# Gm-Realization of Controlled-Gain Current Follower Transconductance Amplifier

Authors: Worapong Tangsrirat
Journal: The Scientific World Journal
 (2013)

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## Abstract

This paper describes the conception of the current follower transconductance amplifier (CFTA) with electronically and linearly current tunable. The newly modified element is realized based on the use of transconductance cells (Gms) as core circuits. The advantage of this element is that the current transfer ratios (iz/ip and ix/iz) can be tuned electronically and linearly by adjusting external DC bias currents. The circuit is designed and analyzed in 0.35 μm TSMC CMOS technology. Simulation results for the circuit with ±1.25 V supply voltages show that it consumes only 0.43 mw quiescent power with 70 MHz bandwidth. As an application example, a current-mode KHN biquad filter is designed and simulated.


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## Body

## 1.  Introduction

Since its introduction in 2003, the current differencing transconductance amplifier (CDTA) has been proven to be a versatile active building block for current-mode signal processing circuits [1]. A large number of analog signal processing/signal generation circuit solutions based on this device have already been presented in the technical literature [1–12]. However, some earlier circuits described in [6–12] do not fully use the potential of the CDTAs, since always one of the input terminals p or n is not used. This may cause some noise injection into the monolithic circuit. Moreover, the current differencing property at an input stage can be achieved by the current feedback connection via the ±x terminals. This implies that the input terminals p or n are not necessarily required for some applications. In order to alleviate the mentioned problems, the modified version of the CDTA so-called current follower transconductance amplifier (CFTA) was recently introduced [13, 14]. The CFTA is a simplified variant of the CDTA element by replacing the current differencing unit with the simple current follower. Thus, this element can be thought of as a combination of the current follower, the current mirror, and the multioutput operational transconductance amplifier. As a result, a number of researches were published on CFTA-based applications [14–18]. As shown in Figure 1, the terminal relations of an ideal CFTA with its schematic symbol can be described by the following expression:
(1)iz=ip,ix+=ix-=gmvz=gmZziz,
where gm is the transconductance gain of the CFTA and Zz is an external impedance connected to the z-terminal. From (1), it can be seen that an ideal CFTA has a unity small-signal current transfer ratio (α=1) between iz and ip. In fact, for some applications such as automatic gain control circuit and tunable active filters, one wishes to alter the circuit transfer characteristics by electronic means. Thus, the usefulness of the CFTA is clearly an advantage to be gained, if α can be controlled electronically instead of a fixed one, in which case a more generalized CFTA is obtained. In the following, we have named the introduced device as the controlled-gain current follower transconductance amplifier (CG-CFTA).Figure 1
Schematic symbol of the CFTA.In this paper, we present a generalized approach based on only transconductance (Gm) elements for designing a CFTA with linearly and electronically current controllable. The proposed circuit consumes average power of 0.43 mW at ±1.25 V supply voltages. It operates as a linear circuit element and has a 3 dB bandwidth up to 70 MHz for 0.35 μm TSMC CMOS technology. As an application example, a current-mode KHN-equivalent universal filter topology is implemented adopting the proposed circuit. PSPICE simulation results confirm the expected performances of the proposed circuit and its application in terms of linearity, tenability, and time and frequency responses.


## 2. Proposed Circuit Realization

In the following subsection, an approach to implement the proposed CG-CFTA using only tunableGm elements is described, and its performance is also discussed.


### 2.1. BasicGm Cell

A particularly simple CMOS realization and the symbol of the tunableGm cell, which will be used as a fundamental circuit for implementing the proposed circuit, are shown in Figures 2(a) and 2(b), respectively. The circuit is mainly composed of two Arbel-Goldminz transconductances [19]. For this element, the value of the transconductance (Gm) can be determined by the output transistor transconductance, which can be approximated as
(2)Gm≅(gm1gm2gm1+gm2)+(gm3gm4gm3+gm4),
where gmi=Kn(p)IB(i=1,2,3,4) and Kn(p) is the transconductance parameter of NMOS (PMOS) transistor, and IB is an external DC bias current of this element, respectively. Note that in (2) the value of Gm is electronically tunable by changing the bias current IB.BasicGm cell.
(a)
CMOS implementation
(b)
Circuit symbol


### 2.2. Linearly Tunable Current Amplifier

In Figure3, the current-controlled current amplifier (CCCA) is realized by employing two Gm cells of Figure 2. In this case, the current gain of this circuit is given by
(3)α=ioutiin=GmBGmA≅IBBIBA.Figure 3
Current-controlled current amplifier (CCCA).This expression shows that the current gainα is determined by the current ratio IBB/IBA, but it is in the form of square-root function. To alleviate this nonlinearity, we intend to realize the current amplifier that is possible to tune its gain linearly. In Figure 4, a possible realization of linearly tunable small-signal current amplifier is given, which is simply obtained from the cascade connection of two CCCAs in Figure 3. We also name this scheme as linearly tunable current amplifier (LT-CA). Hence, the current gain of this circuit can be found as follows:
(4)α=ioutiin=GmB1GmB2GmA1GmA2≅IBBIBA.Figure 4
Linearly tunable current amplifier (LT-CA).Equation (4) clearly indicates that the current gain α of Figure 4 can be tuned electronically and linearly by means of the current ratio IBB/IBA. Furthermore, this cell will be used to design the input stage of the proposed CG-CFTA.


### 2.3. Linearly Tunable Transconductance Amplifier

Using the tunableGm cell of Figure 2 and the CCCA of Figure 3, the electronically and linearly tunable transconductance amplifier (LT-TA) can be realized as shown in Figure 5. The output current (iout) of Figure 5 can be expressed as
(5)iout=Gm4GmB3GmA3vin.
Substituting (2) into (5), the current iout can be rewritten as
(6)iout=[IBC(Kn+Kp)2IBD]vin=GmTvin,
where GmT denotes the transconductance gain of the LT-TA and can be expressed as
(7)GmT=IBCKT,(8)KT=(Kn+Kp)2IBD,
which can usually be kept at constant. It is clear from (7) that the GmT-value of LT-TA in Figure 5 can be electronically and linearly tuned by the bias current IBC.Figure 5
Linearly tunable transconductance amplifier (LT-TA).


## 2.1. BasicGm Cell

A particularly simple CMOS realization and the symbol of the tunableGm cell, which will be used as a fundamental circuit for implementing the proposed circuit, are shown in Figures 2(a) and 2(b), respectively. The circuit is mainly composed of two Arbel-Goldminz transconductances [19]. For this element, the value of the transconductance (Gm) can be determined by the output transistor transconductance, which can be approximated as
(2)Gm≅(gm1gm2gm1+gm2)+(gm3gm4gm3+gm4),
where gmi=Kn(p)IB(i=1,2,3,4) and Kn(p) is the transconductance parameter of NMOS (PMOS) transistor, and IB is an external DC bias current of this element, respectively. Note that in (2) the value of Gm is electronically tunable by changing the bias current IB.BasicGm cell.
(a)
CMOS implementation
(b)
Circuit symbol


## 2.2. Linearly Tunable Current Amplifier

In Figure3, the current-controlled current amplifier (CCCA) is realized by employing two Gm cells of Figure 2. In this case, the current gain of this circuit is given by
(3)α=ioutiin=GmBGmA≅IBBIBA.Figure 3
Current-controlled current amplifier (CCCA).This expression shows that the current gainα is determined by the current ratio IBB/IBA, but it is in the form of square-root function. To alleviate this nonlinearity, we intend to realize the current amplifier that is possible to tune its gain linearly. In Figure 4, a possible realization of linearly tunable small-signal current amplifier is given, which is simply obtained from the cascade connection of two CCCAs in Figure 3. We also name this scheme as linearly tunable current amplifier (LT-CA). Hence, the current gain of this circuit can be found as follows:
(4)α=ioutiin=GmB1GmB2GmA1GmA2≅IBBIBA.Figure 4
Linearly tunable current amplifier (LT-CA).Equation (4) clearly indicates that the current gain α of Figure 4 can be tuned electronically and linearly by means of the current ratio IBB/IBA. Furthermore, this cell will be used to design the input stage of the proposed CG-CFTA.


## 2.3. Linearly Tunable Transconductance Amplifier

Using the tunableGm cell of Figure 2 and the CCCA of Figure 3, the electronically and linearly tunable transconductance amplifier (LT-TA) can be realized as shown in Figure 5. The output current (iout) of Figure 5 can be expressed as
(5)iout=Gm4GmB3GmA3vin.
Substituting (2) into (5), the current iout can be rewritten as
(6)iout=[IBC(Kn+Kp)2IBD]vin=GmTvin,
where GmT denotes the transconductance gain of the LT-TA and can be expressed as
(7)GmT=IBCKT,(8)KT=(Kn+Kp)2IBD,
which can usually be kept at constant. It is clear from (7) that the GmT-value of LT-TA in Figure 5 can be electronically and linearly tuned by the bias current IBC.Figure 5
Linearly tunable transconductance amplifier (LT-TA).


## 3. Proposed CG-CFTA with Linearly Current Tunable

The circuit implementation and internal structure of the proposed linearly tunable CG-CFTA is shown in Figures6(a) and 6(b), respectively. It should be noted that the proposed circuit configuration is simply realized by the combination of the LT-CA from Figure 4, which is the input stage of the designed element, and the LT-TA from Figure 5, which functions as the output stage. For this realization, all the biasing currents (IBA,IBB,IBC, and IBD) were performed by the simple CMOS current mirrors as depicted in Figure 6(c). The input current flowing through the p-terminal (ip) is then reproduced on the z-terminal (iz) by two CCCAs with linear controlled gain, in such a way that iz=αip. In addition, the copy of the current iz is also available at the zc-terminal (izc). The voltage drop at the z-terminal (vz) is converted into output currents ix+ and ix- by GmT-parameter of the LT-TA, which flows into output terminals x+ and x-. From the basic operation of the proposed CG-CFTA, the voltage-current characteristic of this device can be expressed as
(9)izc=iz=αip,ix+=ix-=GmTvz=GmTZziz,
where its circuit symbol is represented in Figure 7.Proposed CG-CFTA.
(a)
Circuit implementation
(b)
Internal structure
(c)
Simple current mirror used for realizing bias currentsIBk(k=A,B,C,D)Figure 7
Circuit symbol of the proposed CG-CFTA.As compared with the conventional CFTA, the designed CG-CFTA element has an advantage of providing a linear electronic controllability of the current transfer ratiosiz/ip,izc/ip,ix+/iz and ix-/iz via the following parameters: α(=IBB/IBA) and GmT(=IBCKT), respectively. As a consequence, it can be an advantage in a number of applications.


## 4. Simulation Results

The performance of the proposed CG-CFTA in Figure6 has been verified by PSPICE simulation results. The simulation results were obtained using TSMC 0.35-μm CMOS process model parameters. The dimensions W(μm)/L(μm) of the MOS transistors are set to be 56/0.7 for M1-M2, 32/0.7 for M3-M4, 7/0.7 for MM1, MM5–MM7, and 8.5/0.7 for MM2–MM4. The supply voltages used for the CG-CFTA are +V=-V=1.25 V. The simulations are obtained for the following two configurations, that is, current transfer configuration (input current on p and outputs on z and zc) with z and zc grounded, and voltage-to-current configuration (input voltage on z and output currents on x+ and x-) with x+ and x- grounded.For the current transfer configuration, the DC and AC current characteristics of the output currents fromz and zc terminals against the current applied to p terminal are shown in Figures 8 and 9, respectively. In these simulations, the bias current IBB was set to the values of 5 μA, 10 μA, 20 μA, and 30 μA, respectively, while keeping IBA = 10 μA. Figure 8 demonstrates the DC gain of the proposed circuit for α varying from 0.5 to 3. It can be observed that the circuit exhibits good linearity for input current ip in the range from −12 μA to 12 μA. Figure 9 is demonstrating the AC gain. The 3 dB bandwidth also proves to be constant for different AC gain values and is in a high frequency as nearly as 70 MHz. The time responses to a 1 MHz sinusoidal input with 10 μA peak magnitude are also displayed in Figure 10. As shown in the figures, the current transfer characteristics with different α can be obtained by keeping IBA and only varying IBB.Figure 8
i
z
,
i
z
c
-
i
pDC transfer characteristics of the proposed CG-CFTA for different values of IBB.Figure 9
Frequency responses ofiz/ip and izc/ip for different values of IBB.Time responses to a 10μA sinusoidal signal at 1 MHz for different values of IBB.
(a)
i
z
(b)
i
z
cFor the transconductance amplifier configuration, the DC transfer characteristics ofvz and ix± for IBD=10 μA and four different values of IBC are shown in Figure 11. The plots show that the proposed circuit in Figure 6 can linearly convert the voltage signal vz into current signals ix± with nonlinearity of less than 1.5% for vz in the ranges of −44 mV to 44 mV and −26 mV to 26 mV. These results were agreed with the prediction value from (6). For example, for the case of IBC = 20 μA and IBD = 10 μA (GmT≅5.67×10-4 A/V), the conversion error is about 1.32% for vz = 40 mV. The frequency response of GmT for different values of IBC was also studied and is shown in Figure 12, where the 3 dB bandwidth of about 90 MHz is observed. The simulation results show that, under bias condition of IBA=IBB=IBC=IBD=10 μA, the total power dissipation of the CG-CFTA in Figure 6 was 0.43 mW.Figure 11
v
z
-
i
x
± DC transfer characteristics of the proposed CG-CFTA for different values of IBC.Figure 12
Frequency responses ofGmT for different values of IBC.


## 5.  Application Example

Although the current-mode KHN biquad filter realization with ZC-CFTAs has been introduced in [20], an additional current gain block (ZC-CFTA3 and ZC-CFTA4) is required to provide an independently current tuning of the circuit quality factor (Q). In this section, an application example demonstrating the use of the proposed CG-CFTA in realizing current-mode KHN biquad filter is described. This demonstrates that, by employing the proposed CG-CFTA, the derived filter has fewer active components, and has the advantage of an orthogonal electronic control of the natural angular frequency (ω0) and Q by linearly changing the bias current ratio. Figure 13 shows the current-mode KHN biquad realization using CG-CFTAs and grounded capacitors. Routing circuit analysis of this circuit results in low-pass (LP), band-pass (BP), and high-pass (HP) current transfer functions as
(10)ILP(s)Iin(s)=(α1α2GmT1GmT2/C1C2)D(s),IBP(s)Iin(s)=-(α2/α3)(α1α3GmT1/C1)sD(s),IHP(s)Iin(s)=-α1s2D(s),D(s)=s2+(α1α3GmT1C1)s+(α1α2GmT1GmT2C1C2),
where αi and GmTi are the parameters α and GmT of ith CG-CFTA (i=1,2,3). The passband gains of the LP, BP, and HP current responses are found as HLP=1, HBP=-(α2/α3), and HHP=-α1, respectively.Figure 13
Current-mode KHN filter using CG-CFTAs.From (10), the important parameters ω0 and Q of the filter in Figure 13 can be given by
(11)ω0=α1α2GmT1GmT2C1C2,Q=1α3α2GmT2C1α1GmT1C2.
For simplicity, if we let α=α1=α2 (IBA=IBA1=IBA2) and (IBB=IBB1=IBB2), GmT=GmT1=GmT2(IBC=IBC1=IBC2), and C=C1=C2, then (11) turns to
(12)ω0=(IBBIBCIBA)(KTC),Q=IBA3IBB3.It should be noted from (12) that the filter parameters ω0 and Q are independently controllable. This means that the ω0 can be tuned electronically without disturbing the Q-value by linearly changing the current ratio IBB/IBA and/or the bias current IBC. On the other hand, the value of Q can be tuned linearly and separately by the ratio IBA3/IBB3.As an example, the following setting for the KHN filter of Figure13 has been selected as IBAi=IBBi=IBCi=IBDi=10 μA and C=C1=C2=20 pF, which results in f0=ω0/2π≅1.51 MHz and Q=1. In this setting, the total power consumption was found as 1.58 mW. Figure 14 shows the simulated LP,BP, and HP current characteristics for the filter in Figure 13. To demonstrate the electronic controllability of f0, the tuning bias currents IBB were varied to 5 μA, 10 μA, 20 μA, and 40 μA, respectively, while keeping IBC=IBA3=IBB3=10 μA for Q=1. The resulting BP responses corresponding to different bias current ratios IBB/IBA are given in Figure 15. The f0-values obtained from the plots are approximated to 0.76 MHz, 1.51 MHz, 3.02 MHz and 6.02 MHz, respectively. Figure 16 also shows the simulated BP responses with Q-tuning (i.e., Q = 0.5, 1, 2, and 4). In this case, the bias currents were chosen as IBA=IBB3=IBC=IBD=10 μA, IBB=20 μA, and IBA3=5 μA, 10 μA, 20 μA, 40 μA, respectively, resulting in f0≅3.02 MHz.Figure 14
SimulatedLP,BP, and HP current responses for the filter in Figure 13.Figure 15
SimulatedBP responses for different values of IBB.Figure 16
SimulatedBP responses for different values of IBA3.


## 6. Conclusion

In this paper, we have presented the design of a generalized current follower transconductance amplifier using only transconductance cells. We have named it as the controlled-gain current follower transconductance amplifier (CG-CFTA), since its current transfer ratios (iz/ip,izc/ip and ix±/iz) can be varied linearly by external bias currents. The circuit has the features of low voltage supply, low power consumption, large bandwidth, and convenient for realization in CMOS technology. Simulation results confirm the qualification performances of the circuit. To illustrate the design possibility provided by the newly defined circuit, the current-mode KHN-equivalent biquad filter is constructed and simulated.



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*Source: 201565-2013-11-28.xml*