A Single MO-CFTA Based Electronically/Temperature Insensitive Current-mode Half-wave and Full-wave Rectifiers

The article presents a current-mode fullwave rectifier employing multiple output current follower transconductance amplifier (MO-CFTA). The both circuits description is very simple, it merely comprises only single MO-CFTA, without external passive element. In addition, the magnitude and direction of output currents can be controlled via electronically method. Furthermore, the outputs are independent of the thermal voltage (VT). The performances of the proposed circuits are investigated through PSpice. They show that the proposed circuits can function as a current-mode precision half-wave and full-wave rectifiers where input current range from 0 μA to 514 μA and -518 μA to 518 μA, respectively. They can be achieved at ± 2V power supplies. The maximum power consumption is 3,01 mW.


Introduction
A rectifier has been found widely useful in signal processing circuits, such as a signal polarity detector, a peak signal detector, an RMS to DC converter, an amplitude demodulation circuit, and an automatic gain control system [1], [2].Basically, an op-amp and diode are used to design a voltage-mode precision rectifier [3], its output signal confronts a zero crossing distortion due to characteristic of the diode [4].Thus, novel precision rectifiers are design without a diode [5].
In addition, the precision rectifiers are modified to use high performance active elements to achieve wider frequency response such as current conveyor [6] and current feedback operational amplifier [7].However, these circuits use many active and passive elements.When they are fabricated in IC, it affects to have more chip area.Furthermore, they are lack of electronically adjustment.
There has been much effort to reduce the supply voltage of analog systems since the last two decades.This is due to the command for portable and batterypowered equipments.Since a low-voltage operating circuit becomes necessary, the current-mode technique is ideally suited for this purpose.Presently, there is a growing interest in synthesizing current-mode circuits because of more their potential advantages such as larger dynamic range, higher signal bandwidth, greater linearity, simpler circuitry, and lower power consumption [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19].
In 2008, a reported active element, namely current follower transconductance amplifier (CTFA) [20], [21], seems to be a versatile component in the realization of a class of analog signal processing circuits.It is really current-mode element whose input and output signals are currents.
In addition, output current of CFTA can be electronically adjusted.Furthermore, it can offer advantageous features such as high-slew rate, high speed, wide bandwidth and simple implementation.
The purpose of this paper is to introduce MO-CFTA based current-mode half-wave and full-wave rectifiers.The features of the proposed both circuits are that; output gain can be adjusted via input bias current; magnitude of the output signal is temperatureinsensitive; the proposed circuit consists of only single MO-CFTA and without passive element, which is convenient to fabricate in integrated circuit architecture.
The PSpice simulation and experimental results are also shown, which are in correspondence with the theoretical analysis.

Basic Concept of MO-CFTA
This section describes the operation of MO-CFTA, its symbol and equivalent circuit are display in Fig. 1(a) and Fig. 1(b), respectively.In the ideal case, the voltage and current relationships of MO-CCTA are shown in (1), where g m1 , g m2 and g m3 are the transconductances of the MO-CFTA at x 1 , x 2 , x 3 terminals, respectively V T is the thermal voltage, its value is about 26 mV at 27 • C.

The Current-Mode Half-Wave Rectifier
This section is explained the operating of the half-wave rectifier, it is shown in Fig. 2. It can be seen that it consists of single only MO-CFTA without passive element.From MO-CFTA properties, the I z and V z can be found to be: and Cosequently, the I x1 can be written as: From the half-wave rectifier as demonstrated in Fig. 2, I B1 = I in .Hence, g m1 = I in /2V T , Eq. ( 5) can be modified to be: Fig. 2: Circuit diagram of current-mode half-wave rectifier.

The Current-Mode Full-Wave Rectifier
The proposed full-wave rectifier using MO-CFTA is display in Fig. 3, where I B1 , I B2 and I B3 are current bias currents of the MO-CFTA, respectively.By routine analysis circuit in Fig. 3 and using the properties of MO-CFTA.The output current at z terminal of MO-CFTA is obtained in: and Then, the output voltage at z terminal (V z ) of MO-CFTA can be found to be: Subsequently, the output current at x1 and x2 terminals (I x1 and I x2 ) can be expressed to be: and From Fig. 2, it is found that I in and -I in are equal to I B1 and I B2 respectively.Then, g m1 = I in / 2V T , g m2 = -I in / 2V T and g m3 = -I B3 / 2V T .From MO-CFTA properties, the values of currents bias only are positive.Thus, I x1 and I x2 can be rewritten to be: and From Eq. ( 12) and Eq. ( 9), the output current I out can be found to be: From Eq. ( 6) and Eq. ( 14), it can be seen that the amplitude of the output current can be controlled by I B3 and I C , the polarity of the output signal can be electronically tune by I C .Furthermore, in the ideal case, the current output is temperature-insensitive.

Non-Ideal Case
In non-ideal case, the MO-CFTA can be characterized by: where α and γ are transferred error values, these values can be deviated from one.In the case of non-ideal and reanalyzing the proposed half-wave and full-wave rectifiers in Fig. 2 and Fig. 3, respectively, they yield the output currents as: and From small-signal analysis of MO-CFTA, it can be found that α can be express as: If these error factors are close to unity, the deviations of the output levels in Eq. ( 16) and Eq. ( 17) can be neglected.Practically, the α, and γ originate from intrinsic resistances and stray capacitances in the MO-CFTA.These errors affect the sensitivity to temperature and high frequency response of the proposed circuits.Then the MO-CFTA should be carefully designed to achieve these errors as low as possible.

Non-Linear Case
This section expands the proposed rectifiers operating in non-linear case.From Eq. ( 1) and Eq. ( 2), the currents at x 1 , x 2 and x 3 terminals can be found to be , respectively.These are the first approximation of Taylor's series, it can be describe as: Actually, I x1 , I x2 and I x3 can be express to be: and Subsequently, the output current of the half-wave rectifiers can be obtained by: Likewise, the amplitude of the full-wave rectifier can be found to be: and From Eq. ( 22) and Eq. ( 24), it can be clearly seen that the proposed circuits can be used rectifier while perform in non-linear mode.

Simulation and Experimental Results
The performance of the proposed half-wave and fullwave rectifiers can be proved by simulation and experimental results.The PSpice simulation program was used for the examinations.The circuit diagram of MO-CFTA is used for simulation, it is display in Fig. 4. The PNP and NPN transistors employed in MO-CFTA were simulated by respectively using the parameters of the PR200N and NR200N bipolar transistors of ALA400 transistor array from AT&T [22] with ±2 V supplies voltages and I A was set to 100 µA.full-wave rectifiers, respectively.It can be seen that the proposed circuits offers a wide-range of input current to be both rectifiers.Additionally, its output current direction can be controlled by I C .
The simulation results of the both rectifiers, where I B3 =100 µA, 150 µA and 200 µA are displayed in Fig. 7 and Fig. 8. From these results, they are confirmed that the output amplitude can be controlled by I B3 and I C , respectively.The plot of the current gain relative to the I B3 variations is display in Fig. 6.The transient responses of the output current for different input frequencies are also shown in Fig. 10   The deviation values of amplitude of the output currents relative to the temperature variations are demonstrated in Fig. 13.It is found that the maximum absolute deviation of the magnitude of the output current is less than − 0,7 %, for temperature variations of 0 -100 • C.These deviations originate from the effect of the intrinsic resistances and stray capacitances of the transistors used in the MO-CFTA, as depicted in Section 2.3.
To confirm that the half-wave and full-wave rectifiers can operate practically, they were constructed via using commercial ICs, it is shown in Fig. 14 where it is implemented by using AD844 and LM13700s.In this work, the current follower circuit and OTAs inside the  MO-CFTA can be realized by using two AD844s and LM13700Ns, respectively.
Figure 15 and Fig. 16 demonstrate the practical implementation used for experimental inspection of the proposed half-wave and full-wave rectifiers, respectively.Since, the input signal is voltage form, the CFA1-CFA2 of the half-wave rectifier and the CFA1-CFA4 of the full-wave rectifier are used to be a V to I converters where both R L is used to be able to measure the output current by an oscilloscope.The experimental results the half-wave and full-wave rectifiers are illustrated in Fig. 17    is insisted that the proposed both rectifiers practically work.

Conclusion
The new current-mode half-wave ans full-wave rectifier have been presented in this paper.Its advantages are that; the both rectifiers consist of only one MO-CFTA without any passive element; the output amplitude is slightly dependent on temperature variations.Moreover, they can be electronically adjusted by input bias currents.The proposed circuits can operate at high frequency up to several hundred kilohertz range.The results obtained by PSpice simulation found that the maximum power consumption of the proposed circuits are approximately 3,01 mW at ±2 V supply voltages.The experimental and simulation results are described, and suited well with the theoretical expectation.
Figure 4 and Fig. 5 depict DC transfer characteristics of the half-wave and

Fig. 10 :
Fig. 10: The results of output current of the half-wave rectifier for different input frequencies a) 10 kHz b) 100 kHz.
and Fig. 11.It is concluded that the proposed circuits can operate well for a wide range of frequency; even frequency is up to 100 kHz without disturbing magnitude of the output current.The output signals of the proposed rectifiers relative to temperature variations for 27 • C, 50 • C and 100 • C are respectively shown in Fig. 12.It is clearly observed that the output currents are slightly dependent on the wide temperature variations due to independency of V T , as explained in Section 2.2.

Fig. 11 :
Fig. 11: The results of output current of the current-mode fullwave rectifier for different input frequencies a) 10 kHz b) 100 kHz.

Fig. 12 :
Fig. 12: Output current deviations for different temperature values a) Half-wave rectifier b) Full-wave rectifier.

Fig. 13 :
Fig. 13: The output amplitude deviation of the full-wave rectifier due to temperature variations.
Figure15and Fig.16demonstrate the practical implementation used for experimental inspection of the proposed half-wave and full-wave rectifiers, respectively.Since, the input signal is voltage form, the CFA1-CFA2 of the half-wave rectifier and the CFA1-CFA4 of the full-wave rectifier are used to be a V to I converters where both R L is used to be able to measure the output current by an oscilloscope.The experimental results the half-wave and full-wave rectifiers are illustrated in Fig.17and Fig.18, respectively, it

Fig. 15 :
Fig. 15: Practical implementation for experimental inspection of the proposed half-wave rectifier.

Fig. 16 :
Fig. 16: Practical implementation for experimental inspection of the proposed full-wave rectifier.