Realization of a New Current Mode Second-Order Biquad Using Two Current Follower Transconductance Amplifiers ( CFTAs )

A new circuit for realization of universal current-mode filter using current Follower Transconductance Amplifiers (CFTAs) is presented. The proposed circuit realizes current-mode low pass, high pass and band pass filter functions simultaneously with a single current source at the input. The band reject and all pass filters can also be obtained from the proposed circuit without any extra hardware. The proposed circuit employs three passive grounded elements and two CFTAs. Linear electronic control of natural frequency ω0 is available in the proposed circuit. The quality factor can be independently adjusted through grounded resistor. The proposed circuit employs two grounded capacitors and a grounded resistor along with two CFTAs. The grounded resistor can be replaced by an OTA based circuit for linear electronic control of quality factor Q0. The circuit exhibits low active and passive sensitivities for ω0 and Q0. Simulation results are obtained using PSPICE software which is in conformity with the theoretical findings.


Introduction
Current mode circuits are very popular due to some of their advantages over their voltage mode counter parts.
They are very suitable for high frequency, low voltage and low power applications in portable equipments such as mobile phones, aviation industry, water quality monitoring equipments, medical instrumentation and in satellite communication equipments.Current mode approach in analog processing blocks offers high slew rates, low node impedances, greater linearity, wider bandwidth and sometimes electronic tunability compared with voltage mode circuits.There have been steady and gradual interests to find new schemes for analog building blocks which may serve as an excellent current mode device.Some of the popular and off-the-shelf items have been Current Feedback Amplifiers (AD844) [1], Current Conveyors [2], Operational Transconductance Amplifiers (CA 3080) [3] etc., which have been used for decades as excellent current mode devices.Recently introduced current mode building blocks are Current Differencing Transconductance Amplifiers (CDTAs) [4]- [7], and Current Follower Transconductance Amplifiers (CFTAs) [8]- [23] which provide simple design facility with ample numbers of choices for output current ports for excellent current mode signal processing.CFTA in addition to possessing single current input compared with CDTA also exhibits excellent current mode characteristics along with electronic control of parameters of interest and is therefore attracting the attention of analog circuit designers.CFTA is extensively used in the realization of signal processing as well as signal generation in current mode circuits [7]- [23].In this paper, a new circuit using two CFTAs and two grounded capacitors along with a grounded resistor is presented.The proposed circuit realizes basic current mode filter functions such as low pass (LP), band pass (BP), and high pass (HP) for a single input current source.Also, band reject (BR) and all-pass (AP) filter functions can be realized by proper combinations of current responses.Various papers are published on different applications of CFTAs such as current-mode (CM) or voltage-mode (VM) universal filters, oscillators, amplifiers, etc.
[7]- [23].In this paper, a new current-mode second-order CFTA biquad filter is presented which uses two active elements and three passive grounded elements.The main attractive feature of this circuit is the facility of linear control of pole frequency ω 0 and quality factor Q 0 .While pole frequency can be changed electronically through g m , the quality factor Q 0 can be adjusted independently through grounded resistor.The grounded resistor can further be realized through an additional transconductance amplifier making this control again an electronic one.The simulation results are obtained using PSPICE software.Simulation results validate the theoretical findings.

Proposed circuit Realization of Current Follower Transconductance Amplifier (CFTA)
The Current Follower Transconductance Amplifier (CFTA) [6], whose schematic symbol and behavioral model are shown in Figure 1(a)-(b), consists of an input current follower that transfers the input current to the z terminal and an output transconductance amplifier stage, which is used to convert the voltage at the z-terminal into output currents.Relations between the individual terminals of CFTA can be described by the following hybrid matrix: Assuming the standard notations, the terminals defining relations of this device can be characterized by the following set of equations 0, and , where g m is transconductance gain of the CFTA which is directly proportional to the external bias current I B , which is given by Equation ( 3) where the V T is the thermal equivalent voltage (= 26 mV at 27˚C) and I B is the control bias current adjusting the transconductance g m of the CFTA.The operation of the CFTA will be dependent on temperature variations.z z is external impedance connected to the z-terminal.
The proposed current mode biquad filter is shown in Figure 2. It consists of two CFTAs, one grounded resistor and two grounded capacitors.The internal construction of CFTA used for simulation is shown in Figure 3.
A routine analysis of the proposed circuit as shown in Figure 2 yields the following current transfer functions.
( ) ( ) Adding the output current reponses I lp and I hp , one obtains ( ) whereas for current-mode all-pass filter response ( ) where ( ) From ( 4)-( 9), the pole frequency 0 ω and quality factor Q 0 are given as Equations ( 12) and ( 13) show that 0 ω can be linearly and electronically varied through g m .Whereas quality factor Q 0 can be linearly changed through grounded resistor R 1 independent of 0 ω .

Tracking Errors
There are Current Tracking Errors of the proposed circuit.The characteristic equations of CFTA are 0, , , where 1 i α = −  where i  denotes the current tracking error of the current follower from the terminal f into the terminal-z ( 1 i  ).from the non-ideal properties of CFTAs, the characteristic equation of the proposed circuit according to Figure 2 is It is thus, seen that the proposed circuit is capable of realizing all the five basic functions, without requiring any component-matching or realization conditions.From ( 4)-( 9), the various filter parameters are given by

Sensitivity Analysis
The effect of changes in active and passive element values is determined by evaluating sensitivity coefficients which are found to be From ( 12)-( 20), it is clear that all the sensitivities of the various parameters of the filters realized from the proposed configuration are very low.

Simulation Results
The performance of the proposed circuit in Figure 2 has been verified by PSPICE simulation results.The PMOS and NMOS transistors have been simulated by respectively using the parameters of a 0.25 µm TSMC CMOS technology [9] as shown in Table 1.The aspect ratios of PMOS and NMOS transistors are indicated in Table 2.
The circuit was biased with ±1.5 V power supply voltage, V BB = −0.55V,I B1 = I B2 = 80 µA.The values of the capacitors and resistor were chosen as: C 1 = C 2 = 1nF, R 1 = 0.5 kΩ.In Figure 4(a), simulated results of proposed LP, HP, BP, BR filters are shown using PSPICE 16.3 which shows the validity of design equations of filter shown in Equations ( 10) and (11).Pole frequency was found to be f 0 = 245 kHz and quality factor Q 0 = 0.7 which are very close to theoretical values.In Figure 4(b), phase response of current mode all-pass filter is shown.In Figure 4(c), simulation results are shown for the pole frequency f 0 = 245 kHz and quality factor Q 0 which varies from 0.7 to 3. The results show independent control of Q 0 .Similarly, in Figure 4(d) for the quality factor Q 0 = 0.7, pole frequency f 0 is varied from 245.6 kHz to 245 MHz.However it is seen that H 0 in this case is slightly changing with frequency which may be the effect of output parasitic capacitance of CFTA or due to tracking errors between I f and I z .Hence, from the PSPICE simulation results it is proved that the practical results nearly match to the theoretical results.

Conclusion
In this paper, a new current-mode second-order biquad filter using CFTAs (Current Follower Tranconductance Amplifier) is presented.The circuit realizes all types of filter functions, i.e.LPF, BPF, HPF, and BRF simultaneously for a single current input.It consists of two CFTAs, one grounded resistor and two grounded capacitors.Hence, the low numbers of active and passive elements are used.The circuit has the features of low voltage supply, and large bandwidth.It has low-input and high-output impedances and also is convenient for electronic controllability through transconductance gain g m of CFTAs, so it can be used in battery-powered or portable electronic equipments.The only apparent drawback is the use of a grounded resistor.However, grounded resistor can be simulated with additional transconductor and its value can be controlled through g m3 .Hence, electronic control of quality factor is possible.

Figure 3 .
Figure 3.A CMOS implementation of CFTA used for simulations.

Figure 4 .
Figure 4. (a) Simulated frequency response of LP, HP, BP, and BR proposed CFTA current-mode second order biquad filter according to Figure 2; (b) Phase response of all pass proposed biquad filter; (c) Simulated frequency responses of the BP filter when Q 0 is varied for f 0 = 245 khz; (d) BP filter with different f 0 (keeping Q 0 approximately constant).

Table 1 .
The SPICE model parameters of MOS transistors for level 3, 0.25 µm CMOS process from TSMC.

Table 2 .
Dimensions of the transistors.