*3.3. Large-Signal Performances*

The large-signal performance of the proposed OTA has been investigated by assuming that the load capacitance *CL* is much larger than the other circuit capacitances. The slew-rate is thus determined by the output stage, and it can be assumed that the output voltage *vO*<sup>2</sup> of stage2, which drives stage3, is a rail-to-rail signal.

With reference to Figure 5, the output current is given by *Io* = *I*5*<sup>B</sup>* + *I*8*<sup>A</sup>* − *I*6*<sup>B</sup>* − *I*7*A*; positive and negative slew-rates are given by *SRp* = *Iomax*/*CL* and *SRm* = *Iomin*/*CL*, where *Iomax* and *Iomin* are the maximum positive and negative values of *Io*.

For the current, we use the standard relationship for sub-threshold current:

$$I\_{\rm tr,p} = I\_{0\_{\rm n,p}} e^{\frac{|V\_{\rm av} - |V\_{\rm th\_{\rm n,p}}|}{n\_{\rm v,p} \cdot L\_t}} \tag{2.4}$$

where *Ut* = *kT*/*<sup>q</sup>* is the thermal voltage and |*Vthn*,*<sup>p</sup>* | = *Vthn*,*p*<sup>0</sup> − *<sup>α</sup>n*,*p*|*Vbs*|.

For the positive slew-rate, we have *v*<sup>1</sup> = *VDD* and *v*<sup>2</sup> = 0, and we can assume that the body voltages of *M*6*<sup>B</sup>* and *M*7*<sup>A</sup>* are approximately 0. By denoting with *Iref* , the quiescent current of the devices of stage3, we obtain:

$$I\_{0\max} = I\_{ref} \left[ 1 + e^{\frac{n\_t |\Lambda V\_{BH}|}{n\_H L\_t}} + e^{\frac{\Lambda |V\_{GH}|}{n\_P L\_t}} \right] \tag{25}$$

where: Δ*VBH* = −*VB*0, Δ*VGH* = *VDD* − *VGP* with *VB*<sup>0</sup> and *VGP* the quiescent voltage at body and gate terminals of the NMOS and PMOS devices.

For the negative slew-rate, we have *v*<sup>1</sup> = 0, *v*<sup>2</sup> = *VDD* and in this case we derive:

$$I\_{o\_{niv}} = I\_{ref} \left[ 1 - e^{\frac{n\_n|\Delta V\_{BL}|}{n\_RU\_t}} \left( 1 + e^{\frac{|\Delta V\_{GL}|}{n\_RU\_t}} \right) \right] \tag{26}$$

where: Δ*VBL* = *VDD* − *VB*<sup>0</sup> and Δ*VGL* = *VDD* − *VGN* with *VGN* as the quiescent voltage at gate terminals of NMOS devices. In this case, we assume that the body terminals of *M*6*<sup>B</sup>* and *M*7*<sup>A</sup>* are approximately *VDD*. Equations (25) and (26) show that, in general, positive and negative slew-rates give different results.
