# Design of Electronically Controllable Multifunction Active Filter with Amplitude Controllability Using Two Commercially Available ICs

Authors: Narumol Onanong; Piya Supavarasuwat; Daungkamol Angamnuaysiri; Surapong Siripongdee; Amornchai Chaichana; Winai Jaikla; Peerawut Suwanjan
Journal: Journal of Electrical and Computer Engineering
 (2022)

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## Abstract

In this contribution, the design and analysis of an active multifunction biquad filter that provides five voltage-mode filtering configurations in the same core filtering circuit are presented. The design emphasizes using the commercially available ICs, LT1228, which are easy for off-the-shelf implementation and cheaper compared with the chip implementation. The proposed multifunction filter is realized from two commercial LT1228 ICs as the active function block, combined with five passive elements (three resistors and two capacitors) with three input voltage nodes and a single output voltage node. The following advantages are given for this design: (i) it provides high-pass (HP), low-pass (LP), band-stop (BS), band-pass (BP), and all-pass (AP) filtering functions; (ii) orthogonal and electronic tuning of the natural frequencyω0 and bandwidth (the quality factor: Q); (iii) output voltage node of the proposed circuit is low impedance; (iv) passband voltage gain is controllable; and (v) matching condition and extra double gain voltage-mode amplifier are not required. The effect of the parasitic element in LT1228 on the filter performance is analyzed and included to strengthen the design idea. The PSpice simulation results using LT1228 with ±5 V and the experimental results tested from the hardware implementation are given to prove the validity of the designed multifunction filter.


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## Body

## 1. Introduction

Filters are one of the most important circuits in analog signal processing systems. They are used extensively in many fields, such as electronics, communication systems, control systems, measurement systems, and instrumentation [1]. It can be said that most of the electronic devices in the above works have filters as part of the circuit. For this reason, the filter circuit is continuously developed, researched, and implemented. In particular, a frequency filter that can provide several responses or multiple functions in the same circuit structure has received a lot of attention [2–6]. It is called a multifunction filter circuit. The design of an analog active multifunction filter in the category of multiple-input single-output (MISO) type continues to gain popularity [7, 8]. This is due to the filtering functions, high-pass (HP), low-pass (LP), band-stop (BS), band-pass (BP), and all-pass (AP), which can be selected by controlling on or off the input signals at the input voltage nodes. This feature can be controlled by the digital approach by employing a microcontroller or microprocessor. The voltage-mode analog active filters are always designed to obtain a low-output impedance feature, which makes it convenient to connect with other circuits without the need for buffers. In addition, the filtering parameters should be able to control by an electronic method. Nowadays, electronic devices tend to use a microcontroller or microprocessor to control all functions of these devices. Nevertheless, the MISO voltage-mode filtering topology necessitates reconnection of the inputs once a specific input must be grounded, and another port must be disconnected from ground to be used as a new voltage input. Solely voltage-mode filtering solutions with a single input and a single output (SIMO) can be referred to as “no-reconnect” solutions. In exchange, a low-impedance node lacks a voltage response.Electronic circuit design using active building blocks (ABBs) is very popular. As it provides a great deal of convenience and flexibility for designers, the circuits designed using active building blocks are simple in structure and often contain a few passive devices [9–11]. Currently, there are a variety of active building blocks with bipolar junction transistor structures or C-MOS transistor structures. Its advantage is that it can operate at a low power supply and low power consumption. In addition, the transistor level-based circuits can work at high frequencies as well. However, the circuits realized at the transistor level are most efficient when they are fabricated into an integrated circuit. The cost of fabricating an integrated circuit into a chip is also expensive. For these reasons, it is always found that the performance of the circuits realized at the transistor or C-MOS level will be verified through simulation only due to cost reasons. In addition, the implementation of circuits into the chip should be manufactured in large quantities to achieve break-even. Therefore, using the commercially available active building blocks to realize the new active circuits with a few amounts for specific applications is more interesting and cheaper. It can be easily purchased commercially ICs in the electronic market. It is also easy to implement cheap circuits for real performance testing [12–14]. An interesting commercial active building block is the LT1228. An LT1228 has an internal structure that consists of the operational transconductance amplifier (OTA) and the current feedback amplifier (CFA). So, it can be used in a variety of applications, such as being used in voltage-mode circuit design, where the output terminal is low impedance, and the input terminals are high impedance. It is also electronically controllable, making it easy to control circuit operations with a microcontroller or microprocessor.According to the study, the MISO multifunction active filters employing various active building blocks have been presented [15–44]. However, those studies may still have some disadvantages. For example, the ABB is not easily realized from the commercially available ICs [15, 22, 26, 27, 29–34, 36, 40–43]; the filtering parameters are not controlled electronically [17–21, 24–32, 34, 35]; the output impedance node is not low [15, 16, 18–23, 29, 30, 32–37, 40–44]; the matching condition is needed for selecting the filtering functions [20, 28, 31–34, 42, 43]; the extra double gain amplifier is needed [33, 41, 43, 44], and the performance of the proposed multifunction active filters is verified through simulation only [15, 16, 19, 22, 24, 26, 27, 29–34, 36, 37, 40–44]; the quality factor cannot be controlled without affecting the natural frequency [15–38, 40–42, 44]; and the passband gain of the proposed filters cannot be controlled [15–30, 32–44]. The comparison of the proposed commercially available IC-based MISO multifunction active filter and others is given in Table 1.Table 1
Comparison of this MISO multifunction active filter and other works.
RefABBNo. of ABBNo. ofR + CAll grounded passive elementsCommercial ICElectronic tuneLow output impedanceNo need of matching conditionNo need of double inputExperimental resultControlQ without affecting f0Passband gain control15OTA60 + 2YesYesYesNoYesYesNoNoNo16OTA + CCII30 + 2NoYesYesNoYesYesNoNoNo17CCII + VF43 + 2NoYesNoYesYesYesYesNoNo18CCII23 + 2NoYesNoNoYesYesYesNoNo19CCII22 + 2NoYesNoNoYesYesNoNoNo20CCII23 + 2NoYesNoNoNoYesYesNoNo21CCII22 + 2NoYesNoNoYesYesYesNoNo22CCCII20 + 2NoNoYesNoYesYesNoNoNo23CCTA1∗2 + 2NoYesYesNoYesYesYesYesNo24CDBA2∗4 + 2NoYesNoYesYesYesNoYesNo25CFA and VF22 + 2NoYesNoYesYesYesYesNoNo26DDCC22 + 2NoNoNoYesYesYesNoNoNo27DDCC32 + 2YesNoNoYesYesYesNoNoNo28FTFN and CFA2∗3 + 2NoYesNoYesNoYesYesYesNo29FDCCII13 + 2NoNoNoNoYesYesNoYesNo30FDCCII22 + 2YesNoNoNoYesYesNoNoNo31OTRA14 + 4NoNoNoYesNoYesNoNoYes32DXCCII14 + 2NoNoNoNoNoYesNoYesNo33VDTA10 + 2NoNoYesNoNoNoNoNoNo34DVCC12 + 2NoNoNoNoNoYesNoNoNo35CFA∗∗13 + 2NoYesNoNoYesYesYesNoNo36VD-DIBA11 + 2NoNoYesNoYesYesNoNoNo37LT122811 + 2NoYesYesNoYesYesNoNoNo38VDDDA2∗0 + 2YesYesYesYesYesYesYesNoNo39VDDDA3∗0 + 2YesYesYesYesYesYesYesYesNo40VDDDA12 + 2NoYesYesNoYesYesNoYesNo41VDDDA11 + 2NoYesYesNoYesNoNoNoNo42VDTA11 + 2NoNoYesNoNoYesNoYesNo43OTA90 + 3YesYesYesNoNoNoNoYesNo44LT122812 + 2NoYesYesNoYesNoNoYesNoThis workLT122823 + 2NoYesYesYesYesYesYesYesYes∗The CCTA in [23] is constructed from two commercial ICs, OPA861 and MAX435. The CDBA in [24] is structured from two commercial ICs of AD844. The FTFN in [28] is constructed from two commercial ICs of AD844. The VDDDA in [38, 39] is constructed from two commercial ICs, LT1228 and AD830. ∗∗In [35], reconnection of the proposed filter to obtain several filtering functions is required.For the reasons presented above, a commercially available LT1228 IC-based multifunction active filter is proposed in this research paper. The rest of this research contribution is prepared as follows: the basic concept of the commercially available LT1228 IC and the proposed voltage-mode MISO multifunction active filter are given in Section2, while Section 3 presents, in detail, the analysis and study of the effect of the parasitic impedances in LT1228. The simulation results obtained from the PSpice program are depicted in Section 4. In Section 4, the experimental results obtained from the real circuit test are shown and discussed. Finally, the conclusion of this study is depicted in Section 5.


## 2. Principle of the Proposed Circuit

### 2.1. Active Building Block and Its Properties

The commercially available LT1228 IC is a voltage input and current/voltage output active building block that consists of a cascading connection of the transconductance amplifier and the current feedback amplifier [45, 46]. It has five terminals where v+ and v− are the high-impedance (ideally infinity) voltage input terminals. The y is a high-impedance (ideally infinity) current output terminal of the transconductance amplifier, and this terminal is also the voltage input terminal of the current feedback amplifier section. The low-impedance (ideally zero) terminals x and w in LT1228 are the voltage input and output of the current feedback amplifier, respectively. The LT1228 electrical circuit symbol is depicted in Figure 1(a), while the equivalent circuit of LT1228 is shown in Figure 1(b). The pin configuration of the LT1228 is an 8-pin dual-in-line package IC as shown in Figure 2. The LT1228 terminal characteristics are presented in the following equation [46]:(1)Iv+Iv−IyVxVw=0000000000gm−gm00000100000RT0V+V−VyIxIw,where RT denotes the transresistance gain of LT1228 and gm denotes the transconductance gain. For ideal consideration, RT is an inﬁnite value. gm of LT1228 depends on the DC bias current IB as depicted in the following equation [46]:(2)gm=10IB.Figure 1
LT1228. (a) Electrical symbol. (b) Equivalent circuit.
(a)(b)Figure 2
An 8-pin dual-in-line package of LT1228.Equation (2) indicates that the LT1228-based circuits are electronically tuned, which makes it easy to control circuit parameters with a microcontroller or microprocessor.


### 2.2. Proposed Multifunction Active Filter

This design focuses on employing the LT1228 IC to obtain the electronic control of the natural frequency and bandwidth (the quality factor), which will be easy for off-the-shelf implementation and cheaper compared with the chip implementation. The presented multifunction active filter is depicted in Figure3. It contains two LT1228 ICs (LT1228-1 and LT1228-2) as the main active building blocks with three resistors (R, Ra, and Rb) and two capacitors (C1 and C2). It has three input voltage nodes, VinI, Vin2, and Vin3, and a single-output voltage node, V0. Considering the proposed filter in Figure 3, the output voltage node, V0, is at the w terminal of LT1228-2, which is low impedance. So, the output voltage node of the proposed active filter designed in Figure 3 can be directly connected to the next stage without using any voltage buffers. The input voltage node, Vin3, is also high impedance. However, the input voltage nodes, Vin2 and Vin1, are not high impedance. Moreover, some passive elements in the proposed circuit are floating, which can be considered as the drawback when it is compared to the MISO filters proposed in [15, 27, 30, 38, 39, 43]. Considering the ideal properties of the LT1228, the equation of V0 of the proposed circuit is obtained as follows:(3)vo=RbRa+1s2vin2+sgm2vin3/C2+gm1vin1/C1C2Rs2+sgm2/C2+gm1/C1C2R.Figure 3
Proposed multifunction active filter.Based on the denominator of equation (3), the natural frequency (ω0) of the active filter designed in Figure 3 is obtained as follows:(4)ω0=gm1C1C2R.Subsequently, the quality factor (Q) of the proposed multifunction active filter designed in Figure 3 is obtained as follows:(5)Q=1gm2gm1C2RC1.The passband voltage gain of the proposed multifunction active filter designed in Figure3 is given as follows:(6)Gp=RbRa+1.The filtering parameters,ω0 and Q, which appear in equations (4) and (5), indicate that the control of Q can be done electronically via the transconductance, gm2 of LT1228-2 without affecting ω0. Moreover, ω0 can be electronically adjusted via the transconductance, gm1 of LT1228-1. For practical design, ω0 should be first tuned electronically by gm1, and then, the bandwidth or the Q should be electronically adjusted through gm2. In addition, it is observed from equation (6) that the passband gain of all filtering functions can be controlled via the resistor, Ra or Rb, without affecting ω0 and Q. So, if the input magnitude signal driven to the proposed multifunction active filter is at a low level, the amplitude of the output voltage can be controlled without using any additional amplifiers.Considering the output voltage depicted in (3), five second-order filtering functions can be achieved as follows:(i)
The band-pass biquad function can be realized from the proposed active filter designed in Figure3 by driving the input voltage signal to node vin3 and connecting nodes vin1 and vin2 to the ground(ii)
The low-pass biquad function can be realized from the proposed active filter designed in Figure3 by driving the input voltage signal to node vin1 and connecting nodes vin2 and vin3 to the ground(iii)
The high-pass biquad function can be realized from the proposed active filter designed in Figure3 by driving the input voltage signal to node vin2 and connecting nodes vin2 and vin3 to the ground(iv)
The band-stop biquad function can be realized from the proposed active filter designed in Figure3 by driving the input voltage signal to nodes vin1vin1 and vin2 and then connecting node vin3 to the ground(v)
The all-pass biquad function can be realized from the proposed active filter designed in Figure3 by driving the input voltage signal to nodes vin1 and vin1 and driving the inverting input voltage signal to node vin3. An inverting amplifier with unity gain is required for the all-pass function.It is found from the above statement that the presented multifunction active filter designed in Figure3 can provide five responses, named band-pass filter, low-pass filter, high-pass filter, band-stop filter, and all-pass filter, in the same circuit without the need for the double gain amplifier and the passive element matching condition. Moreover, the selection of the output voltage-mode filtering functions can be done by the digital approach employing a microcontroller or microprocessor.In the case of the all-pass function, the phase response is given as follows:(7)θAP=−2tan−1ωgm2C1Rgm1−ω2C1C2R.Equation (7) indicates that the phase difference in the input and output waveform for the AP function is shifted from 0° at low frequencies to −360° at high frequencies with a flat amplitude response where the phase of the output voltage waveform lags the phase of the input voltage waveform.


## 2.1. Active Building Block and Its Properties

The commercially available LT1228 IC is a voltage input and current/voltage output active building block that consists of a cascading connection of the transconductance amplifier and the current feedback amplifier [45, 46]. It has five terminals where v+ and v− are the high-impedance (ideally infinity) voltage input terminals. The y is a high-impedance (ideally infinity) current output terminal of the transconductance amplifier, and this terminal is also the voltage input terminal of the current feedback amplifier section. The low-impedance (ideally zero) terminals x and w in LT1228 are the voltage input and output of the current feedback amplifier, respectively. The LT1228 electrical circuit symbol is depicted in Figure 1(a), while the equivalent circuit of LT1228 is shown in Figure 1(b). The pin configuration of the LT1228 is an 8-pin dual-in-line package IC as shown in Figure 2. The LT1228 terminal characteristics are presented in the following equation [46]:(1)Iv+Iv−IyVxVw=0000000000gm−gm00000100000RT0V+V−VyIxIw,where RT denotes the transresistance gain of LT1228 and gm denotes the transconductance gain. For ideal consideration, RT is an inﬁnite value. gm of LT1228 depends on the DC bias current IB as depicted in the following equation [46]:(2)gm=10IB.Figure 1
LT1228. (a) Electrical symbol. (b) Equivalent circuit.
(a)(b)Figure 2
An 8-pin dual-in-line package of LT1228.Equation (2) indicates that the LT1228-based circuits are electronically tuned, which makes it easy to control circuit parameters with a microcontroller or microprocessor.


## 2.2. Proposed Multifunction Active Filter

This design focuses on employing the LT1228 IC to obtain the electronic control of the natural frequency and bandwidth (the quality factor), which will be easy for off-the-shelf implementation and cheaper compared with the chip implementation. The presented multifunction active filter is depicted in Figure3. It contains two LT1228 ICs (LT1228-1 and LT1228-2) as the main active building blocks with three resistors (R, Ra, and Rb) and two capacitors (C1 and C2). It has three input voltage nodes, VinI, Vin2, and Vin3, and a single-output voltage node, V0. Considering the proposed filter in Figure 3, the output voltage node, V0, is at the w terminal of LT1228-2, which is low impedance. So, the output voltage node of the proposed active filter designed in Figure 3 can be directly connected to the next stage without using any voltage buffers. The input voltage node, Vin3, is also high impedance. However, the input voltage nodes, Vin2 and Vin1, are not high impedance. Moreover, some passive elements in the proposed circuit are floating, which can be considered as the drawback when it is compared to the MISO filters proposed in [15, 27, 30, 38, 39, 43]. Considering the ideal properties of the LT1228, the equation of V0 of the proposed circuit is obtained as follows:(3)vo=RbRa+1s2vin2+sgm2vin3/C2+gm1vin1/C1C2Rs2+sgm2/C2+gm1/C1C2R.Figure 3
Proposed multifunction active filter.Based on the denominator of equation (3), the natural frequency (ω0) of the active filter designed in Figure 3 is obtained as follows:(4)ω0=gm1C1C2R.Subsequently, the quality factor (Q) of the proposed multifunction active filter designed in Figure 3 is obtained as follows:(5)Q=1gm2gm1C2RC1.The passband voltage gain of the proposed multifunction active filter designed in Figure3 is given as follows:(6)Gp=RbRa+1.The filtering parameters,ω0 and Q, which appear in equations (4) and (5), indicate that the control of Q can be done electronically via the transconductance, gm2 of LT1228-2 without affecting ω0. Moreover, ω0 can be electronically adjusted via the transconductance, gm1 of LT1228-1. For practical design, ω0 should be first tuned electronically by gm1, and then, the bandwidth or the Q should be electronically adjusted through gm2. In addition, it is observed from equation (6) that the passband gain of all filtering functions can be controlled via the resistor, Ra or Rb, without affecting ω0 and Q. So, if the input magnitude signal driven to the proposed multifunction active filter is at a low level, the amplitude of the output voltage can be controlled without using any additional amplifiers.Considering the output voltage depicted in (3), five second-order filtering functions can be achieved as follows:(i)
The band-pass biquad function can be realized from the proposed active filter designed in Figure3 by driving the input voltage signal to node vin3 and connecting nodes vin1 and vin2 to the ground(ii)
The low-pass biquad function can be realized from the proposed active filter designed in Figure3 by driving the input voltage signal to node vin1 and connecting nodes vin2 and vin3 to the ground(iii)
The high-pass biquad function can be realized from the proposed active filter designed in Figure3 by driving the input voltage signal to node vin2 and connecting nodes vin2 and vin3 to the ground(iv)
The band-stop biquad function can be realized from the proposed active filter designed in Figure3 by driving the input voltage signal to nodes vin1vin1 and vin2 and then connecting node vin3 to the ground(v)
The all-pass biquad function can be realized from the proposed active filter designed in Figure3 by driving the input voltage signal to nodes vin1 and vin1 and driving the inverting input voltage signal to node vin3. An inverting amplifier with unity gain is required for the all-pass function.It is found from the above statement that the presented multifunction active filter designed in Figure3 can provide five responses, named band-pass filter, low-pass filter, high-pass filter, band-stop filter, and all-pass filter, in the same circuit without the need for the double gain amplifier and the passive element matching condition. Moreover, the selection of the output voltage-mode filtering functions can be done by the digital approach employing a microcontroller or microprocessor.In the case of the all-pass function, the phase response is given as follows:(7)θAP=−2tan−1ωgm2C1Rgm1−ω2C1C2R.Equation (7) indicates that the phase difference in the input and output waveform for the AP function is shifted from 0° at low frequencies to −360° at high frequencies with a flat amplitude response where the phase of the output voltage waveform lags the phase of the input voltage waveform.


## 3. Analysis and Study of the Parasitic Effects on the Proposed Filter

In this section, the effect of the LT1228 parasitic element on the performance of the presented voltage-mode versatile active filter designed in Figure3 is analyzed and studied. The commercially available LT1228 IC with the parasitic elements at the LT1228 input and output terminals can be drawn in Figure 4. The capacitance and resistance connecting in parallel configuration appear at the high-impedance input and output terminals V+ (R+//C+), V− (R−//C−), and y (Ry//Cy) and the transresistance impedance RT//CT. The resistor rx and rw series at the low-impedance terminals x and w, respectively. The parasitic effect appeared in the proposed filer is depicted in Figure 5, where YA = s(C+1 + C−2 + Cy1 + Cy2)+G+1 + G−2 + Gy1 + Gy2, Y−1 = sC−1 + G−1, YT1 = sCT1 + GT1, and YT2 = sCT2 + GT2. The frequency limitations at low frequencies of the proposed filter (especially for the BP and HP functions) mostly stem from the parasitic resistances at the first LT1228. Ideally, the first LT1228, R, and C1 are constructed as the lossless inductance simulator. However, the parasitic resistances cause this sub-circuit to work as the lossy inductance simulator (series LR circuit). If iy1 is the current going through the lossy inductance simulator (Figure 5), then the relationship between iy1 and vin1 and vA is as follows:(8)iy1=1sLeq+Reqvin1−vAsC1R+1−Reqgm1−sLeqgm1,where(9)Leq=C1Rgm11+rx1RT11+rw1R−1+rw1RT11+rx1R,and(10)Req=rx1rw1Rgm1RT1rx1//Rrw1//R−1.Figure 4
LT1228 parasitic elements.Figure 5
Proposed multifunction active filter with parasitic elements.From equation (10), the frequency limitations at low frequencies of the proposed filter (especially for the BP and HP functions) stem from the resistance, Req. To reduce this effect at low frequencies, the value of the external resistor, R, should be low. However, if RT1 and R−1 are greater than rx1, rw1, and R, then Req ≅ 0 and Leq ≅ C1R/gm1. The effect of the parasitic resistances at the first LT1228 is negligible (we also want to shorten the equation of the output voltage too).At high frequencies, there are two poles/zeros (we will consider them as the poles) that appear at the inductance simulator. Ifrw1 is more less than R−1 and rx1 is more less than RT1, these pole frequencies are fp1 ≅ 1/(2πC−1rw1) and fp2 ≅ 1/(2πCT1rx1). The CFA in the second LT1228, Ra, and Rb is constructed as the voltage amplifier. If RT2 is greater than rx2, rw2, and Ra, the bandwidth of the amplifier is determined by 1/(2πCT2Rb) [47]. From the simulation in [47], it is indicated that Cy = 6 pF, Ry = 8 MΩ, C− = C+ = 3 pF, RT = 197.66 kΩ, CT = 5.95 pF, rx = 46.92 Ω, and rw = 19.80 Ω [47]. If Rb and C1 used in the proposed circuit are 1 kΩ and 1 nF, the pole frequencies, fp1 and fp2, and bandwidth of the amplifier are approximately 2.68 GHz, 570.09 MHz, and 26.75 MHz, respectively. Thus, if the bandwidth of the proposed filter is less than 26.75 MHz, the effect of the parasitic elements, C−1, R−1, CT1, RT1, rw1, and rx1 at the first LT1228 and RT2, CT2, rx2, and rw2 at the second LT1228, is neglected. So, the most effect is caused by the parasitic elements, C+1, R+1, Cy1, Ry1, C−2, R−2, Cy2, and Ry2. Thus, the output voltage of the presented multifunction active filter with parasitic elements is obtained by(11)vo=RbRa+1s2C2/C2+CAvin2+sgm2/CA+C2vin3+gm1/C1RCA+C2vin1s2+sGA+gm2/CA+C2+gm1/C1RCA+C2,where  CA = C+1 + C−2 + Cy1 + Cy2  and GA = G+1 + G−2 + Gy1 + Gy2. From equation (11), the natural frequency with the parasitic effect is given as follows:(12)ω0∗=gm1C1RCA+C2.Subsequently, the quality factor with the parasitic effect is given as follows:(13)Q∗=1GA+gm2gm1CA+C2C1R.It is observed that the parasitic elements in the LT1228 affect the passband gain, phase response, natural frequency, quality factor, and the operating limitations at low and high frequencies. As discussed above, the value of the external resistor,R, should be low to reduce the parasitic effect at low frequencies. Also, the external resistor Rb should be low to enhance the bandwidth of the proposed circuit. In addition, to control the passband voltage gain with constant bandwidth, the value of Ra should be adjusted [47].


## 4. Experiment and Simulation Results

The proposed filter is verified with the hardware setup as depicted in Figure6. The experiment is carried out using the supply voltages ±5 V. The filter is designed to obtain f0 = 200 kHz, Q = 1, and the passband Gp = 2 by choosing IB1 = 157.91 µA, IB2 = 125.66 µA, R = Ra = Rb = 1 kΩ, and C1 = C2 = 1 nF. The magnitude frequency response of the proposed active filter for the functions, LP, HP, and BP filter, obtained from the experiment is illustrated in Figure 7. The experimental result shows f0 = 199.53 kHz (0.23% error) and Q = 1.05 (5% error). The passband voltage gains of the proposed active filter for the functions, LP, HP, and BP filter, obtained from the experiment are 5.95 dB (1.16% error), 5.92 dB (1.66% error), and 5.79 dB (3.82% error), respectively. The magnitude and phase frequency response of the band-stop filtering function obtained from the experiment is depicted in Figure 8. The experimental passband voltage gains of the band-stop function at low and high frequencies are 5.95 (1.16% error) and 5.92 (1.66% error), respectively. The error of the experimental filtering parameters is caused by the parasitic resistances and capacitances in the commercial LT1228 IC as analyzed and discussed in Section 3. The gain and phase frequency behavior of the AP function obtained is depicted in Figure 9. The inverting unity gain amplifier is implemented by AD844 and two resistors (0.47 kΩ). It is seen that the phase behavior of the AP function is shifted from 0° at low frequencies to −360° at high frequencies with a flat amplitude response. The measured sinusoidal input and output waveform of the BP filter is illustrated in Figure 10, where the frequency of the sinusoidal input voltage is 200 kHz @ 50mVp-p. It is found that the sinusoidal input and output voltage signals are in phase at the center frequency (f = 200 kHz), while the BP output voltage is 98.7 mVp-p, which is around twice as large as the input. The total harmonic distortion (THD) of the BP output voltage is 0.191%. As expected in equation (5), the control of the Q is done without affecting the f0 by setting IB2 to 37.67 µA, 66.75 µA, and 125.66 µA (IB1 = 157.91 µA). This advantageous feature is confirmed by the experimental result in Figure 11. The experimental quality factors obtained from these values of IB2 are, respectively, varied to 2.69, 2.15, and 1.05. From the experimental result in Figure 12, changing IB1 to 79.34 µA, 125.66 µA, and 304.90 µA (IB2 = 125.66 µA) results in the natural frequency changing to 144.54 kHz, 199.53 kHz, and 288.40 kHz, respectively. However, adjusting IB1 will also affect the quality factor. So, in the practical design step, the natural frequency should be first tuned electronically by IB1, and then, the bandwidth or the Q is electronically adjusted through IB2. As mentioned in Section 3, the frequency limitation at high frequency of the proposed filter depends on the resistor, Rb. So, to control the passband voltage gain with constant bandwidth, the value of Ra should be adjusted [47]. The control of passband gain is experimentally verified via the BP function by adjusting the value of Ra to 0.5 kΩ, 1 kΩ, and 2 kΩ, respectively (Rb = 1 kΩ), as depicted in Figure 13. The experimental passband gains for these Ra values are 9.30 dB (2.52% error), 5.79 dB (3.82% error), and 3.27 dB (7.10% error), respectively. It is found that at a high value of Ra, the voltage gain error is quite high. So, the Rb can be decreased (Ra must be decreased too) to get a higher voltage gain. Also, if Rb is set to a low value, it can make the proposed circuit’s bandwidth wider. The experimental result confirms that the passband gain is controllable as expected in equation (6). The step response of the low-pass filter is shown in Figure 14 for an input step amplitude of 50 mVp-p (f = 15 kHz).Figure 6
Experimental setup.Figure 7
Experiment gain responses of LP, HP, and BP functions.Figure 8
Experiment gain response of band-stop function.Figure 9
Experiment gain and phase response of all-pass function.Figure 10
Measured input and output waveform of the BP filter.Figure 11
Experimental magnitude frequency response of BP function whenIB2 is varied.Figure 12
Experimental magnitude frequency response of BP function whenIB1 is varied.Figure 13
Experimental magnitude frequency response of BP function whenRa is varied.Figure 14
Measured input and output waveform of LP filter.In addition, the PSpice software is used to evaluate the performance of the proposed multifunction active filter. The macro-model of PSpice is at level 3. The input dynamic range of the proposed filter is evaluated by testing the THD of the output voltage versus the amplitude of the input voltage for band-pass filtering functions. Figure15 depicts the dependence of THD on the amplitude of the sinusoidal input voltage signal obtained through simulation, where the frequency of the sinusoidal input signal was 200 kHz. When the input voltage is less than 180 mVp-p, the THD of the band-pass filtering function falls below 1 percent. The band-pass function of the proposed multifunction filter is analyzed using the Monte Carlo method to examine the influence of passive elements on the performance of the circuit. In this simulation, the Gaussian variation of the resistance and capacitance is 5%, while the other active elements are identical to those observed in the previous experiment. Statistical analysis is performed on the Monte Carlo 100 simulation. After 100 runs, the band-pass filter’s center frequency varies between 186.26 kHz and 207.93 kHz, with a standard deviation of 4247.02 Hz as depicted in Figure 16.Figure 15
Simulated THD of the band-pass filter versus the input amplitude atf = 200 kHz.Figure 16
Histogram of Monte Carlo analysis of the band-pass filter witha ±5% passive element tolerance.


## 5. Conclusions

In this design, the voltage-mode versatile biquadratic filter with amplitude controllability using the commercially available LT1228 ICs is proposed. The proposed filter contains two LT1228 ICs, three resistors (R, Ra, and Rb), and two capacitors (C1 and C2). The low-impedance output voltage node of the proposed circuit is achieved, which is able to connect to other circuits without the need for external buffer circuits. Five standard filter responses, including HP, BP, BS, LP, and AP filtering functions, can be obtained in the same core filtering structure without any matching conditions and a double gain amplifier. With this advantage feature, the filtering function of the proposed versatile active filter can be chosen by the digital approach. Both parameters (f0 and Q) can be electronically adjusted by IB1 and IB2. Moreover, Q can be tuned by the bias current, IB1, without affecting the parameter, f0. The passband gain is controllable by adjusting the resistors Ra and Rb without disturbing the parameters, Q and f0. However, the inverting unity gain amplifier is required for the AP filtering function. The input voltage nodes, vin2 and vin1, are not high impedance. The simulation results from the PSpice program and experiment results from the hardware test are carried out to investigate the proposed multifunction active filter. With the supply voltages ±5 V and choosing IB1 = 157.91 µA, IB2 = 125.66 µA, R = Ra = Rb = 1 kΩ, and C1 = C2 = 1 nF, the natural frequency obtained from the experiment is 199.53 kHz (0.23% error). The quality factor obtained from the experiment is 1.05 (5% error).



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*Source: 4932284-2022-08-04.xml*