use ptat current for opamp

rbic ptat

hi all

we use PTAT current to bias opamp, making the gain of opamp unchange with temperature, anyone can explain why?

thanks

gm=f(I)

Ro=f2(I).

Av=f3(I)

can you explain it in detail?

av=gm*ro=sqrt(2*beta/(I*lambda^2)), i.e. av is a function of I

Neglect process variation that we always cannot handle, everything is controlled by current. If current is constant, then your rest of designs will be constant.

perhaps you can use the current Igm which bias the input device, generates another current Iro to bias the output device. The relationship between Igm and Iro is,
Iro=Ksqrt(Igm).

Using PTAT can help make an Opamp's gain constant if you are using BJTs.

For a BJT:

gm = VT/Ic --> making Ic ~ VT will make gm constant

for MOS current mirror Veff = sqrt (2I/(uCxW/L)), so that (deltaVeff)/Veff = (deltaI)/I, for PTAT current, (deltaVeff) is worse. MOS mirror is worse match in PTAT current.

ygu_sanjose said:

for MOS current mirror Veff = sqrt (2I/(uCxW/L)), so that (deltaVeff)/Veff = (deltaI)/I, for PTAT current, (deltaVeff) is worse. MOS mirror is worse match in PTAT current.

Click to expand...

but for a current mirror, output current Io=Ii*w2/w1. when the current changes with temperature, the Veffs in both MOSs are changes, and i think it don't influence the current mirroring

Like elbadry said in case of BJT's since you have gm = Ic/Vt where Vt is proportional to temperature so if Ic is PTAT then your gain should remain constant. Similarly for MOS gm = 2Ids/(Vgs-Vth) and Vth decreases with temperature and thus you need to increase Ids to make gm constant.

hi,aryajur
Vth decreases with temperature？why do you get the result?

the threshold voltage of MOS has a negative temperature dependence indeed

sissi said:

hi,aryajur
Vth decreases with temperature？why do you get the result?

Click to expand...

Well thats what it comes out to be, to be more comfortable you can verify it using the threshold voltage formula:
Take the case for NMOS:

Vth = Φms - Qi/Cox - Qd/Cox + 2φf

where Φms = work function difference, take it const wrt temp.
Qi= interface charge, take it const
Cox is Gate capacitance per unit area, take it const.
Qd= Charge in the depletion = √(4q NA εs φf)
where q = electronic charge = const
NA = P substrate doping = constant
εs = permittivity of silicon
φf = Fermi potential = kT/q ln(NA/ni)
T = temperature
k = Boltzmann Constant
ni = intrinsic carrier concentration = √(Nc Nv) exp(-Eg/2kT)
Eg = Bandgap of semiconductor = constant
Nc = effective density of states in the conduction band = 2 √[(2 Π mn k T/h²)³]
Well take mn and h constants (effective electron mass and plank's constant)
Nv = effective density of states in the valence band = 2 √[(2 Π mp k T/h²)³]

take mp constant in this.

Well if you have the time then do the derivative, I did it once and I remember it comes out to be a negative temperature coefficient.