Bandwidth Extension of High Compliance Current Mirror by Using Compensation Methods

Due to the huge demand of high-speed analog integrated circuits, it is essential to develop a wideband low input impedance current mirror that can be operated at low power supply. In this paper, a novel wideband low voltage high compliance current mirror using low voltage cascode current mirror (LVCCM) as a basic building block is proposed. The resistive compensation and inductive peaking methods have been used to extend the bandwidth of the conventional current mirror. By replacing conventional LVCCM in a high compliance currentmirror with the compensated LVCCM, the bandwidth extension ratio of 3.4 has been achieved with no additional DC power dissipation and without affecting its other performances. The circuits are designed in TSMC 0.18μm CMOS technology on Spectre simulator of Cadence.


Introduction
In today's electronics world, the demand of high-speed analog devices has increased tremendously due to the explosive growth of communication systems [1,2].Moreover, the importance of low power and low voltage analog and mixedsignal circuits is increasing with the need of portable electronics devices.Since the current-mode devices can operate at low voltage and has higher bandwidth than that of voltagemode devices, these devices are becoming the first preference of designers for signal processing applications [3,4].
Current mirror is one of the most widely used currentmode circuit in analog integrated circuits such as operational amplifiers, current-mode analog-to-digital and digital-toanalog data converters, artificial neural networks, current sensing circuits, current-mode filters, current conveyors, and translinear loops [5][6][7][8][9][10].Current mirrors are basically used for current amplification, level shifting, biasing, and loading in a circuit.A current mirror should have low input impedance and high output impedance for proper functionality.Other desirable features of a current mirror include wide input and output current swings, high linearity, accurate current copy, and low standby power dissipation.But a conventional current mirror (i.e., a current mirror which consists of two MOS transistors) has low output impedance and high current transfer error.Cascoding of transistors improves the output impedance and accuracy, but it also increases the power supply requirement and decreases input/output compliances.Several low voltage current mirrors are reported in [11][12][13][14].A low voltage cascode current mirror (LVCCM) is one of the efficient and simple current mirrors.It provides low input impedance and high output impedance with reduced power supply requirement (shown in Figure 1).It has been used in many analog and mixed signal circuits [15][16][17][18].
The input impedance and input voltage can be lowered to the minimum value by applying input current at the output node of the flipped voltage follower (FVF) of LVCCM as shown in Figure 2.
In this paper, conventional LVCCM (Figure 2) is analyzed at high frequency and its bandwidth is calculated.It is found that the bandwidth of LVCCM is not large enough for high-speed applications.The bandwidth of a circuit can be enhanced by using resistive compensation technique [20,21], inductive peaking technique [22,23], negative capacitance compensation [24], feedforward compensation [25], and so Figure 1: Conventional low voltage cascode current mirror (LVCCM), when input current is fed at the drain terminal of transistor 3.forth.The bandwidth of LVCCM has been enhanced by Gupta et al. in [26] by using resistive compensation method.In this work, both resistive and inductive compensation techniques are used to extend the bandwidth of conventional LVCCM, and the maximum obtained bandwidth extension ratio (BWER) is 3.82 by using 20 nH inductance between gate terminals of transistors 1 and 2 in LVCCM (Figure 2).
The FVF based LVCCM has an offset which can be reduced by providing a negative feedback in the circuit.Javad Azhari et al. [19] have developed a current mirror which has reduced offset effect at the output.In this paper the −3 dB frequency of the high compliance current mirror [19] is enhanced by using compensated high frequency LVCCM.
Figure 3: Small signal model of LVCCM (shown in Figure 2).
The paper is organized in 6 sections.Section 2 includes small signal analysis of conventional LVCCM.The application of compensation methods in conventional LVCCM is explained in Section 3. The wideband high compliance current mirror is proposed in Section 4. Simulation results are given in Section 5 and then conclusions are drawn in the last section.

Small Signal Analysis of Conventional LVCCM
The small signal model of conventional LVCCM is shown in Figure 3.The channel-length modulation effect of transistors has been ignored.It has also been assumed that the substrate of each transistor is connected to the source terminal of transistor, so that there is no body effect and simulations are also performed on the same basis.
In analytical derivations   and   are the gate to source capacitance and transconductance of transistor , respectively (where  = 1 to 4).
Applying KCL at nodes (b) and (c) in Figure 3, we get Substituting  1 from (1) into (2), Neglecting channel-length modulation effect, the output current  out is Using ( 4) in (3), we obtain Also, on performing nodal analysis at node (c), we get Then V 2 can be obtained as Substituting V 4 from ( 4) into (7), At node (d), we have Substituting V 3 and V 2 from ( 10) and ( 8), respectively, into (5), Simplifying (11) to obtain small signal current gain   (), Let us assume  1 =  2 and  3 =  4 =   ; then, If we choose The bandwidth of conventional LVCCM is given by

High Frequency LVCCM
The circuit of the modified LVCCM is shown in Figure 4.An impedance  is inserted between the gates of transistors 1 and 2 [20][21][22][23].The impedance  can be a resistance () or inductance ().3.1.Small Signal Analysis.The small signal model of the modified LVCCM is shown in Figure 5.The analysis has been done on the basis of same assumptions as taken in Section 2.

Bandwidth Extension Using Resistive Compensation
Method.On taking  =  (i.e., resistive compensation method), then the current transfer function becomes Again, if we assume  1 =  2 and  3 =  4 =   , then (20) gets transformed into Let us suppose  3 =  4 =   ; then,   () is Equation ( 22) can be expressed as The transfer function of modified LVCCM is of second order with one zero and two poles.The zero and poles of the modified LVCCM are At  = 1/  , one pole-zero pair ( 1 −  1 ) gets cancelled and the current transfer function (see (23)) will transform into single pole low pass system and has bandwidth  0 = (2  /  ) which is double of the conventional LVCCM (see ( 15)).

Bandwidth Extension Using Inductive Peaking Method.
On taking  =  (i.e., inductive peaking method), the current transfer function of the modified LVCCM is given by The effect of using an inductor on small signal current gain can be observed from (25); it adds a zero and a pole to the transfer function which allows more control over the frequency response of the LVCCM [27].
By definition [28], at  =  0 ,       ( 0 ) where |  (0)| 2 = 1 of a current mirror.From ( 25) and ( 26), the bandwidth of the proposed LVCCM is given by It is obvious form (27) that the −3 dB frequency of the inductively peaked LVCCM depends on the value of inductor.At  = (  /5 2  ), the bandwidth of the wideband current mirror becomes The bandwidth of the inductively peaked LVCCM which is thrice of the conventional LVCCM for the chosen value of inductor as shown in (28).

Proposed High Frequency Current Mirror
Due to the low voltage requirement, low input impedance, and high accuracy, LVCCM is used as a basic building block in many analog and mixed signal systems.Javad Azhari et  al. [19] have implemented a high compliance current mirror (shown in Figure 6) with a feedback mechanism to eliminate the offset current produced in LVCCM (when input current is fed at the drain terminal of transistor 1; Figure 2).
The performance of current mirror has been improved in [19] by providing a feedback network, but its bandwidth is degraded.In this paper, we have modified the current mirror [19] by replacing the conventional LVCCM with the proposed wideband LVCCM to obtain a wideband high performance current mirror.The proposed current mirror is shown in Figure 7.
The bandwidth of the current mirror is enhanced with no additional DC power dissipation and without affecting the DC characteristics such as linearity.

Simulation Results and Discussion
The circuits are designed in TSMC 0.18 m CMOS technology and simulated with Spectre simulator of Cadence.The circuit parameters of LVCCM are given in Table 1.The simulated values of transconductances, gate to source capacitances, and overdrive voltages of transistors 1, 2, 3, and 4 are given in Table 2.
The −3 dB frequencies of designed current mirrors are obtained at 1 kΩ, 6 kΩ, 10 nH, and 20 nH values of impedance.The peaking in the frequency response depends upon the value of impedance used for compensation and this limits the value of impedance.
Figure 8 is the plot of output voltage requirement of modified LVCCM.In Figure 8, the output current gets saturated after 0.25 V and thus it can be concluded that the minimum output voltage requirement of the compensated LVCCM is 0.25 V.
The frequency responses of conventional and wideband LVCCM are shown in Figure 9.The bandwidth is extended from 4.95 GHz to 11.10 GHz by using  = 6 kΩ and 18.94 GHz by using  = 20 nH.
The input impedance of both conventional and compensated LVCCM is approximately 8 Ω.Table 3 summarizes the bandwidth of conventional and compensated LVCCM.
The circuit parameters of the proposed wideband high compliance current mirror are the same as taken in [19].The input impedance of the proposed wideband high frequency current mirror is approximately 8 Ω and does not change with the modification in the mirror.The output current variation with output voltage is shown in Figure 10.The output compliance voltage is 66.368 mV.The output compliance voltages of the conventional and proposed current mirror are the same.
The DC power dissipation in the proposed current mirror is the same as that in the conventional one [19] and it is 21.611 W.The frequency response of the proposed current mirror is shown in Figure 11 and it is compared with the conventional current mirror introduced in [19].The BWER of the proposed current mirror is 3.40 and it is obtained by using 20 nH inductance.
The Monte Carlo simulation of the proposed current mirror with resistively compensated LVCCM ( = 6kΩ) results in mean deviation of −496.63− 12 and standard deviation of 11.516 − 9.The current mirror with inductively peaked LVCCM ( = 20 nH) has shown a mean deviation of −532.47− 12 and a standard deviation of 11.941 − 9 in the Monte Carlo simulation by using Pspice (OrCAD).The simulation results of the proposed current mirror are given in Table 4.

Conclusion
In this work, the bandwidth of a high compliance current mirror is extended without affecting its DC characteristics.The FVF based LVCCM is the basic building block of the proposed current mirror; therefore, in this paper we have modified LVCCM by using compensation techniques; namely, resistive compensation and inductive peaking.The BWER of high frequency LVCCM is 2.24 and 3.82 by using 6 kΩ resistance and 20 nH inductance, respectively.The high frequency LVCCM is then used to replace the conventional one in the proposed current mirror.The BWER of the proposed wideband high compliance current mirror is 2.16 by using 6 kΩ resistance and 3.40 by using 20 nH inductance, without affecting its linearity and input impedance.The analytical derivations and simulation results are justifying the approach used in this paper for bandwidth extension.The proposed wideband current mirror can be employed

Figure 2 :
Figure 2: Conventional LVCCM, when input current is fed at the drain terminal of 1.

Figure 5 :
Figure 5: Small signal model of the compensated LVCCM.

Figure 7 :
Figure 7: Proposed wideband high compliance current mirror.

Figure 8 :
Figure 8: Variation of output current with respect to output voltage of LVCCM.

Figure 10 :
Figure 10: Variation of output current with respect to output voltage of the proposed current mirror.

( 4 .Figure 11 :
Figure 11: Frequency responses of the conventional and proposed current mirrors (where CM refers to current mirror).