Electronically Tunable Triple-Input Single-Output Voltage-Mode Biquadratic Filter Implemented with Single Integrated Circuit Package

A R T I C L E I N F O A B S T R A C T Article history: Received: 30 September, 2020 Accepted: 31 January, 2021 Online: 25 February, 2021 This article proposes a compact and simple design of electronically adjustable voltage-mode biquadratic filter using fundamental active cell implemented on a single integrated circuit (IC) package as LT1228. The proposed circuit having triple inputs and single output (TISO) employs namely one resistor and two capacitors as the passive components. All the five possible biquadratic filtering responses, namely low-pass (LP), band-pass (BP), high-pass (HP), band-stop (BS) and all-pass (AP), are realized by the appropriate selection of the relevant input signals. The pole angular frequency and the quality factor of the proposed TISO filter are electronically tunable through the bias current of the IC chip LT1228. Nonideal effects and sensitivity performance are carried out. The theoretical results are satisfactorily validated by both PSPICE simulation results and experimental measurements using commercially available LT1228.

In this communication, an electronically tunable voltage-mode biquadratic filter with three input and one output terminals (TISO) consisting of only single active IC package LT1228, one resistor and two capacitors is introduced. The proposed TISO filter can realize the five standard biquadratic filtering responses, namely low-pass (LP), band-pass (BP), high-pass (HP), band-stop (BS) and all-pass (AP), all at a single output terminal without modifying a circuit structure. It also provides an electronic adjustability of its pole angular frequency (o) and quality factor (Q) via the external bias current of the LT1228 IC chip. The theoretical propositions are confirmed by PSPICE simulations with LT1228's model parameters, and the simulated results corroborate the theory. In addition, all conclusions discussed in this work are also verified by ASTESJ ISSN: 2415-6698 the measurement results of an experimentally test circuit with a single IC package LT1228, and the experimental findings are found to be in agreement with the theoretical values.

Description of IC Package LT1228
Our design utilizes only one active cell of a commercially available IC LT1228 from Linear Technology Company [46]. An active cell LT1228 is internally a combination of an operational transconductance amplifier (OTA) and a current feedback operational amplifier (CFA) in 8-pin IC package, as demonstrated in Figure 1. This device has three high impedance input terminals (p, n, and z), and one low impedance output terminal (o). It provides the output current iz at intermediate terminal z which is the difference of two input voltages vp and vn (vpvn) multiplied by transconductance gain (gm). An external impedance Zz is connected to the terminal z, and the potential vz developed across Zz will transfer to the output voltage vo at the terminal o by the CFA. Its ideal terminal characteristics can be described as: Thanks to the LT1228 manufacturing, the gm-value can be altered to the desired value through the external DC bias current IB by the following relation: [46] 10 m B g I = . (2)

Proposed TISO Biquadratic Filter
The realization of an electronically tunable TISO voltage-mode biquadratic filter is given in Figure 2. The proposed TISO filter is implemented with a single LT1228 together with one resistor and two capacitors. A straightforward analysis of the proposed TISO filter reveals the following output voltage function: where the denominator D(s) is found to be: From an inspection of Equations (3)-(4), it appears the five standard biquadratic filter functions can be obtained all at the terminal vout of the proposed circuit by the following conditions.
(v) The AP response is obtained by setting vin = v1 = -v2 = v3. Therefore, the proposed TISO filter of Figure 2 does not require any element matching conditions or equality constraints for the desired filter function realizations. In all types, the important characteristics o, and Q are respectively found as: In case of practical design, if C = C1 = C2, then the o and Q simplify to: In view of the above expressions, the parameters o and Q of the proposed TISO filter can be altered electronically by means of gm-value. According to Equation (2), the gm variation can be obtained by an adjustment of the bias current. Also note that since the major contribution of this work is to design a compact and minimum configuration voltage-mode TISO filter with electronic tunability, an orthogonal control of o or Q is not expected.

Non-Ideal Analysis and Sensitivity Performance
In consideration of the non-ideal behavior, the terminal behaviors of LT1228 can be rewritten as: where  = (1 -gm) and  = (1 -v), where |gm | << 1 and |v | << 1 are the transconductance inaccuracy and the voltage transfer error, respectively. Taking this effect into account, the characteristics o and Q given in Equations (5) and (6) are modified to: and 12 1 In this case, all sensitivity coefficients of o and Q with respect to the active and passive components are derived and found to be as follows: and 1 1 2 It is clear from Equations (12)-(15) that the absolute values of the oand Q-sensitivities are all equal to 0.5. These values ensure that the sensitivity performance of the circuit is to be of low value.

Simulation Results
In this section, the proposed circuit and its filtering responses are simulated and discussed through the PSPICE simulation program. For ideal simulation, the LT1228 macro-model parameters obtained from Linear Technology Company and DC supply voltages of ±5V were employed. To demonstrate the functionality of the proposed filter, the circuit is designed for fo = 159.15 kHz and Q = 1. In this case, the various component values have been set as IB = 100 μA for gm = 1 mA/V, R1 = 1 kΩ and C1 = C2 = 1 nF. The simulation results for all filter responses are shown in Figures 3-7, which demonstrates very close agreement with the theoretical responses. For time-domain responses, a 159-kHz sine-wave input voltage with 50 mV peak amplitude was applied to the filter. The simulation results show that the error in fo-value was found to be less than 1%. Furthermore, the electronic tuning of gain characteristic for BP filter concerning IB is observed. The related gain expressions of the proposed BP filter, as shown in Figure 8, are plotted for IB = 50 μA, 200 μA, and 500 μA, which resulted in gm = 0.5 mA/V, 2 mA/V, and 5 mA/V, respectively. From Figure 8, the simulation conditions, and corresponding theoretical and simulated fo and Q are summarized in Table 1.

Experimental Results
To further validate the practical workability of the TISO biquadratic filter in Figure 2, the prototype circuit built with readily available IC element LT1228 and discrete passive elements were used to execute experimentally laboratory tests. The circuit was measured using Keysight EDUX1002G digital storage oscilloscope. All of the measured results were performed   Table 2. It can be concluded that the measured results are close to the theoretical analysis, and also verify the functionality of the proposed circuit. Another set of measurements have been carried out to examine the electronic adjustability of the proposed TISO filter. BP filter response is used for illustrative purposes. Figure 14 illustrates the measured BP frequency responses for various bias current IB. The gm-values of the considered filter have been set as 0.5 mA/V, 2 mA/V, and 5 mA/V, for IB = 50 μA, 200 μA, and 500 μA, respectively. As follows from Equations (5) and (6)

Conclusions
This contribution describes the practical implementation of an electronically tunable voltage-mode biquadratic filter with triple input terminals and single output terminal. The proposed filter employs only a single commercially available IC LT1228 together with one resistor and two capacitors. The filter can realize all five standard biquadratic filtering functions all at a single output terminal by an appropriate input signal selection. The characteristics of ωo and Q can be controlled electronically and linearly in an electronic manner via the external bias current. Simulation results obtained from the PSPICE macro-model of the LT1228 by Linear Technology as well as constructed in prototype hardware using commercially available IC LT1228 are performed to confirm the properties of the proposed circuit.

Conflict of Interest
The authors declare that they have no conflict of interest.