Reliable Circuit Techniques for Low-Voltage Analog Design in Deep ...

24 Fayomi, Sawan and Roberts
fully differential inverting opamp configuration into a
low-voltage design. In this case, two current sources or
two resistors are required to connect to the fully differential
opamp inputs, and the values of the current
sources or resistors can be determined based on the
input and output common-mode voltages. Adding the
current source or resistor induces minimal effects on
the low frequency response since they are connected to
the virtual ground of the opamp. However, at high frequency,
the bandwidths of the two schemes are different.
The obtained reduction in supply voltage, however,
comes with a price of increasing the overall noise. The
mean squared output noise Vno 2 for both circuits shown
in Fig. 3 can be written as:
vno 2 = ( (
Inl 2 + I nf 2 + I n 2 )
R
2
f + vna
2 1 + R ) 2
f
(6)
R 1 //R x
Fig. 2.
Level Shifter transfer function.
hence the minimum supply voltage of the circuit is
V DS,sat + 2V SD,sat +|V th,p |.Ifthe input stage of the
opamp is realized using nMOS differential pair, setting
v x close to V DD with a pMOS current source I B connected
between the opamp negative input terminal and
V DD will minimize the supply voltage. A resistor or a
MOSFET operating in the triode region can be used to
bias the opamp input common-mode voltage as shown
in Fig. 3(b). The resistance R B can be determined as:
R B =
v x
V DD
2
− v x
(R 1 //R f ) (5)
The second approach has the advantage of setting
v x to a value lower than one V DS,sat (but greater than
the ground). The method can be extended to convert a
where I nl , I nf and V na are the equivalent noise currents
of R 1 , R f and the equivalent noise voltage of the opamp
respectively. When compared to the case without the
addition of R B and I B , additional terms In 2 and R x are
presented in (6). For Fig. 3(a), R x is equivalent to r ds ,
and In 2 is due to the noise current of I B.With v x =
V DS,sat , In 2 can then be derived using (4) as
In 2 = 16 V DD
3 kT − v
2 x
v x (R f //R 1 )
(7)
where only thermal noise is considered. For Fig. 3(b),
R x is equal to R B , and In 2 is due to the equivalent noise
current of R B that can be also described using (7) except
that the scaling factor 16/3 is now equal 4. In
most cases, the term due to the opamp noise V 2
na is
usually the dominant factor. Since R B < R 1 < r ds , the
circuit shown in Fig. 3(a) has lower noise than the circuit
shown in Fig. 3(b). Furthermore, due to the term
In 2 ,ithas a slightly higher noise than the case when
Fig. 3.
Biasing schemes for low-voltage CMOS opamp in a single-ended configuration using: (a) a current source and (b) a resistor.