieved by cascading the NBPF signal with an inverting loss integrator, and Equation (39) becomes (40) According to Equations (37), (39), and (40), the second proposed VM second-order multifunction filter system structure can be synthesized. The output signals of NBPF and ILPF, and the second filter parameters of ω o and Q can be derived as follows.
Equations (43) and (44) indicate that the parameter Q can be independently tuned by adjusting the voltage gain building block of k 2 without affecting the parameter ω o . In the special case of τ 3 = τ 4 = τ, the parameter ω o can also be independently tuned by τ without affecting the parameter Q. Based on the DC bias current I B of the corresponding LT1228, the second proposed filter parameters of ω o and Q can be controlled electronically and orthogonally.
In Equation (34), the VM NHPF second-order transfer function is decomposed into the VM NBPF and ILPF second-order transfer functions, and the synthesis of the system block diagram can be achieved. Equations (37), (39), and (40) can be rearranged as Equation (45) in the form of an input-output matrix equation, and the system block diagram synthesis for the second proposed VM LT1228-based second-order multifunction filter design is shown in Figure 5. It uses one input voltage node and three output voltage nodes, and consists of a non-inverting lossless integrator, an inverting lossless integrator, and a voltage gain building block.    In Figure 5, taking the system blocks of τ3 = C3/gm4, τ4 = C4/gm5, and k2 = gm6R, Equation (45) can be rewritten as where C3 and C4 are two capacitors, gm4, gm5, and gm6 are three LT1228 transconductanc amplifiers, and R is a resistor. Solving Equation (46), the parameters ωo and Q of the sec ond filter and the three VM second-order transfer functions of the NBPF, ILPF, and NHPF can be obtained as follows.
(50 Figure 5. Synthesis of the second proposed VM LT1228-based filter system module with two integrator loops and a voltage gain building block. In Figure 5, taking the system blocks of τ 3 = C 3 /g m4 , τ 4 = C 4 /g m5 , and k 2 = g m6 R, Equation (45) can be rewritten as where C 3 and C 4 are two capacitors, g m4 , g m5 , and g m6 are three LT1228 transconductance amplifiers, and R is a resistor. Solving Equation (46), the parameters ω o and Q of the second filter and the three VM second-order transfer functions of the NBPF, ILPF, and NHPF can be obtained as follows.
V NBPF V in = sC 4 g m4 g m6 R s 2 C 3 C 4 + sC 4 g m4 g m6 R + g m4 g m5 (47) V ILPF V in = −g m4 g m5 g m6 R s 2 C 3 C 4 + sC 4 g m4 g m6 R + g m4 g m5 (48) V NHPF V in = s 2 C 3 C 4 g m6 R s 2 C 3 C 4 + sC 4 g m4 g m6 R + g m4 g m5 (49) ω o = g m4 g m5 C 3 C 4 (50) Equations (50) and (51) indicate that the parameter Q can be independently tuned by adjusting g m6 and/or R without affecting the parameter ω o . In the special case of C 3 = C 4 , and g m4 = g m5 = g m , the parameter ω o can also be independently tuned by g m without affecting the parameter Q. Based on the DC bias current I B of the corresponding LT1228, the filter parameters of ω o and Q can be controlled electronically and orthogonally. Based on Figure 5 and Equation (46), Section 2.4 discusses the second proposed high-input impedance electronically tunable VM one-input five-output second-order multifunction filter based on three LT1228 ICs.

Second Proposed VM LT1228-Based Second-Order Multifunction Filter
Based on the synthesis of the system block diagram in Figure 5, the second proposed VM LT1228-based second-order multifunction filter configuration using three commercial LT1228s, five resistors and two capacitors connected to the ground is shown in Figure 6. The nodal analysis of the second proposed VM LT1228-based second-order multifunction filter configuration can be written as follows.  (51) indicate that the parameter Q can be independently tuned b adjusting gm6 and/or R without affecting the parameter ωo. In the special case of C3 = C and gm4 = gm5 = gm, the parameter ωo can also be independently tuned by gm without af fecting the parameter Q. Based on the DC bias current IB of the corresponding LT1228, th filter parameters of ωo and Q can be controlled electronically and orthogonally. Based o Figure 5 and Equation (46), Section 2.4 discusses the second proposed high-input imped ance electronically tunable VM one-input five-output second-order multifunction filte based on three LT1228 ICs.

Second Proposed VM LT1228-Based Second-Order Multifunction Filter
Based on the synthesis of the system block diagram in Figure 5, the second propose VM LT1228-based second-order multifunction filter configuration using three commercia LT1228s, five resistors and two capacitors connected to the ground is shown in Figure 6 The nodal analysis of the second proposed VM LT1228-based second-order multifunctio filter configuration can be written as follows. Figure 6. Second proposed VM LT1228-based second-order multifunction filter configuration.
In Equations (61) and (62), the second filter has two independent gain-controlled BPF and LPF transfer functions at the V o4 and V o5 outputs, and its four resistors of R 5 , R 6 , R 7 , and R 8 can be tuned to independent gain control without affecting the design parameters of ω o and Q. In Figure 6, the three output voltage nodes V o3 , V o4 , and V o5 are connected to the corresponding W terminal of each LT1228 to provide low output impedance. If C = C 3 = C 4 , g m4 = g m5 = 10I B4 , and g m6 = 10I B6 , the parameters ω o and Q in Equations (50) and (51) can be rewritten as In this particular case, the parameter ω o can be tuned electronically and independently by the bias current I B4 of LT1228 without affecting the parameter Q, and the parameter Q can also be tuned electronically and independently by the bias current I B6 of LT1228 without affecting the parameter ω o .

Simulation and Experimental Results
To verify the operation of the two proposed filter topologies in Figures

Verification of the First Proposed VM LT1228-Based Multifunction Filter
To verify the operability of the first proposed VM LT1228-based multifunction filter at f o = 159.15 kHz and Q = 1, two capacitors C 1 = C 2 = 1 nF, five resistors R = R 1 = R 2 = R 3 = R 4 = 1 kΩ, and three commercial LT1228 ICs with bias currents of I B1 = I B2 = I B3 = 100 µA were chosen.  Figure 16 shows that the simulation results of the Q-value can specify the recommended independent control without affecting the pole frequency. In Figure 16, the simulated Q-value was varied for Q = {2.56, 4.06, 5.01, 5.95} via the three bias currents I B1 = I B2 = 100 µA and I B3 = {40, 25, 20, 16.6} µA. This is expected since the output swing distortion limits the Qvalue below 6, and the Q-value error remains below 2%. Figure 17 shows the frequency tunability results of the first proposed filter simulated at the V o1 output voltage. In Figure 17 Figures 18 and 19 show the frequency tunability results of the first proposed filter simulated at the V o2 and V o3 output voltages, respectively. In Figure Table 2 shows the measured phase error between the output and input waveforms at an operating pole frequency of 159.15 kHz. In Table 2, the maximum phase error measured in the timedomain at an operating pole frequency of 159.15 kHz is less than 0.97 • . Figure 28 shows the NBPF total harmonic distortion (THD) measured at V o1 versus different input voltage signals. In Figure 28, the THD is below 2% when the input peak-to-peak voltage increases to 220 m V pp . Figure 29 illustrates the simulated noise performance at the V o1 output voltage of the first proposed circuit. As shown in Figure 29, the total equivalent input and output noise voltages at the operating pole frequency were 86. 33 Table 3 shows the simulated and measured pole frequency errors for the first proposed circuit. In Table 3, the maximum percentage error of the pole frequency measured in the frequency-domain is less than 1.22%. According to   Table 3, the amplitude and phase responses of the first proposed circuit agree with the simulated and measured results.

Verification of the First Proposed VM LT1228-Based Multifunction Filter
To verify the operability of the first proposed VM LT1228-based multifunct at fo = 159.15 kHz and Q = 1, two capacitors C1 = C2 = 1 nF, five resistors R = R1 = R4 = 1 kΩ, and three commercial LT1228 ICs with bias currents of IB1 = IB2 = IB3 = were chosen. Figures 11-15 illustrate the simulation results of the filter magnit phase responses of the first proposed circuit in Figure 4. From Figures 11-15, the   Figure 4. Based on the ideal pole phase marked in the frequency-domain characteristics, Table 3 shows the simulated and measured pole frequency errors for the first proposed circuit. In Table 3, the maximum percentage error of the pole frequency measured in the frequency-domain is less than 1.22%. According to   Table 3, the amplitude and phase responses of the first proposed circuit agree with the simulated and measured results.       Figure 4. Based on the ideal pole phase marked in the frequency-domain characteristics, Table 3 shows the simulated and measured pole frequency errors for the first proposed circuit. In Table 3, the maximum percentage error of the pole frequency measured in the frequency-domain is less than 1.22%. According to   Table 3, the amplitude and phase responses of the first proposed circuit agree with the simulated and measured results.                                             Figures 42 and 43 illustrate the calculated, simulated, and measured filter amplitude responses at the V o1 output voltage. As shown in Figures 42 and 43, the electronic tunability of the first filter parameter f o does not affect the parameter Q. Figure 44 shows the quality factor tunability results for the first proposed filter at the V o1 output voltage. In Figure 44, the measured quality factor varied for Q = {0.92, 1.56, 1.97, 2.79} via the three bias currents I B1 = I B2 = 100 µA and I B3 = {142, 66.6, 50, 33.3} µA. Figure 45 illustrates the calculated, simulated, and measured amplitude responses of the first filter at the V o1 output voltage. As shown in Figure 45, the electronic tunability of the first filter parameter Q does not affect the parameter f o . To show the linearity of the first proposed VM LT1228-based multifunction filter in Figure 4, a 1-dB power gain compression point (P1dB) of the NBPF was measured at the V o1 output voltage. Figure 46 shows that the measured input P1dB point is approximately −7.1 dBm. Figure 47 shows the spectrum analysis measured at the V o1 output voltage of the first proposed circuit when the frequency and amplitude of the input sine wave are 159.15 kHz and 180 m V pp , respectively. As shown in Figure 47, the spurious-free dynamic range (SFDR) between the first tone and the highest spur of the other levels is 45.02 dBc. To show the non-linearity of the first proposed circuit in Figure 4, a two-tone test has been performed. The intermodulation distortion (IMD) performance of the first proposed circuit at the V o1 output voltage is further investigated using equal-amplitude two-tone signals with frequencies f 1 = 158.15 kHz and f 2 = 160.15 kHz. Using the Keysight-Agilent N9000A CXA signal analyzer, Figure 48 illustrates the IMD results measured at the V o1 output voltage of the first proposed circuit. In Figure 48, the third-order IMD (IMD3) and thirdorder intercept (TOI) point were measured as −48.84 dBc and 4.133 dBm, respectively. Table 4 summarizes the measured performance of the first proposed VM LT1228-based second-order multifunction filter.

Verification of the Second Proposed VM LT1228-Based Multifunction Filter
To verify the operability of the second proposed VM LT1228-based multifunction filter at f o = 159.15 kHz and Q = 1, two capacitors C 3 = C 4 = 1 nF, five resistors R = R 5 = R 6 = R 7 = R 8 = 1 kΩ, and three commercial LT1228 ICs with bias currents of I B4 = I B5 = I B6 = 100 µA were chosen. Figures 49-53 illustrate the simulation results of the filter magnitude and phase responses of the second proposed circuit in Figure 6. From Figures 49-53, the second proposed VM LT1228-based multifunction filter provides five output responses in the frequency-domain. Figure 54 shows that the simulation results of the Q-value can specify the recommended independent control without affecting the pole frequency. In Figure 54, the simulated Qvalue varied for Q = {2.56, 4.06, 5.01, 5.95} via the three bias currents I B4 = I B5 = 100 µA and I B6 = {40, 25, 20, 16.6} µA. This is expected since the output swing distortion limits the Qvalue below 6, and the Q-value error remains below 2%. Figure 55 shows the frequency tunability results of the second proposed filter simulated at the V o1 output voltage. In Figure 55, the simulated pole frequency was varied for f o = {46.77, 125.02, 235.5, 879.02} kHz via the three bias currents I B4 = I B5 = {30, 80, 150, 550} µA and I B6 = 100 µA. Figures 54 and 55 confirm that the second VM multifunction filter provides electronic control of the f o and Q parameters. Figures 56 and 57 show the frequency tunability results of the second proposed filter simulated at the V o2 and V o3 output voltages, respectively. In Figure 56 Figures 58-60 show the NBPF, ILPF, and NHPF operating at different temperatures, respectively. From Figures 58-60, the temperature varies from −5 • to 50 • . The simulated NBPF varied from 174.18 kHz to 144.54 kHz, which affects the operating pole frequency of 159.15 kHz in the range of 9.44% to −9.17%. The simulated ILPF varied from 173.78 kHz to 144.21 kHz, which affects the operating pole frequency of 159.15 kHz in the range 9.19% to −9.38%. The simulated NHPF varied from 174.18 kHz to 144.54 kHz, which affects the operating pole frequency of 159.15 kHz in the range 9.44% to −9.17%. Figures 61-65 illustrate the calculated, simulated, and measured filter amplitude and phase responses of the second proposed circuit in Figure 6. Based on the ideal pole phase marked in the frequency-domain characteristics, Table 5 shows the simulated and measured pole frequency errors for the second proposed circuit. In Table 5, the maximum percentage error of the pole frequency measured in the frequency-domain is less than 1.55%. According to Figures 61-65 and Table 5, the amplitude and phase responses of the second proposed circuit were in agreement with the simulated and measured results. Figures 66 and 67 illustrate the calculated, simulated, and measured amplitude responses of the second filter at the V o1 output voltage. In Figure 66 Table 6 shows the measured phase error between the output and input waveforms at an operating pole frequency of 159.15 kHz. In Table 6, the maximum phase error measured in the time-domain at an operating pole frequency of 159.15 kHz is less than 2.55 • . Figure 73 shows the spectrum of the second proposed filter measured at the V o1 output voltage. In Figure 73, the frequency and amplitude of the input sine wave were 159.15 kHz and 180 m V pp , respectively. As shown in Figure 73, the SFDR between the first tone and the highest spur of the other levels is 45.88 dBc, and the calculated THD value is 0.6%. Figure 74 shows the THD measured at V o1 versus different input voltage signals. In Figure 74, the THD is below 2% when the input peak-to-peak voltage increases to 220 m V pp . The P1dB performance of the second proposed circuit is measured at the V o1 output voltage, and the measured input P1dB point is approximately −7 dBm, as shown in Figure 75. The IMD performance of the second proposed circuit NBPF at the V o1 output voltage is investigated using equal-amplitude two-tone signals with frequencies f 1 = 158.15 kHz and f 2 = 160.15 kHz. Figure 76 shows the IMD results in Figure 6 for the second proposed circuit NBPF at the V o1 output voltage. In Figure 76, the IMD3 and TOI point were measured as −49.65 dBc and 4.316 dBm, respectively. Table 7 summarizes the measured performance of the second proposed VM LT1228-based second-order multifunction filter. as shown in Figure 75. The IMD performance of the second proposed circuit NBPF at the Vo1 output voltage is investigated using equal-amplitude two-tone signals with frequencies f1 = 158.15 kHz and f2 = 160.15 kHz. Figure 76 shows the IMD results in Figure 6 for the second proposed circuit NBPF at the Vo1 output voltage. In Figure 76, the IMD3 and TOI point were measured as −49.65 dBc and 4.316 dBm, respectively. Table 7 summarizes the measured performance of the second proposed VM LT1228-based second-order multifunction filter.     as shown in Figure 75. The IMD performance of the second proposed circuit NBPF at the Vo1 output voltage is investigated using equal-amplitude two-tone signals with frequencies f1 = 158.15 kHz and f2 = 160.15 kHz. Figure 76 shows the IMD results in Figure 6 for the second proposed circuit NBPF at the Vo1 output voltage. In Figure 76, the IMD3 and TOI point were measured as −49.65 dBc and 4.316 dBm, respectively. Table 7 summarizes the measured performance of the second proposed VM LT1228-based second-order multifunction filter.                                                                                  Figure 72. Measured output and input characteristics of the second proposed circuit at

Conclusions
This paper presents the syntheses of two new VM electronically tunable one-input five-output second-order BPF, LPF, and HPF transfer functions based on three LT1228 ICs. Both configurations with a single input voltage terminal and five output voltage terminals use three commercial LT1228 ICs and seven passive components. These two newly synthesized VM second-order multifunction filters can simultaneously provide the following eight attractive advantages: (i) Both circuits can generate BPF, LPF, and HPF transfer functions simultaneously, making them suitable for use in three-way crossover networks. (ii) Both circuits have one high-impedance input, making them suitable for cascading input voltages. (iii) Both circuits have three low-impedance outputs, making them suitable for cascading three output voltages. (iv) The parameters ωo and Q of the two filters permit electronic and orthogonal tuning. (v) The parameter Q of the two filters has

Conclusions
This paper presents the syntheses of two new VM electronically tunable one-input five-output second-order BPF, LPF, and HPF transfer functions based on three LT1228 ICs. Both configurations with a single input voltage terminal and five output voltage terminals use three commercial LT1228 ICs and seven passive components. These two newly synthesized VM second-order multifunction filters can simultaneously provide the following eight attractive advantages: (i) Both circuits can generate BPF, LPF, and HPF transfer functions simultaneously, making them suitable for use in three-way crossover networks. (ii) Both circuits have one high-impedance input, making them suitable for cascading input voltages. (iii) Both circuits have three low-impedance outputs, making them suitable for cascading three output voltages. (iv) The parameters ωo and Q of the two filters permit electronic and orthogonal tuning. (v) The parameter Q of the two filters has

Conclusions
This paper presents the syntheses of two new VM electronically tunable one-input fiveoutput second-order BPF, LPF, and HPF transfer functions based on three LT1228 ICs. Both configurations with a single input voltage terminal and five output voltage terminals use three commercial LT1228 ICs and seven passive components. These two newly synthesized VM second-order multifunction filters can simultaneously provide the following eight attractive advantages: (i) Both circuits can generate BPF, LPF, and HPF transfer functions simultaneously, making them suitable for use in three-way crossover networks. (ii) Both circuits have one high-impedance input, making them suitable for cascading input voltages. (iii) Both circuits have three low-impedance outputs, making them suitable for cascading three output voltages. (iv) The parameters ω o and Q of the two filters permit electronic and orthogonal tuning. (v) The parameter Q of the two filters has independent and electronic tuning capability. (vi) Passive components do not require matching conditions. (vii) The passband gains of the BPF and LPF responses can be controlled effectively and independently without affecting the filter parameters ω o and Q. (viii) Synthesis method of the electronically tunable VM second-order multifunction filter topologies based on the non-inverting/inverting HPF second-order transfer functions. Circuit design and implementation results were obtained to demonstrate these two VM LT1228-based secondorder multifunction filters. The measured input P1dB, IMD3, TOI, and SFDR of the first filter were −7.1 dBm, −48.84 dBc, 4.133 dBm, and 45.02 dBc, respectively. The measured input P1dB, IMD3, TOI, and SFDR of the second filter were −7 dBm, −49.65 dBc, 4.316 dBm, and 45.88 dBc, respectively. Both circuits use a topology synthesis method based on the VM second-order non-inverting/inverting HP filter transfer functions to generate the BP, LP, and HP filter transfer functions simultaneously, making them suitable for three-way crossover network high-fidelity loudspeaker applications. Three commercial LT1228 ICs and seven passive components were used in OrCAD PSpice simulations and experimental measurements to verify the operation of the two proposed VM LT1228-based second-order multifunction filter topologies.